EFFECT OF ACOUSTIC VIBRATION ON THE SATELLITE STRUCTURE AT LAUNCH STAGE

Kurdistan Regional Government Iraq Ministry of Higher Education and Scientific Researches University of Salahddin-Hawler

EFFECT OF ACOUSTIC VIBRATION ON

THE SATELLITE STRUCTURE

AT LAUNCH STAGE

A THESIS

SUBMITTED TO THE COUNCIL OF THE COLLEGE OF

ENGINEERING UNIVERSITY OF SALAHADDIN-HAWLER

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF MASTER OF SCIENCE

IN MECHANICAL ENGINEERING/APPLIED MECHANIC

By

AbdulRahman Bahaddin Shakir B.Sc./Mechanical Engineering /2002

Supervised by

Dr.Safeen Y.Al-Qassab Assistant Professor

July 2009 Rejeb 1430 Poshpar 2709

DEDICATION To my

Father and Mother

To my

Brother and Sister

To all

those Whom I love

ACKNOWLEDGEMENTS

First and foremost, thank you God for all the incredible blessings you have always given me through my whole life and especially during my thesis years. I would like to thank my advisor, Ass.Professor " Dr. Safeen Y. Al-Qassab", for his invaluable guidance. His encouragement and support were instrumental to the successful completion of this project. I was indeed very fortunate to have him as my project guide. My special thanks are for my age friends "Mr. Azher Kareem" and "Mr. Nyaz Taher", master students for the invaluable discussions and help during the course of this work. I like to express my special thanks to "Mr. Dlawar Ali" in Ministry of

Electricity for the help on creating the experimental work. And also wish to express my deeply thankful to Engineers " Hussain Hamad " and " Karaman Maulud" in the Ministry of Electricity. I like to thank the members of the mechanical workshop to disturbance them with high noise during my project tests, and I would like to thank "Mr.Emad Odish" in mechanical department. Also, I would like to thank my mother, my brothers, and all family. They provided me with great love and encouragement to continue whenever I meet difficulties in life.

AbdulRahman

I

ABSTRACT

The launch of satellite generates extreme conditions, such as vibrations and acoustics that can affect the launch pad, satellite, and their payloads. The noise at launch and liftoff causes intense acoustic loads. These acoustic loads are the result of an intense acoustic environment generated by the interaction of the rocket-engine exhaust stream mixing with the atmosphere.

Acoustic load among the most critical quantity measures before all the satellites when launches to space. Vibrations that produced by use one side of the satellite structure can contain valuable information about the state of acoustic on the satellite. This work was planned and carried out in such a way to provide detailed information on effect of the acoustic vibration on the plate of satellite structure. The focus of this study is to find a correlation between acoustic and the plate vibration. A Vibrometer measurement device was used to measure displacement and velocity in horizontal directions to obtain the vibration information. Stress in (x , y)-directions on the plate are measured by applying a strain gage technique. The ranges of acoustic parameters in the present study were quite limited: starting sound pressure level (80, 90, 100, and 108 dB), frequency of sound (31.5, 63,125, 250, 500, 1000, 2000, 4000, 8000 Hz) and strain gage directions (horizontal, and vertical). The pressures of the sound and pressure spectral density are calculated by sound pressure level (dB). In this study also the finite element technique were used by software ANSYS to appearance acoustic parameters, to analytical predictions. Structural modeshapes and assessed with ANSYS. The plate was completed initially to define the procedure and a method required in ANSYS to complete a plate assessment, and by ANSYS was showed high level and low level of deformation and stress at each place on the plate.

II

List of Symbols

A Amplitude CTE Coefficient of Thermal Expansion

DC Direct current

E Modulus of Elasticity (GPa) e.g. "Exemplum gratia" (Latin) = for example ELV Expendable launch vehicles EM The electrical model EGSE Electrical Ground Support Equipment Etc. Et cetera (Latin) = and so on f Frequency (Hz) FEA Finite element analysis

FM The Flight model

xf Frequency in any octave band

reff Frequency in reference level i.e. "id est" (Latin) = that's it/in other words NASA National Aeronautics and Space Administration P Sound pressure (Pa) Reference pressure (Pa) Pressure spectral density The root-mean-square pressure

Q Quality factor QM The qualification model RLV Reusable Launch Vehicles RMS Root main square

RSLVF Representative Small Launch Vehicle Fairing

sP

rmsP

refP

III

SM The Structural model SPL The sound pressure level (dB) t Time (sec) T3 Solution Heat Treatment ,cold worked and Natural Aging

T6 Solution Heat Treatment ,artificially aged T7 Solution Heat Treatment ,stabilized

VRMS Voltage root main square Center frequency (Hz)

Maximum frequency (Hz) Minimum frequency (Hz)

Natural frequency

Period (sec) x Displacement (m) x& Velocity (m/sec)

x&& Acceleration (m/sec2 ) yield Yield stress (MPa)

Ultimate Ultimate stress (MPa) Stress (MPa)

Strain (m/m)

cf

minfmaxf

IV

Contents Subject Page

Abstract .... I List of Abbreviations ... II Contents ... IV

List of Figures . VII

List of Tables ... X

CHAPTER ONE: INTRODUCTION AND LITERATURE REVIEW 1-1 Introduction .. 1 1-2 Payload ....

4

1-3 Design satellite .

4

1- 4 Materials .....

5 1-5 Vibration Frequency.. 7 1-6 Acoustic Noise . 7 1-7 Acoustic Vibration ...

8

1-8 Random Vibration 8 1-9 Sound Pressure Level .. 10 1-10 Launch Vehicle Systems . 12

1-11 Vehicle Launch Loads . 13 1-12 Vibration modes .. 18 1-13 Literature review of acoustic vibration ... 19 1-14 The aim of this study ... 24

CHAPTER TWO: THEORITICAL AND FINITE ELEMENT OF ACOUSTIC VIBRATION

2-1 Introduction .. 25 2-2 Decibels ....

25

x &

xx&

x&

V

Subject Page 2-3 Octaves ..

26 2-4 Pressure spectral density ...

29 2-5 Analysis of vibration data .

30

2-6 Finite Element Analysis ...

33

2-7 Procedure of software programming ....

34

CHAPTER THREE: EXPERIMENTAL WORK

3-1 Introduction ..

43 3-2 Materials and equipment apparatus ...

44

3-2-1 The plates material 44

3-2-2 Vibrometer .. 45 3-2-3 Strain measuring device setup .... 46 3-2-4 Determination of the modulus elasticity of tool holder by using the tensile test method ..

47

3-2-5 Oscillator 48 3-2-6 Oscilloscope ... 48 3-2-7 Sound level meter ...

49 3-2-8 Loudspeaker. 50 3-3 Experimental work .... 53 3-4 Experimental results .

56

CHAPTER FOUR: RESULTS AND DISCUSSION

4-1 Introduction ... 72 4-2 Data groups ...

72

4-3 Relationship between frequency and sound pressure level...

77

4-4 Relationship between frequency and displacement ..

79 4-5 Relationship between frequency and velocity ... 85

VI

Subject Page 4-6 Relationship between frequency and acceleration 91 4-7 Determination of stress .

97 4-8 Relationship between frequency and stress ..

100

4-9 Pressure spectral density ...

105 4-10 Relationship between frequency and pressure spectral density .. 108 4-11 Relationship between frequency and pressure

109

4-11 Finite element analysis ...

111

CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORKS

5-1 CONCLUSION .

113

5-2 Future works .

114

REFERENCES ...

