Assign02 Vibration

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STAFFORDSHIRE UNIVERSITY

Assignment 2:

Vibration Analysis of Tower Rig

Submitted by: Mohamed Humaid Al-Badri (09032170)

Email: [email protected]

Award Title: Mechanical Engineering

Module Title: Applied Structural Integrity

Module Code: CE00449-7

Submitted to: Prof. Peter Ogrodnik

Submission Date: 21/12/2011
mailto:[email protected]:[email protected]


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Abstract

The vibration is a natural phenomenon that occurs as results of

affected force. This report is based on the lab experiment for tower

rig which consist of four floors and apply some vibration load in each

floor to determine the natural frequencies and modes of the tower.

Also, the tower is modeled in Ansys as 3D and 2D model, and

calculated the frequencies by classic theoretical. Then, we got the

results for each method and made the compression between these

results for each mode.


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Table of Contents:

Table of Contents: ......................................................................................... 3

List of Figures: ............................................................................................... 4

List of Tables: ................................................................................................. 4

1.0 Introduction: ........................................................................................... 5

2.0 Experiment of Tower Rig: ........................................................................ 5

2.1 Aim of the Experiment: ....................................................................... 5

2.2 Apparatus and Procedure: .................................................................. 6

2.3 Readings from Experiment: ................................................................. 8

3.0 Theoretical of the experiment: ............................................................... 9

3.0 Ansys Analysis: ...................................................................................... 11

3.1 3D Ansys Analysis: ............................................................................. 11

3.2 (Line Body) 2D Ansys Analysis: .......................................................... 13

4.0 Results and Conclusions: ....................................................................... 16

5.0 References: ............................................................................................ 19

6.0 Appendix A: ........................................................................................... 20


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List of Figures:

Figure 1 Tower rig model .............................................................................. 7

Figure 2 Bodies masses for tower rig [2] ..................................................... 10

Figure 3 3D Ansys model boundary conditions ........................................... 12

Figure 4 Different modes of 3D model ........................................................ 13

Figure 5 Line Body model boundary conditions .......................................... 14

Figure 6 Mesh refinements for line body .................................................... 15

Figure 7 Different modes of line body ........................................................ 16Figure 8 Compression results for tower rig ................................................. 17

List of Tables:Table 1 Experiment readings ......................................................................... 8

Table 2 Frequencies for Theoretical calculations ........................................ 11


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1.0 Introduction:

The vibrations of the floors have become a significant design

consideration for engineers in order to avoid any failure in their

structural design. The study of vibrations for a cretin constructionneeds a lot of information to be considered in the analysis. At the

same time, the analysis should be more accuracy or otherwise the

construction will be failed. The use of accurate predictive model is

sensitive laboratory and manufacturing equipment in these

structures [1]. For prediction of the vibrations the FEA is an

impractical technique as it is too computationally intensive for most

full scale structures [1].

In this experiment we will analysis and simulate the harmonic

response of a structure known a tower rig under the impression of

load. The harmonic response can be defined as the steady state

response of the system to the application of load. We will obtain the

graphical representation of the response of the system, which is

basically amplitude for deformations and accelerations for various

frequencies. The peak of frequencies gives us an indication of the

sustainability of our design against fatigue [2].

2.0 Experiment of Tower Rig:

2.1 Aim of the Experiment:

The aim of the experiment is to study, understand, analysis and

measure the vibration models for a four story tower rig by using the

spectral analyzer. The vibration analysis needs to understand mode


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shapes for lightweight construction and reduce oscillation in flexible

structures [1].

2.2 Apparatus and Procedure:

The main components of the experiment are tower rig,

accelerometer, oscilloscope, transducer and electrical motor. The

tower rig consists of four floors, each side welded to two structural

steels as shows in Figure 1. Each floor represented here by steel

plate, we will call them plate 1, 2, 3, and 4. Also, there is two

accelerometer attached on the base of the rig (plate 1) and the other

is moved from one plate to another to record the frequency

response. The oscilloscope is an electric device that allows signal to

be viewed and used to measure the amplitude of the signal wave

shape and frequency of the system. The electric motor is used to

apply a load on the floor one (plate 1) and allow the tower to vibrate

in order to take the readings for some intervals of frequency. There

are some assumptions for the experiment:

The system consider is equilibrium, The friction and the damping of the system are

negligible,

The stiffness of the spring to be same as structuralsteel, and

The system moves in one direction only (1 axis).