115

@

VII

List of Figures Figures Page

Figure (1-1) Indicate acoustic vibration and random vibration 9 Figure (1-2) Sketch of the rocket flow and contour overall

sound- pressure level for flight and launch cases 11

Figure (1-3) Launch Vehicle and satellite 14 Figure (1-4) Sketch of loads at lunch stage 15 Figure (1-5) First and second harmonic modes for a simply

supported beam 19

Figure (2-1) Harmonic motion 30 Figure (2-2) Harmonic motion as projection of a point moving

on a circle

31

Figure (2-3) In harmonic motion the velocity and acceleration lead the displacement by and

31

Figure (2-4) indicate mesh of the model 35 Figure (2-5) Indicated ten modeshape of plate by using ANSYS

Workbench programs 38

Figure (2-6) Indicated deformation of plate at different frequency and pressures by using ANSYS Workbench programs

40

Figure (2-7) Indicated stress of plate at different frequency and pressures by using ANSYS Workbench programs

42

Figure (3-1) Vibroacoutic testing system 43 Figure (3-2) Vibrometer device 45 Figure (3-3) Indicate place of reading of vibration in the plate 46 Figure (3-4) Insulation of strain measurement instrument on the

plate (A: horizontal, B: vertical) 46

2/pi pi

VIII

Figures Page Figure (3-5) Digital strain indicator and switch balance unit

strain measuring device 47

Figure (3-6) Electronic Oscillator 48 Figure (3-7) Tektronix type Oscilloscope 49 Figure (3-8) BK Precision's (model 732A) Sound Level Meter 50 Figure (3-9) Structure of loudspeaker 52 Figure (3-10) ECHO JASCO amplifiers and loudspeakers 52 Figure (3-11) Screen of Ulead video studio program 54 Figure (3-12) The reading the record data 54 Figure (3-13) Experimental Procedure describes input variables

and output investigation 55

Figure (3-14) Indicates the direction of foil strain gage on the plate (A: Vertical , B: Horizontal)

67

Figure (4-1) Variation of level sound values with frequency for average condition

78

Figure (4-2) Variation of high level sound values with frequency 79 Figure (4-3) Displacement versus frequency in border of the

plate with starting sound pressure level at (80,90,100, and 108 dB)

80

Figure (4-4) Displacement versus frequency in center of the plate with starting sound pressure level at (80,90,100, and 108 dB)

82

Figure (4-5) Velocity versus frequency in border of the plate with starting sound pressure level at (80,90,100, and 108 dB)

86

Figure (4-6) velocity versus frequency in center of the plate with starting sound pressure level at (80,90,100, 108 dB)

88

IX

Figures Page

Figure (4-7) Acceleration versus frequency in border of the plate with starting sound pressure level at (80,90,100, and 108 dB)

92

Figure (4-8) Acceleration versus frequency in center of the plate with starting sound pressure level at (80,90,100, and 108 dB)

94

Figure (4-9) Stress versus frequency at (horizontal direction and vertical direction) in the plate at starting sound pressure level (80 ,90 ,100 , and 108 dB)

100

Figure (4-10) Variation of pressure spectral density with frequency

108

Figure (4-11) Variation of pressure of sound with frequency 110

X

List of Tables Tables Page

Table (1-1) Distribution of dynamic loads at launch stages 14 Table (2-1) Some example on band centers 27 Table (2-2) Relative bandwidth 28 Table (2-3) Centre frequencies octave and one-octave frequency 29 Table (2-4) Indicate ten modeshape of plate 35 Table (3-1) Conditions of test and experimental results 56 Table (3-2) values of x , x& and sound pressure level with different

frequency on the left side in the plate

57

Table (3-3) values of x , x& and sound pressure level with different frequency on the right side in the plate

59

Table (3-4) values of x , x& and sound pressure level with different frequency on the center side in the plate

61

Table (3-5) values of x , x& and sound pressure level with different frequency on the bottom side in the plate

63

Table (3-6) values of x , x& and sound pressure level with different frequency on the top side in the plate

65

Table (3-7) values of strain and sound pressure level with different frequency in vertical direction in plate

67

Table (3-8) values of strain and sound pressure level with different frequency in horizontal direction in plate

69

Table (4-1) average values in x , x& , x&& and sound pressure level with different frequency in each side of border of the plate

74

XI

Tables Page Table (4-2) Values in center of plate acceleration parameters 80 Table (4-3) Indicate value of stress at horizontal direction (x-

direction) position of plate 98

Table (4-4) Indicate value of stress at vertical direction (y-direction) position of plate

99

Table (4-5) Show the result of the pressure , and pressure spectral density

107

Chapter 1

INTRODUCTION AND INTRODUCTION AND INTRODUCTION AND INTRODUCTION AND

LITERATURE REVIEWLITERATURE REVIEWLITERATURE REVIEWLITERATURE REVIEW

Chapter one: INTRODUCTION AND LITERATURE REVIEW

1

CHAPTER ONE

INTRODUCTION AND LITERATURE REVIEW 1-1 Introduction Spacecraft is a craft or machine designed for spaceflight. On a sub-orbital spaceflight, for an orbital spaceflight, a spacecraft enters a closed orbit around the planetary body. A spacecraft orbiting the earth, another planet in our solar system or even beyond that, is a part of a complex infrastructure consisting of the launch vehicle, which positions the spacecraft in a certain orbit and ground based stations that cater for the communications. A spacecraft is generally divided into two parts (Payload and Service modules), the payload carries out the set task, i.e. the radio communications in a communication satellite. The spacecraft bus consists of several support systems (subsystems), such as attitude control, propulsion, power supply, thermal control, structure, deployable mechanisms (solar arrays) and telemetry. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and space tourism. Spacecraft and space travel are common themes in works of science fiction. Practical applications of space flight have become part of our lives in the form of weather and environmental satellites as well as communication satellites. The latter usually circle in a geostationary orbit at 36000 km above the equator. Space flight produces new technologies and has become economically viable. There is, for example, a great need for communication satellites as well as rockets to carry them into orbit. Space flight is a comprehensive and innovative part of technology. It encompasses many fields of technology [1]. The widespread use of satellite telecommunication technology in both the civil and military sectors has increased the competition between a growing number of satellite launch providers , Satellites used today for many purposes from communications to reconnaissance to weather prediction, and much more. Like all other products, satellites undergo design, fabrication, test, and shipment.


2

However, the shipment of a satellite to its final destination in orbit is far more complicated than for all other products. Launching satellites is the launch vehicle-induced vibration and shock environment that a satellite must endure on its trip to orbit. Excessive dynamic and shock loads can be a satellite killer causing permanent damage to electronics, optics, and other sensitive equipment. To compensate for the harsh dynamic environment, payloads must be designed and tested to very high dynamic levels, greatly increasing the cost of many payload components. An excellent alternative is to reduce the launch dynamic loads through the use of whole-spacecraft passive vibration isolation [2]. At the end of the 20th century, remarkable progress had been made in design, analysis, and fabrication of advanced composite structures. Structures and mechanisms are integral parts of any satellite, and the launch vehicle is required to place the satellite into orbit. The structures and mechanisms subsystem serves as the physical backbone supporting all other subsystems. Although other subsystems are not directly affected by the launch vehicle [3]. During the launch of space vehicles, there is a large external excitation

generated by acoustic and structural vibration. This is due to acoustic pressure fluctuations on the vehicle fairing caused by the engine exhaust gases. This external excitation drives the fairing structure and produces large acoustic pressure fluctuations inside the fairing cavity. The acoustic pressure fluctuations not only produce high noise levels inside the cavity but also cause damage such as structural fatigue, and damage to, or destruction of, the payload inside the fairing. This is an important problem because one trend of the aerospace industry is to use composite materials for the construction of launch vehicle fairings. The use of these materials

has resulted in large-scale weight reductions of launch vehicles, but one of its potential disadvantages is the increase of noise transmission with a resulting increase in acoustic levels inside the fairing [4]. Rocket motors generate tremendous acoustic energy at liftoff. Turbulent mixing of the hot exhaust gas with the surrounding air is the dominant acoustic source. The


3

exhaust gas may also have aerodynamic shock waves, which further add to the noise. Combustion instability and rough burning may also contribute to the noise Consider a rocket vehicle which has a payload enclosed in a nose cone firing [5]. The acoustic energy propagates to the payload fairing. The energy is then transmitted through the fairing wall to the enclosed air volume. The payload may be sensitive to the transmitted acoustic excitation, especially if the payload has solar panels or delicate instruments. Excessive vibration and shock can cause permanent damage to satellite electronics, optics, and other sensitive equipment. To compensate for the environment, payloads must be designed and tested to high vibration and shock levels, greatly increasing the cost of many components. An excellent alternative is to reduce the launch loads through the use of isolation systems. Because, the primary source of structural vibrations and internal loads during launch is due to these acoustic loads. Once the vehicle achieves supersonic speed, the effect of rocket exhaust noise are generally minimal compared with the turbulent flow noise excitation [5, 6]. The rocket engines produce noise throughout the whole frequency range of interest, but the high frequency content is particularly intense. High frequency noise remains a matter of concern in space vehicles, since during launch it can be enhanced due to deflected jet flow noise and associated acoustical reflections. High frequency noise adds concern because it causes a large number of stress reversals in space vehicles structures, space station payloads, satellites, and electronic packages. These stress reversals can cause fatigue failure during launch and the two-minute flight phase through the atmosphere.

Excessive noise levels inside the payload bays of launch vehicles are blamed for as many as 60% of first day satellite failures. It is claimed that 40% of the mass of a satellite is present just to enable the satellite to survive the harsh vibro-acoustic launch environment. If payload bay interior noise levels could be reduced, the probability of satellite survival would increase and the mass of a satellite could be


4

reduced, which has obvious financial benefits for both the cost of a satellite and the associated launch costs [7].

1-2 Payloads The payload is dependent upon the mission of the satellite, and is typically regarded as the part of the satellite "that pays the bills". Typical payloads could include scientific instruments (cameras, telescopes, or particle detectors, for example), cargo, or a human crew [8].

1-3 Design satellite Based on the design and development plan, the design specifications are further tested and elaborated on during the design process by means of design studies, computer simulations, analyses, trade-off studies, detailed testing, as well as designing and testing test models. During each step of the process the level of detail is increased in such a way that, through design drawings, the design can be finalized in production documents (drawings, manufacturing sheets), test plans and procedures. Testing and studying certain aspects by means of test models form an important part of the design process. These are not complete models. In most cases the following will be used: The structural model (SM, dynamic aspects). The thermal model (TM, thermal behavior in vacuum). The electrical model (EM, the electrical behavior of all systems combined and in relation to the ground testing equipment or EGSE: Electrical Ground Support Equipment). The qualification model (QM, qualification of the design for production of the flight model, FM). For the development of attitude control systems an attitude control model is added.


5

Tests on the test models may lead to changes in the design. Deviations from the design specifications need to be approved by the client [1].

1-4 Materials Mechanics of materials describes how structural members react to environmental loads. Since the satellite structure is by function a load-bearing structure, the stresses and deformations must be modeled for strength verification. The structures ability to withstand normal and shearing stresses as well as in-plane and out-of-plane deformations should be adequate for the structures desired lifetime [9]. Materials used in the fabrication of satellite hardware shall be selected by considering the operational requirements for the particular application and the engineering properties of the candidate materials. Satellite structural designs also use several different materials. Materials are chosen based on their properties, cost, and complexity. There are two typical materials used in satellite applications: metals and fiber composites [10]. Aluminum alloys are the most widely used metallic materials in satellite manufacturing. The advantages include high strength to weight ratios, high ductility and ease of machining. The stiffness to weight ratio is comparable to steel; however, the strength to weight ratio is typically higher. The disadvantages include low hardness and a high coefficient of thermal expansion (CTE). The alloys are typically tempered to increase the material strengths. Two typical alloys used in manufacturing are 6061-T6 and 7075-T7. Aluminum 6061-T6 contains silicon and magnesium which strengthens the alloy during tempering. This alloy has good machinability and corrosion resistance. Aluminum 7075-T7 contains zinc and trace amounts of magnesium. The alloy exhibits higher strength than (6061-T6), but is more difficult to machine [11]. Beryllium is used for very high-stiffness aerospace applications. It has a

specific modulus 6.2 times the specific modulus of aluminum. The material is non-isotropic and therefore exhibits low ductility and fracture toughness in its short grain


6

direction. It is low CTE and high thermal conductivity. However, beryllium is expensive, difficult to machine, and sparsely available in the US. Beryllium must be machined in a controlled environment because its powder is a known carcinogen when inhaled. The parts may be safely handled once machined. Steel is mainly used in aerospace applications where low-volume strength and stiffness are important. Steel provides high wear resistance; however it is generally difficult to machine and is not efficient for structural stability. Steels are combined with many trace elements to address a wide range of needs. Austentic stainless steel is by far the most abundant steel alloy used in satellite. It contains 12% chromium which results in a tough chromium-oxide coating that protects parts from corrosion. Stainless steel is non-magnetic and certain low carbon alloys can be welded without sensitization. Stainless steels are generally used for fasteners and mechanisms whereas many heat-resistant alloys are used for heat shields, rocket nozzles, and other high-temperature applications [12]. Titanium and titanium alloys are used for applications requiring very high strength materials. The materials exhibit high strength to weight ratios, low coefficients of thermal expansion, and excellent corrosion resistance. However, they are difficult to machine and some alloys exhibit poor fracture toughness. Ti-6Al-4V, which contains 6% aluminum and 4% vanadium, is the most popular titanium alloy used in aerospace applications. The alloy has heritage in wings and missile bodies. Perhaps its most famous applications are the castings used to connect the external fuel tank to the Space Shuttle and its boosters [11]. Fiber Composite structures consist of a matrix and reinforcement. The matrix (metal, epoxy) binds the reinforcing fibers (carbon, graphite) together into a continuous system. The efficiency of composite structures is due its high specific modulus and unique load path. The flexural shear loads are transferred from the matrix to axial loads on the high-strength fibers, creating a structure 3 to 5 times as stiff as aluminum at 60% of the mass [12].


7

1-5 Vibration Frequency Acoustic excitation is often referred to as a high frequency test because, as

previously mentioned, it covers the frequency range from 30 to 10000 Hz. Random vibration is often considered a low or mid frequency test because excitation occurs typically in the range from 20 to 2000 Hz. At frequencies above 2000 Hz, the acoustic noise field contains considerable energy, while random vibration occurs only as a result of harmonics.

The higher frequency content in acoustic vibration is also due to differences in the input location. Since random vibration is input at the base of a component, excitation frequencies above the fundamental mode begin to be attenuated. At higher frequencies, more vibration modes from the initial input become filtered out. For acoustic vibration, the input is along the surface of the structure. High frequency energy is not attenuated because no soft spring low pass filter exists between the structure and the excitation source [13].

1-6 Acoustic Noise Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound (all mechanical waves in gases, liquids, and solids). The application of acoustics in technology is called acoustical engineering [8]. The largest acoustic noise excitation occurs at point of lift-off when the reflected noise from the launch pad and ambient air pressure are greatest. Acoustic noise can be critical for the design of lightweight structures with large area and low mass such as dish type antenna reflectors and solar array panels. When the resonant frequency of such items is known .the sound pressure level (SPL) at the corresponding centre band frequency can be used to calculate the magnitude of response. Acoustic test results from similar previous designs are often used to estimate the responses of complex structures. Structural response to acoustic noise is predicted and measured in terms of random vibration [14].


8

Acoustic noise is generated by engine noise, buffeting and boundary layer noise. The level is highest at lift-off (137.9 dB) and in the transonic phase (135 dB) with a reference pressure of ( -5102 Pa = 0 dB). Noise is substantially lower outside these periods. During the lift-off and ascent flight phases, significant acoustic energy will be imparted onto payload hardware. For payloads which are susceptible to acoustic impingement (those with large surface areas or low mass density) [15]. The satellite has a mode or natural frequency that is the same as that generated by the

launch vehicle. These loads are significant from frequencies of 20 Hz to well over 1000 Hz [16].

1-7 Acoustic Vibration The object of structural acoustics is to model and analyze the propagation of structural borne acoustic vibration in order to predict and design for the overall acoustic behavior of the structure. It is important to perform an acoustic vibration analysis to predict the satellites response to a worst case acoustic load and ensure the structure is designed to satisfactory levels and will maintain integrity throughout all cycles of the mission.

The acoustic vibration analysis for this structure was simplified. Only the simple case of a plate with fixed boundary conditions was treated; due to the complexity of the problem [17], as shown in figure (1-1).

1-8 Random Vibration It is a physical reality that the satellite will be exposed to loading conditions that are not known, and at best can only be predicted. These predictions are based on experience and statistical analysis and are considered to be the random vibration of the structure. There is no way to ensure that the predicted random excitation will actually take place, and at best it can only be hoped that the actual excitation of the satellite will not deviate too much from the predicted case. Therefore it should be


9

apparent that the actual response of the structure can not be evaluated any better then the excitation can be predicted [17], as shown in figure (1-1).