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Figure 1 Tower rig model

The experiment starts by switch on the electric motor which

produces a reciprocating motion force to the plate 1, and fixing the

accelerometer in the same plate in order to decide the suitable

frequency for the first mode which is no vibration on the plate 1.

Then, repeat the same method but this time moving the

accelerometer from one plate to another to decide the suitable

frequency for each floor (plate), and take the readings for

frequencies and amplitudes from oscilloscope.

The tower rig dimensions:

Height = 700 mm Width = 150 mm Length = 200 mm Dimension of the plate = (200 150 25) mm Dimension of the 4 steel rods = (700 12 3.2) mm Center to center between plates = 225 mm


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2.3 Readings from Experiment:

The readings are decided to be taken at frequencies/ modes 5, 8, 12

and 25 Hz because at these values the vibration of one plate is

almost zero while the other plate vibrate. The readings taken from

the experiment at for all plates are as shown in Table 1.

Table 1 Experiment readings

Frequency Plate 1 Plate 2 Plate 3 Plate 4

CH1

(V)

CH 2

(V)

CH1

(V)

CH 2

(V)

CH1

(V)

CH 2

(V)

CH1

(V)

CH 2

(V)

2.030 5.200 0.240 5.200 0.232 5.200 0.204 5.200 0.220

3.010 5.200 0.432 5.040 0.416 4.800 0.560 4.320 0.400

4.000 1.320 0.148 1.360 0.188 1.240 0.256 1.320 0.264

5.010 1.280 0.084 1.360 0.160 1.440 0.196 1.400 0.276

5.520 1.000 0.148 1.080 0.180 0.960 0.248 1.000 0.316

6.000 1.000 0.184 0.960 0.136 1.040 0.296 1.000 0.312

7.000 0.760 0.256 0.760 0.104 0.700 0.344 0.860 0.392

7.590 0.780 0.384 0.640 0.960 0.640 0.312 0.700 0.464

8.030 1.000 0.640 1.000 0.300 1.040 0.440 1.080 0.680

9.000 3.520 1.600 3.440 0.760 3.520 0.640 3.600 1.280

10.020 2.080 1.600 2.440 0.920 2.360 0.440 2.200 1.320

11.040 1.360 1.000 1.600 0.800 1.680 0.200 1.580 0.920

11.470 1.360 0.860 1.460 0.700 1.440 0.100 1.420 0.740

12.010 1.180 0.580 1.220 0.700 1.360 0.060 1.440 0.640

13.020 0.900 0.460 0.900 0.780 1.160 0.180 1.000 0.700

14.000 1.080 0.240 1.020 0.940 1.060 0.320 1.080 0.74015.010 0.940 0.200 0.900 0.960 0.940 0.500 1.040 0.780

16.020 1.020 1.840 0.940 2.440 0.960 1.760 0.860 2.120

17.060 2.560 2.040 2.240 1.400 2.400 1.640 2.400 1.520

18.080 2.320 1.240 2.360 0.480 2.280 1.000 2.200 0.760

19.040 2.120 1.000 2.160 0.080 2.120 1.000 2.080 0.640

20.010 2.080 0.760 2.200 0.480 2.040 1.200 1.880 0.640

21.000 1.640 0.340 1.720 1.640 1.520 2.400 1.520 1.080

22.300 1.520 1.320 1.640 1.440 1.640 1.160 1.560 0.520

23.000 1.480 1.120 1.520 0.840 1.480 0.600 1.560 0.280

24.200 1.400 0.980 1.360 0.540 1.400 0.288 1.400 0.120

25.000 1.480 0.960 1.320 0.448 1.360 0.216 1.400 0.080

25.500 1.360 0.940 1.280 0.400 1.320 0.176 1.400 0.064


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3.0 Theoretical of the experiment:

The vibration models equations of this experiment are derived based

on Newtons second law where:

(1)

And

(2)

Where a is acceleration and kx is based on Hookes law, based on

Hartogs work [2]. The frequencyfcan be expressed as:

(3)

Where Tis the time and defined as:

(4)

So, the frequencyfcan be defined as:

(5)

The velocity and acceleration of motion according to circular

frequency are defined as:

(6)

And acceleration


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(7)

The tower rig model can be divided into 4 bodies mass as shown in

Figure 2, affected by force F, and the total value of this force can be

defined as:

Figure 2 Bodies masses for tower rig [2]

(8)

(9)

By repeating for the other 3 mass bodies, so we will have 4

equations which they can be solved in matrix form to get the

unknown values. The mass of the floor (plate) can be determined by:

(10)


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Since the density of the steel is 7850 kg/m3

and using the dimensions

of the plate, so the mass of each plate can be calculated. Also, the

moment of inertia and stiffness coefficient can be defined as:

(11)

(12)

Where Eis the Youngs Modulus and equal 2 1011

Pa.