Figure (1-1) Indicate acoustic vibration and random vibration [13]


10

1-9 Sound Pressure Level (SPL) The sound pressure level (SPL) is generally given in decibels. The SPL gives an indication of the strength of the noise source but nothing about the direction. In fact, a noise field is governed by two quantities: the sound pressure level and the direction. In a free space, a vibrating sphere will radiate sound in all directions, while in a closed space the noise field will reflect off the walls from several sides. A noise field is called reverberant or diffuse when the noise strength is equally high from all directions. In the case of a reverberant noise field, the direction of sound is insignificant and only the noise strength is important. The sound in a room consists of that coming directly from the source plus sound reflected or scattered by the walls and by objects in the room. Sound is called reverberant after having undergone one or more reflections. Relative noise levels around a launch vehicle during lift-off and flight are shown in Figure (1-2). The exhaust noise of the engines causes considerable acoustic loads within the nose cone of the launch vehicle. The highest acoustic loads occur during lift-off and in transonic flight. Generally, a reverberant noise field is assumed. The strength of the noise field (SPL) is expressed in (dB), depending on the frequency. The frequency band is the octave- or one-third octave band. The sound pressure level (SPL) is defined in the following way:

= 2

2

log10refP

PSPL ..................................................................................... (1.1)

where the reference value of the sound pressure, 5102 =refP Pa and P is the

effective value of the occurring sound pressure. The sound pressure is measured in a certain centre frequency with associated bandwidth. In acoustics it is common to work with a constant relative bandwidth (the so called octave or one-third octave band filters) [1].


11

Figure (1-2) Sketch of the rocket flow and contour overall sound-pressure level for flight and launch cases [18]


12

1-10 Launch Vehicle Systems Much of the design of a satellite will be constrained by the size and weight

restrictions particular to the launch system. In general, there are five steps to

selecting a launch system for a particular mission. First step involves defining the requirements and constraints for the mission. At this point, issues such as mission timeline, funding constraints, and satellite dimensions are addressed. Second step involves identifying and analyzing acceptable configurations for the launch system. During this step the reliability, performance, and lifting capacity are considered in addition to other factors including acceleration imparted to the satellite and vehicle vibration. Third step is the selection of the potential launch system. A potential launch system will be evaluated using the following criteria: lifting capability, cost, performance margin available, reliability, and schedule versus vehicle availability. Fourth step is the environments created by the launch system are determined, as well as the satellite design envelope. This step is required to determine how the launch system may negatively affect the satellite. Fifth step, for selecting a launch system is

to iterate the previous four steps in an effort to meet constraints on performance,

cost, risk, and schedule. [9] The launch vehicle is used to propel the satellite from the Earth's surface, through the atmosphere, and into an orbit, the exact orbit being dependent upon mission configuration. The launch vehicle may be expendable or reusable a launch system is a launch vehicle comprised of one or more stages, and the infrastructure for support from the ground [8].The launch vehicle positions the satellite in the required orbit and attitude. During launch, the satellite is exposed to loads and protected from the environment by the nose cone (fairing). Therefore the choice of the launch vehicle is of course dependent on the satellite mission, the launch vehicle sets restrictions for the satellite, such as the possible launch mass and the available volume. Launch vehicles can be divided into two groups: Expendable launch vehicles (ELV) (where the rocket is used once) and Reusable Launch Vehicles, (RLV) (where parts can be used several times).


13

In Europe the ARIANE 5 and SOYUZ launch vehicles are well known while in the USA the Shuttle, the DELTA family, the ATLAS family and the TITAN family of launch vehicles are well known [1].

1-11 Vehicle Launch Loads During flight, the payload is subjected to static and dynamic loads induced by the launch vehicle. Such excitation may be of aerodynamic origin (wind, gusts, buffeting at transonic velocity), or may be due to loading induced by the propulsion systems (longitudinal acceleration, thrust build-up or tail-off transients, structure-propulsion coupling, attitude control operation, etc.). The various types of mechanical environment experienced by the payload are described in the following paragraphs. Typical data are given for sine, acoustic, random and shock environments. If not explicitly stated all mechanical loads in this Users are defined as maximum operational loads. For the launch vehicle and payload coordinate system, refer to Figure (1-3) [15]. Launch vehicle and satellite low frequency loads are driven by transients such as engine ignition, engine shutdowns, wind gusts or wind shears, and quasi-static loads. Other environments are acoustics, random vibration, sine vibration, and shock, as shown in table (1-1).The maximum loads (flight limit loads) at any stage in the life cycle of a satellite or other space system are used to design and dimension the primary, secondary and other parts [1].


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Table (1-1) Distribution of dynamic loads at launch stages [1]

Stage of launched Acoustics Random Vibration Sine

Vibration Shock

Lift-off X X

Aerodynamics /Buffet X X

Separation (stage, fairing, satellite)

X

Motor burn /Combustion/ POGO

X X

Figure (1-3) Launch Vehicle and satellite [15]

The dynamic mechanical loads are occurring along the lifetime of a satellite as shown in figures (1-4).


15

Figure (1-4) Sketch of loads at launch stage [1, 19]

Launch loads

Handling loads

Transportation loads

Loads/influences on the satellite in orbit (In-service loads)

Vibration tests required for the qualification of the satellite structure

Dynamic loads during launch

Re-entry loads

(Emergency) landing loads

Acoustic pressures

Random vibrations

Sinusoidal vibrations

Acoustic pressures

Random vibrations

Sinusoidal vibrations

Steady-state acceleration

Pressure variations

Shock loads

Loads following launch

Transfer orbit loads

Micro-meteorites /

0g loads

Temperature gradients

Extension of folded elements,


16

1-11-1 Steady-state static loads The maximum steady-state acceleration in the launch direction occur at the end of the propulsion phase of a rocket stage. The acceleration increases because the mass of the launch vehicle decreases, while the overall thrust remains the same. The vibrations are superimposed on the steady state acceleration. The lateral steady-state accelerations are usually much smaller than the acceleration in the launch

direction. (Longitudinal acceleration > Lateral acceleration) Steady-state static loads as a result of: The propulsion of the engine

Crosswind loads Manoeuvres [1].

1-11-2 Mechanical Dynamic loads The mechanical dynamic loads during launch can subdivided into: Low frequency sinusoidal vibrations in a frequency domain of 5100 Hz. Random vibrations in a frequency range of 20 2000 Hz [1].

Sinusoidal loads Low frequency sinusoidal vibrations occur as a result of the interaction between launch vehicle mode forms and loads occurring during. Lift-off, the fast build-up of thrust causes a shock load that excites the low frequency domain. Combustion of the engines, during combustion of the engines sinusoidal vibrations occur, both in, and adjacent to, the launch direction [20].


17

Random load Acoustic loads and boundary layer turbulence are transformed into mechanical vibrations in the launch vehicle, which affect the satellite at its base. It is assumed that the acoustic loads will cover the random mechanical vibrations [1].

Acoustic loads The noise of the launch vehicle engines, the separation of the airflow along the

launch vehicle and the aerodynamic noise generate acoustic loads in a broad frequency spectrum from 20-10000 Hz. This acoustic environment generates

random vibration loads due to the sound pressure acting on the surfaces of the satellite. Acoustic loads are developed during powered ascent, the first 3 to 4 minutes of ascent. Compression waves are particularly significant for structures with

a ratio of high cross-sectional area to low mass [16].

Shock load Shock loads as a result of the separation of the stages and the separation of the satellite from the launch vehicle, the ignition and the stopping of the engines. The separation of the satellite results in the highest shock load [1].

Pressure variations (Pressure changes) The absolute pressure decreases during launch, which can influence the systems unless suitable ventilation systems have been fitted [1].

Micro-meteorites/Debris Space surrounding Earth is full of millions of micro meteoroids and man-made orbital debris. Orbital debris consists not only of large redundant stages of rockets and old satellite but, also small parts such as bits of paint and other fragments. Even minute parts can seriously damage a satellite because these parts move at very high velocities. Orbital debris flies with a velocity of 7.5 km/s (27000 km/h) in an orbit around the earth [1].


18

1-12 Vibration modes A standard manner in which a particular system can vibrate is known as a vibration mode. Each vibration mode is associated with a particular natural frequency and represents a degree of freedom. A single-degree-of-freedom system will have only one vibration mode and only one resonant frequency [21]. In the study of vibration in engineering, a mode shape describes the expected curvature (or displacement) of a surface vibrating at a particular mode. To determine the vibration of a system, the mode shape is multiplied by a function that varies with time, thus the mode shape always describes the curvature of vibration at all points in time, but the magnitude of the curvature will change. The mode Shape is dependent

on the shape of the surface as well as the boundary conditions of that surface [8]. The fundamental resonant mode of a vibrating system is usually called the natural frequency or the resonant frequency of the system. Sometimes it is called the first harmonic mode of the system. For example, a simply supported uniform beam vibrating at its fundamental resonant frequency has the mode shape of a half sine wave as shown in Figure (1-5 a). When this beam is vibrating at its second natural frequency, in its second harmonic mode, it has the mode shape of the full sine wave shown in Figure (1-5 b). The first harmonic mode of a system, with the lowest natural frequency, is the fundamental resonant mode; this often has the greatest displacement amplitudes and usually the greatest stresses. The second harmonic mode, or second resonance, usually has a smaller displacement than the first harmonic mode, so the stresses are usually smaller. The displacements continue to decrease for the higher resonant

modes [21].


19

Figure (1-5) first and second harmonic modes for a simply supported beam [21]

1-13 Literature review of acoustic vibration Some key background references and their contributions to the force limited acoustic vibration technology described in this monograph are summarized in chronological order in this section, There exists both published and unpublished material that is of particular relevance to the successful completion of this project. Presented below is a sample of the most relevant literature

Salter J. P., [1964] calls for two test improvements to alleviate overtesting: 1) multi-point control to reduce the impact of fixture resonances and 2) force limiting to account for the vibration absorber effect at test item resonances. It proposes a very simple method of computing the force limit, i.e. the force is limited to 1.5 times the mass times the peak acceleration, i.e. the acceleration specification. His

approach, in conjunction with a review of the force data obtained in the system acoustic tests of the Cassini spacecraft, provides the impetus for what in this monograph is called the semiempirical method of predicting force limits [22]. Kurng Y. Chang , Terry D. Scharton, [1996] describe the force limited vibration test of the Cassini spacecraft. Over a hundred acceleration responses were monitored in the spacecraft vibration test, but only the total axial force is used in the control loop to notch the input acceleration. The force limit specified in the spacecraft


20

vibration test plan is used in the test without any modifications. The force limit for the complete spacecraft vibration test, as well as the limits for many of the Cassini instrument vibration tests, are developed using a simple, semi-empirical method which requires only the acceleration specification and data from a low level pre-test to determine the apparent mass of the test item. The instrument force limits derived with the semi-empirical method are generally equal to or less than those derived with the two-degree-of-freedom method, but are still conservative with respect to the

interface force data measured in the acoustic test [23]. John C. Forgrave, Kin F. Man , et al.,[1997] This paper describes a method for optimizing acoustic and random vibration trials to reduce cost and schedule, without incurring undue risk to the hardware depending on the surface area, mass, and geometry of the test object, one vibration test is normally more effective as a failure screening mechanism. Random vibration is found to be more effective in spring-mass systems with input frequencies ranging from 20 to 2,000 Hz, whereas acoustic

testing is more effective for plate-like structures with input frequencies ranging from

30 to 10,000 Hz. By calculating a test article response in each environment and comparing the relative response magnitudes. Investigation the effects sound pressure level and frequencies on the spacecraft when become acoustic vibration and random vibration, when there was used sound pressure level to 135 dB [13]. Terry Scharton , [1998] Instead of conducting the acoustic test with the spacecraft in a reverberant room, as is the usual practice, the test was conducted with the spacecraft mounted on a shaker slip-table in a nearly anechoic, vibration test cell. The spacecraft was surrounded with a three-meter high ring of large, large, electro-dynamic speaker, spaced approximately 1.3 meters away from the two-meter diameter, 900 kg spacecraft. The thirty-one speaker cabinets were driven audio amplifier power, the acoustic specification, with an overall sound pressure level of 135 dB. This study was presented a detailed experimental investigation for the effect of maximum displacement with low frequency [24].


21

Craig L. Stevens, [2002] The purpose of this thesis was to design, analyze, fabricate, and test a nanosatellite for flight qualification aboard the NASA STS. Investigated several materials and methods used to optimize the structural properties of spacecraft assemblies. chose aluminum isogrid as the most efficient design for this program. This thesis was described the design of the spacecraft and the entire satellite configuration, and applied the theory to results of the finite element analysis to arrive at the design. Thesis was verified the models using modal analysis

techniques, and performed environmental testing on the satellite assembly at NASA Wallops Flight Facility, and was devised integration methods to raise the fundamental frequency of the structure and reduce the dynamic amplification of the loading on critical components [11]. Deyu Li., [2003] this work has focused on the goal of better characterization of the noise transmission into advanced composite cylindrical structures, which leads to better noise transmission controls. The task is by no means complete, but all the theoretical models and design schemes can be used for full size composite cylindrical structures for characterizing their noise transmission behavior and conducting noise transmission control. In this thesis was used four speaker with amplifier and frequency range was used between (0- 2000 Hz) and sound level range to 110 dB, finally there was analyzed the cylinder shape by finite element was obtained mode shapes and relation between frequency and sound level [3]. Peter Davidsson , [2004] investigates structure-acoustic systems by using of finite element analysis. The systems studied here are limited to those that consist of an enclosed acoustic fluid cavity, which is coupled to a flexible structure and/or a porous sound absorbing material domain. The typical procedure of structure-acoustic analysis is discussed, including the generation of the governing system of equations and the solution of the generated systems using sub structuring and modal reduction. This study was presented a detailed experimental investigation for the effect of maximum displacement with frequency (0-2000Hz) and sound pressure level between (100-147 dB) [25].


22

Simon J. Estve, [2004] has demonstrated that a lightweight and compact noise reduction treatment can significantly increase low frequency transmission loss of a composite cylinder representative of a payload fairing. This is possible because in such structures the lower part of the internal acoustic spectrum is composed of sharp structural and acoustic resonances, which cannot be effectively damped by traditional acoustic blankets. Therefore, damped vibration absorbers and Helmholtz resonators represent an efficient way to add damping to these resonances without

adding a significant amount of weight or volume [26]. Aidan Bettridge, [2004] deals with the investigation into the design and analysis of developing the structural subsystem of a picosatellite capable of carrying a scientific payload into orbit. The design of the satellite is constrained by the specifications defined by the CubeSat Standards. Provide a detailed design and analysis of the CASsat structural subsystem only (without experimental) because data of this thesis came from CASsat company, by using finite element analysis computer programs Strand7 .when Strand7 is respective programs in Sydney university networks. There was analyzed acoustic vibration and random vibration of one side of plate and all sides with them (box) [17]. William O. Hughes [2005] This paper compares the results obtained from the Normal Tolerance Limit method with those obtained from the Bootstrap method. The Bootstrap is a statistical subsampling method which utilizes sample data to generate replicates which are utilized for parameter and confidence interval estimation. The Bootstrap makes no assumption on the underlying distribution of the data, whereas the Normal Tolerance Limit assumes normality. It was using MATLAB computer programs to analyzing with Bootstrap method [27]. K. Renji, M. Mahalakshmi, [2006] Vibration energy transfer in a system of three plates separated by a small distance and connected at a few discrete points, like solar panels in a spacecraft, is investigated. Coupling loss factors are obtained experimentally using the power injection technique. The system is then subjected to the acoustic excitation in a reverberant chamber. The measured responses of the


23

inner plate are significant. But the measured responses of the inner plates are higher than the responses estimated based on the coupling loss factors obtained. When the system is subjected to mechanical excitation the measured responses of the inner plate closely match with the estimated responses. Investigation the effect frequency in acceleration by using accelerometers in each plate of three plates was used in this study [28]. Mir Md. Maruf, [2008] establishes theoretical and numerical models for the prediction of external sound pressure loading on composite structures representing launch vehicles, such as a large composite cylinder referred to as a Boeing cylinder and a Representative Small Launch Vehicle Fairing (RSLVF). To predict the external sound pressure loading, various incident wave conditions were investigated. For the theoretical model, both the incident and scattered sound pressure fields due to incident plane waves; perpendicular to an idealized long cylinder were investigated. The results show that the scattered sound pressure field plays a major role in determining the total circumferential sound pressure field at the surface of the cylinder and cannot be ignored for the launch case. The theoretical model was developed further for a point source, line source and oblique incident waves, and modified to determine the incident, scattered and total sound pressure fields away from the cylinder. The approach developed overcomes some limitations of previous analytical derivations. An experiment was undertaken to determine the sound pressure patterns at the surface of a cylinder at various frequencies due to a point source positioned at a finite distance from the cylinder surface. The experimental work confirmed the accuracy of the theoretical model for a point source at a finite distance from the cylinder [4].