By using the matrix equations, the natural frequencies can be

calculated for the tower rig, and it is found as shown in Table 2.

Table 2 Frequencies for Theoretical calculations

Sr. No W2

F (HZ)

1 503.827 3.57

2 4247.133 10.37

3 9982.175 15.90

4 15025.482 19.50

3.0 Ansys Analysis:

3.1 3D Ansys Analysis:We designed the tower rig as 3D model in Ansys using the same

dimensions (700 200 150) mm and then we applied the boundary

conditions. The force is applied in the bottom plate in the longitude

direction as shown in Figure 3. Also, the displacement is applied in


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the bottom surface of the same plate. The harmonic responses for

both deformations and accelerations are taken in order to compare

with the experimental and theoretical results. Some of these

harmonic responses are shown in Appendix A.

(a) Applied Force (b) Displacement

Figure 3 3D Ansys model boundary conditions

The calculations done by Ansys are at 4 different modes of

frequency. The modes for 3D model are 5, 8, 12 and 25 HZ and they

are shown in Figure 4.


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(a) 1st

Mode (b) 2nd Mode

(c) 3rd

Mode (d) 4th Mode

Figure 4 Different modes of 3D model

3.2 (Line Body) 2D Ansys Analysis:

We designed the tower rig as 2D model in Ansys and then we applied

the boundary conditions. The force is applied in the bottom plate in

the longitude direction as shown in Figure 5. Also, the displacement

is applied in the bottom surface of the same plate.


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Figure 5 Line Body model boundary conditions

Since the mesh refinement plays a critical role in the calculations and

accuracy of the model, we refine the default mesh for 2D line body

model at sizes 15mm, 10mm and 5mm as shown in Figure 6.


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(a) Default mesh (b) 15mm mesh

(c) 10mm mesh (d) 5mm mesh

Figure 6 Mesh refinements for line body

Then, after some trails of calculations, we found that the suitable

size for the mesh for 2D model is 10mm, which can gives optimum

results. The calculations done by Ansys are at 4 different modes of

frequency. The modes are 5, 8, 12 and 25 HZ and they are shown in

Figure 7.


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(a) 1st

Mode (b) 2nd Mode

(c) 3rd

Mode (d) 4th Mode

Figure 7 Different modes of line body

4.0 Results and Conclusions:

From the above analysis, we plotted the experiment, 3D Ansys and

2D line body for the four plates as shown in Figure 8.


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(a) First Plate(b) Second Plate

(c) Third Plate (d) Fourth Plate

Figure 8 Compression results for tower rig

According to the compression results, the experimental values for

the first and second plates matches the results obtained from Ansys

for 3D and line body. Also, the 3D and line body results are very close

to each other. For the third plate, the experimental values still close

to the line body results, but the values of 3D are little bit far from


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experimental results and 2D Ansys analysis. For the fourth plate, also

the results of experiment and 2D are close but 3D is not matching.

It is observed that, there are some difference in the results between

the experimental and Ansys 3D and 2D, and this is due to the human

error and accuracy of the modeling in Ansys. Also, the mesh

refinement affects the accuracy of the results. In addition, the

experiment values obtained are based on circumstances of set up,

level of noise and understanding of steps.


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5.0 References:

[1] S. G. Kelly, Fundamental of Mechanical Vibrations, McGraw Hill,

New York (2000).

[2] W. T. Thomson, Theory of Vibration with Application (4th ed.),

Nelson Thornes Ltd. Cheltenham (2003).

[3] C. T. F. Ross, Advanced applied stress analysis, Ellis Horwood

Limited, New York (1987).


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6.0 Appendix A:

Harmonic Responses for 3D Ansys Model:

Figure A1.1: 3D Model Ground Floor

Figure A1.2: 3D Model First Floor


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Figure A1.3: 3D Model Second Floor

Figure A1.4: 3D Model Third Floor

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