24

1-14 The aim of this study The aim of this study is investigate the effect of acoustic vibration on the satellite structure in all frequency (0 10000 Hz) especially, at low frequencies (lower from 1000 Hz). The research should have completed a full fractional experimental design and finite element that allowed considering a two level interactions between the sound parameters (frequency, Sound pressure level) with measuring variables (stress and vibration). An important part of the present work is the prediction of the acoustic loading on the external fairing surface as a result of rocket motor noise during launch.

Chapter 2

THEORITICAL AND THEORITICAL AND THEORITICAL AND THEORITICAL AND

FINITE ELEMENT OF FINITE ELEMENT OF FINITE ELEMENT OF FINITE ELEMENT OF

ACOUSTIC VIBRATIONACOUSTIC VIBRATIONACOUSTIC VIBRATIONACOUSTIC VIBRATION

Chapter two: THEORITICAL AND FINITE ELEMENT OF ACOUSTIC VIBRATION

25

CHAPTER TWO

THEORITICAL AND FINITE ELEMENT OF ACOUSTIC VIBRATION

2-1 Introduction This chapter presented the theoretical and finite element analysis of vibration signal and pressure sound pressure level in satellite structure and relationship between frequency and pressure sound level.

2-2 Decibels The decibel is one-tenth of the original unit, the bel (B). This was found inconvenient for practical use, and was divided into 10 decibels. The decibel scale alone, without reference to a standard level, is simply a way of expressing the factor by which an oscillatory quantity, such as voltage, force, pressure, etc., changes. It is defined in terms of power (mean square) values. So, for example, if an RMS voltage, 1v , changes to 2v , the change expressed in dB is SPL, say, where:

= 2

1

22

10log10)(v

vdBSPL or 10/21

22 10SPL

v

v= .........................(2.1)

Equation (2.1) can be written as:

=

1

210log20)(

v

vdBSPL or 20/1

2 10SPLv

v= .........................(2.2)

The changes in dB corresponding to some simple multiples of RMS and mean square levels, to sufficient accuracy for most purposes.

When used to express sound pressure levels, the decibel is used in a completely different way. The RMS sound pressure is defined as being SPL in (dB) above a reference level, refP , which is fixed at the assumed threshold of human hearing,


26

taken as an RMS value of 20 Pa, i.e. [ 2-6 N/m 1020 ] (or 2-9 lbf/in 102.90 ).

The sound pressure level (SPL) is then given by:

=

=

refref pp

ppdBSPL 102

2

10 log20log10)( ........................ (2.3)

where P is the RMS value of the pressure concerned, and refP is the RMS reference

level defined above. Equation (2.3) can be written as: [29, 30]

10)(

2

2

10dBSPL

refpp

= ................................................................................... (2.4)

10)(

22 10dBSPL

refpp = ....................................................................................... (2.5)

2-3 Octaves Acoustic spectra are given as dB in bands, with band centers usually spaced at a

given fraction of an octave, although dB levels in 1 Hz bands are also used. An octave, as in music, is an interval over which the frequency doubles. Very often, the center frequencies of the bands are spaced at (1/3) octave intervals, but other fractions, or even whole octaves, can be used. Taking the (1/3) -octave system as an example, and starting at 10 Hz, the band centers, cf , are as shown in table (2-1). These are awkward numbers, but the rounded, standard, values shown are usually close enough for practical purposes.

For a constant relative bandwidth, the ratio between two consecutive frequencies is defined as:

x

ref

x

ff 2=

........................................................................................................ (2.6)


27

x: octave band

xf : Frequency in any octave band

reff : Frequency in reference level

Table (2-1) some example on band centers

Center frequency (Exact) cf (Hz) Center frequency

(standard value )(Hz) 000.10210 0 =

10

599.12210 31 = 5.12

874.15210 32 = 16

000.20210 1 = 20

198.25210 34 = 25

758.31210 35 = 32

etc. etc.

In which case it yields for x:

1=x one speaks of an octave band 12=ref

x

ff and when

31

=x one speaks of an octave band 260.12 31

==

ref

x

ff

If the center frequencies are spaced at (1/3)-octave intervals, the bandwidth associated with each may be regarded as extending (1/6) of an octave below to (1/6) of an octave above, cf . Thus: [29]

ccc fff 2315.022Bandwidth 61

61

=

=

.................................................. (2.7)


28

The centre frequencies in an octave- and one-third octave band are given in

Table (2-3) .The centre frequency centf is the geometric mean of the minimum frequency minf and the maximum frequency maxf in the relative frequency band, and is of course dependent on the octave band used. The centre frequency is:

maxmin fffcent = .............................................................................................. (2.8) Relative bandwidth

The bandwidth f is the difference between the maximum frequency maxf and the minimum frequency minf and is given by:

minmax fff = ............................................................................................ (2.9)

The ratio between the extreme frequencies in the band isx

ff 2

min

max=

. It is then easy

to derive the expression for the bandwidth in terms of the centre frequency

cent

xx

ff

=

22 22 ..................................................................................... (2.10)

Any proportional frequency band is defined by its centre frequency and by x. An octave band (x=1) with a centre frequency 1000 Hz, the extreme frequencies of the frequency band are Hzf 707min = and Hzf 1414max = respectively and the relative bandwidth is Hzf 707= [1]. The relative bandwidth for the one-octave and one-third octave bands are given in Table (2-2) Table (2-2) Relative bandwidth [1]

xst-Octave band Bandwidth (Hz)

1=x

31

=x

centff 7071.0= centff 23161.0=


29

Table (2-3) Centre frequencies octave and one-octave frequency bands [1]

Octave frequency band (Hz)

One-third octave frequency band

(Hz) Octave frequency

band (Hz) One-third octave frequency band

(Hz)

31.5 25

31.5 40

1000

800 1000

1250

63 50 63 80

2000

1600 2000

2500

125 100

125 160

4000

3200

4000

5000

250 200

250 315

8000

6300 8000

10000

500 400 500 630

2-4 Pressure spectral density To obtain the component response due to acoustic excitation, the first value to be

calculated is the sound pressure spectral density ( sP ) at the natural frequency ( nf ) of the component, as follows.

sP is defined as:

2

fPPs

= ........................................... (2.11)

and is calculated from:


30

Substitute equation (2.5) and Equation (2.7) in equation (2.11), it obtain

231.010)102( 1025

n

dB

s fP

=

............................................................................. (2.12)

Equation (2.5) and (2.7) was used to determine pressure spectral density ( sP ) [13].

2-5 Analysis of vibration data The data that obtained from the experiments are the amplitude and the velocity

of a point on the plate. The motion is repeated in equal intervals of time , that it is

periodic motion .The is the period of the oscillation, and its reciprocal. Frequency

( 1=f ), then the time function is x(t)=x(t+ ). The simplest form of periodic motion is harmonic motion .It can be demonstrated by a mass suspended by a light spring, as shown in Figure (2-1). If the mass is displaced from its rest position and released, it will oscillate up and down.

Figure (2-1) Harmonic motion [31] The motion can be expressed by the equation:

tAx

pi12sin=

.......................................................................................... (2.13)

Where A is the amplitude of oscillation, measured from the equilibrium position

of the mass, and is the period. The motion is repeated when =t .


31

sec)] ( /[ xxt &= Then using Microsoft Excel Computer Program the diagram of frequency for any experiment as indicate in figure (2-2).

Figure (2-2) Harmonic motion as projection of a point moving on a circle [31]

Harmonic motion is often represented as the projection on a straight line of a point that is moving on a circle at constant speed, as shown in Figure (2-3). With the angular speed of the line op designated by , the displacement x can be written as:

tAx sin= ............................................... (2.14)

Figure (2-3) In harmonic motion the velocity and acceleration lead the displacement by 2/pi and pi [31]


32

The quantity is generally measured in radians per second, and is referred to as the

circular frequency. Since the motion repeats itself in pi2 radians, the relationship is:

fpi

pi 22 ==

.......................................... (2.15)

Where and f are the period and frequency of the harmonic motion, usually measured in seconds and cycles per second respectively. The velocity and acceleration of harmonic motion can he simply determined by differentiation of Eq. (2.14). Using the dot notation for the derivative, it can obtain:

+==

2sincos pi tAtAx&

.................................. (2.16)

( )pi +== tAtAx sinsin 22&&................................. (2.17)

The velocity and acceleration are also harmonic with the same frequency of

oscillation, but lead the displacement by 2/pi and pi radians respectively. Figure (2-3) shows both time variation and the vector phase relationship between the displacement, velocity and acceleration in harmonic motion. Examination of equation (2.14) and (2.17) reveals that:

xx 2=&& .............. (2.18)

So that in harmonic motion the acceleration is proportional to the displacement and is direct towards the origin. Since Newton's second law of motion states that the acceleration is proportional to the force, harmonic motion can be expected for the

system with linear springs with force varying kx [31].


33

2-6 Finite Element Analysis The finite element method is a powerful mathematical tool used for the

numerical solution of a wide range of engineering problems. In this case finite element analysis was used to estimate the deformations and stresses of one side of satellite body will experience under an acoustic load [17]. The basis of FEA relies on the decomposition of the domain into a finite number of subdomains (elements) for which the systematic approximate solution is constructed by applying the variation or weighted residual methods. In effect, FEA reduces the problem to that of a finite number of unknowns by dividing the domain into elements and by expressing the unknown field variable in terms of the assumed approximating functions within each element [32]. Various phenomena treated in science and engineering are often described in terms of differential equations formulated by using their continuum mechanics models. Solving differential equations under various conditions such as boundary or initial conditions leads to the understanding of the phenomena and can predict the future of the phenomena (determinism). Exact solutions for differential equations, however, are generally difficult to obtain. Numerical methods are adopted to obtain approximate solutions for differential equations. Among these numerical methods, those which approximate continua with infinite degree of freedom by a discrete body with finite degree of freedom are called discrete analysis [33]. Finite Element Analysis (FEA) uses a complex system of points called nodes which make a grid called a mesh. This mesh represents the geometry of the structure and can be programmed to contain the material and structural properties which define how the structure will react to certain loading conditions. The nature of FEA implies its application in computational packages.

There exist a number of structural finite element analysis software packages, such as MatLAB, Strand7, ANSYS, etc. This program was used for the finite element analysis of this structure [17].


34

ANSYS is a general-purpose finite-element modeling package for numerically solving a wide variety of mechanical problems. These problems include static/ dynamic, structural analysis (both linear and nonlinear), heat transfer, and fluid problems, as well as acoustic and electromagnetic problems [33]. Perhaps the simplest of the solution methods used here, the modal analysis is used to determine the natural frequencies of interest. Determination of the fundamental response modes is necessary for several reasons. Most practical problems require using the finite element method to define a model. The finite element method can be formulated with specific damping elements in addition to structural elements for highly damped systems, but its most common use is to model lightly damped structures [34]. The suspension frequency response plot and mode shape plots complement each other and help to develop a visual.

2-7 Procedure of software programming To obtain modeshape, deformation and stress of plate that used in this research by computer programs will be using ANSYS workbench is finite element analyzer computer programs.

After insulation and using ANSYS workbench computer analysis programs the principle step of work is:

Create modal of the plate. Dimension of plate is (0.25 x 0.25 m) and thickness (0.001m).

Addition material properties.

Meshing plates to (1984 nodes) and (254 elements) as shown in figure (2-4). Fixed support at four circle point (fixed point were bolt point). Fixed base modal run to calculate resultant structural shapes and frequency

modes. Modal run from new analysis menu and solving the modal to obtain first 10 modes between 0 and 10000 Hz for the range.


35

After identify some fundamental frequencies of interest such as (31.5, 63, 125, 250, 500, 1000, 2000, 4000, and 8000 Hz) for the Harmonic analysis and samples of pressure ,finally run the Harmonic analysis to obtain deformation and stress in all different stages [35,36 ,37 ].

Figure (2-4) indicate mesh of the model


36

Modeshape When solving programs at step Modal will obtain the modeshape as shown in table (2-4) and the shapes as shown in figure (2-5)

Table (2-4) indicate valve of natural frequency Mode Frequency [Hz]

1. 59.692 2. 107.78 3. 108.54 4. 122. 5. 209.07 6. 248.05 7. 264.8 8. 265.92 9. 353.72 10. 385.07

Displacement (deformation) Finally solving programs at step Harmonic analysis will obtain the deformation shape at different frequency and pressure as shown in figure (2-6).

STRESS After solving programs at step Harmonic analysis and Equivalent (von-Mises) stress type will obtain the stress shape at different frequency and pressure as shown in figure (2-7).


37

First mode First mode other side

First mode other side Second mode

Third mode Forth mode


38

Fifth mode Sixth mode

Seventh mode Eighth mode

Ninth mode Tenth mode Figure (2-5) Indicated ten modeshape of plate by using ANSYS Workbench


39

(Adeformation at frequency 31.5 Hz) (Bdeformation at frequency 63 Hz)

(Cdeformation at frequency 125 Hz) (Ddeformation at frequency 250 Hz)

(Edeformation at frequency 500 Hz) (Fdeformation at frequency 1000 Hz)


40

(Gdeformation at frequency 2000 Hz) (Hdeformation at frequency 4000 Hz)

(Ideformation at frequency 8000 Hz)

Figure (2-6) indicated deformation of plate at different frequency and pressures by using ANSYS Workbench programs


41

(Astress at frequency 31.5 Hz) (Bstress at frequency 63 Hz)

(Cstress at frequency 125 Hz) (Dstress at frequency 250 Hz)

(Estress at frequency 500 Hz) (Fstress at frequency 1000 Hz)


42

(Gstress at frequency 2000 Hz) (Hstress at frequency 4000 Hz)

(Istress at frequency 8000 Hz)

Figure (2-7) indicated stress of plate at different frequency and pressures by using ANSYS Workbench programs

Chapter 3

EXPEXPEXPEXPEEEERIMENTAL WORKRIMENTAL WORKRIMENTAL WORKRIMENTAL WORK

Chapter three: EXPERIMENTAL WORK

43

CHAPTER THREE

EXPERIMENTAL WORK 3-1 Introduction The experimental work for this study was carried out in the workshop measurement laboratory of the mechanical engineering department. This chapter deals with the experimental work and procedure that were followed to prepare plate and equipment for testing. The purpose of this chapter is to explain the necessary steps measuring the vibration and strain on the one side in the satellite structure. The work was planned and carried out in such a way to provide detailed information on effect of acoustic vibration on the satellite structure, the details of equipment, instrumentation. In order to investigate the possibility of measurement of acoustic vibration relationships between sound frequency and plate vibration, an experimental apparatus to measure plate vibrations was installed in plates as shown in figure (3-1).

Figure (3-1) Vibroacoustic testing system


44

3-2 Materials and equipment apparatus The materials and equipment were used in the experimental procedure of this

investigation are listed below:

3-2-1 The plates material The Plate types usually used in the space is Aluminum in series (2024, 7075, and 6061). In this experimental was used type of plate Aluminum (2024). to checking the type of plate, it was used two methods

Mechanical method At first putting piece of scrape plate in the electric furnace, second during (30min) it was heated to (500 oC), third step is put piece of plate into water quickly (quenching method), fourth step it put 10 hours in another electric furnace at temperature (190 oC), finally it measuring Vickers hardness number is (129) compare with Aluminum series Vickers hardness properties the result is (Al 2024-T3).

Chemical method From this test it measured carbon percent from piece of plate .finally, carbon percent is (3.83%C1, C=carbon).After compare this result with Aluminum series properties .finally plate type is (2024 T3)

Plate Properties

Aluminum (2024) plate was used for testing have dimension (25cm X 25cm) and the thickness is (1mm), and mechanical properties are

Mpayield 360= 2475, MpaUltimate = , Vickers hardness number is (129), and 3.83%C1, C=carbon)

1The chemical composition test carried out in chemical department .College of Science .university of

Salahaddin 2The test was carried out in the Mechanical Engineering .Department.(tensile test machine)


45

3-2-2 Vibrometer A Hottinger SM60 (10) type measurement device vibration as shown in figure (3-2). The tip of the vibrometer was transducer the motion on plate to signal in the device, signals such as amplitude (x) or velocity ( x& ) of a point on the plate. In this work we had taken five points in the plate to measure the displacement and velocity, the points in left side, right side, center, bottom and top as shown in figure (3-3). An apparatus have two direction for using horizontal and vertical and this direction depending in vibration direction horizontally or vertically, in this thesis process was horizontally .The measurement range displacement reading is (0.1-600m), velocity range reading is (0.01-60mm/sec) with 9V DC power.

Figure (3-2) Vibrometer device

Vibrometer

Corks Wood


46

Figure (3-3) indicate place of reading of vibration in the plate

3-2-3 Strain measuring device setup In order to determine the value of strain in plate at any sound pressure level, we

must measuring strain value in any direction of plate (horizontal and vertical) as shown in figure (3-4)

Figure (3-4) Insulation of strain measurement instrument on the plate (A: horizontal, B: vertical)

A B

E

C B A

D


47

The foil of strain gages with a gage factor of (2.030) and gage resistance of (120 ) are connected by wires with the strain indicator and switch balance unit to convert the value of strain from the resistance of the foil to the devices and then shows the value from digital gage as shown in figure (3-5) .

Figure (3-5) Digital strain indicator and switch balance unit strain measuring device

3-2-4 Determination of the modulus of elasticity of plate by using the tensile test method The tension test is the most common test for determining such mechanical properties of materials as the modulus of elasticity. Finally data from this test is

Mpayield 360=

MpaUltimate 475=

E=72 GPa


48

3-2-5 Oscillator An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. The harmonic or 'linear'

oscillator produces a sinusoidal output. The basic form of a harmonic oscillator is an electronic amplifier with the output attached to an electronic filter, and the output of the filter attached to the input of the amplifier, in a feedback loop. When the power supply to the amplifier is first switched on, the amplifier's output consists only of the noise. The noise travels around the loop, being filtered and re-amplified until it increasingly resembles the desired signal. Oscillator connected by wires with loudspeaker to obtain the sound under oscillator frequency in side and with oscilloscope to obtain shape of frequency in another side, frequency range between (0.1 ~ 100000 Hz), as shown in figure (3-6).

Figure (3-6) Electronic Oscillator

3-2-6 Oscilloscope Oscilloscopes are widely used when it is desired to observe the exact wave shape of an electrical signal. In addition to the amplitude of the signal, an oscilloscope can measure the frequency, show distortion, show the time between two events, and show the relative timing of two related signals .A typical oscilloscope has a display screen, numerous input connectors, and control knobs and buttons on the front panel.


49

To obtain very accuracy data it must calibrated the display, after choosing required frequency, the signal from oscillator to one of the input of oscilloscope. The oscilloscope displays voltage on its vertical axis and time on horizontal axis .as shown in figure (3-7).

Figure (3-7) Tektronix type Oscilloscope

3-2-7 Sound level meter A sound level meter consists of a microphone, an amplifier and means to process the waveform of the sound-pressure signal from the microphone according to the equations above. There may be an analog or a digital readout or other device to indicate the measured sound levels. Extensive analog, or digital, or a combination of analog and digital signal processing may be utilized. Storage devices may include digital memory, computers, and printers [38]. BK Precision's (model 732A) Sound Level Meters was used in the experimental as shown in Figure (3-8) It was used to measure sound pressure level it came from loudspeakers by oscillator source. The model 732A Sound Level Meter provides (30~130 dB) capability in three convenient measurement ranges Low, Medium and High. The sound level meter meets includes fast and slow time weighting.


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Figure (3-8) BK Precision's (model 732A) Sound Level Meter

3-2-8 Loudspeaker The job of a loudspeaker is to set up vibrations in the air which are acoustic representations of the waveforms of the electrical signals that are being supplied to the input terminals. A loudspeaker is therefore an electro-mechanico-acoustic transducer. Loudspeakers transform the electrical drive signals into mechanical movements which, normally via a vibrating diaphragm, couple those vibrations to the air and thus propagate acoustic waves. Once these acoustic waves are perceived by the ear, we experience a sensation of sound [39].


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To adequately reproduce a wide range of frequencies, most loudspeaker systems require more than one driver, particularly for high sound pressure level or high accuracy. Individual drivers are used to reproduce different frequency ranges. The drivers are named subwoofers (very low frequencies), woofers (low frequencies), mid-range speakers (middle frequencies), tweeters (high frequencies) and sometimes super tweeters optimized for the highest audible frequencies. When multiple drivers are used in a system, a "filter network", called a crossover, separates the incoming signal into different frequency ranges, and routes them to the appropriate driver. A loudspeaker system with n separate frequency bands is described as "n-way speakers": a 2-way system will have woofer and tweeter speakers; a 3-way system is either a combination of woofer, mid-range and tweeter or subwoofer, woofer and tweeter. The most common type of driver uses a lightweight diaphragm or cone connected to a rigid basket, or frame, via flexible suspension that constrains a coil of fine wire to move axially through a cylindrical magnetic gap. When an electrical signal is applied to the voice coil, a magnetic field is created by the electric current in the voice coil which thus becomes an electromagnet field. The coil and the driver's magnetic system interact, generating a mechanical force which causes the coil, and so the attached cone, to move back and so reproduce sound under the control of the applied electrical signal coming from the amplifier, as shown in figure (3-9) [8].


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Figure (3-9) structure of loudspeaker [8] ECHO JASCO was used in the experiments ,as shown in figure (3-10) It has high sounds when came from oscillator by required frequency, have inner amplifire and its a type AS200.

Figure (3-10) ECHO JASCO amplifiers and loudspeakers


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3-3 Experimental work The following steps are shown the experimental procedure:

Step 1:Ossilator was joined computer by wires to record sound will get from ossilator in frequency (31.5 ,63 ,125 ,250 ,500 ,1000 ,2000 ,4000 ,8000 Hz) Step 2: By computers software is Ulead video studio V11 to produced one audio file having nine sequence of different frequencies ,each frequency sound file during 5 second as shown in figure (3-11). Step 3:After checking (Aluminum 2024) type of plate by chemical and mechanical method. The plate was fexed in the wood structure by screw as shown in figure (3-1). When dimension of plate is (25mm X 25mm) and thickness is (1 mm). Step 4: Join the computer with Loudspeaker and play the general audio file to amplified this sound .control starting sound pressure level for example in 80 dB . Step 5:Sound level meter used to measuring sound pressure level. Step 6: After attach this sound wave come from Loadspeaketr on the plate ,at that time difformation will be occur. Step 7:Vibrometer used to measuring displacement and velosity of this deformation on point (A) on the figure (3-3). Step 8: Strain measuring device setup used to measing strain on the plate in horizontal direction as shown in figure (3-4) Step 9: devices indicator was very rapidly changed ,must to record the data by video camera .By Ulead video studio program we was reading data when we was record by video camera, the maximum value from any frequency were choosed , figure (3-12) shown one sample of this videos. Step 10: Repeat step 4 and chaning starting sound pressure level to (90,100, and 108 dB), repeat step 6 and changing place of displacement and velocity measurment to B,C,D,and E as shown in figure (3-3) ,and repeat step 8 and changing stain direction to vertical as shown in figure (3-4). Finally number of tests from this research will become (252) tests. This procedure is sketched and explained in detail, as in the figure (3-13)


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Figure (3-11) screen of Ulead video studio program

Figure (3-12) the reading the record data


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Figure (3-13) Experimental Procedure describes input variables and output investigation

xx &,

Input Frequency


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3-4 Experimental results There are seven groups of experimental tests and results; each group contains thirty six, as they will be explained in details in this chapter. Table (3-1) shows the acting position conditions which were chosen and tests were curried out according to these acting position conditions ,each condition repeated with starting sound level (80 or 90 or 100 or 108 dB) and for frequency (31.5 ,65 ,125 ,250 ,500

EFFECT OF ACOUSTIC VIBRATION ON THE SATELLITE STRUCTURE AT LAUNCH STAGE

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