36 CHAPTER 4 PIEZOELECTRIC MATERIAL BASED VIBRATION CONTROL 4.1 INTRODUCTION This chapter focuses on the development of smart structure using piezoelectric patches in order to control the vibration actively. More advanced technology and materials in industry lead to the implementation of lightweight components for miniaturization and efficiency. Lightweight components and certain materials, however, are susceptible to vibrations. (Autur KK 1997) The flexible structures that make up these systems pose a great problem to vibration control. Flexible structures are extensively used in many space applications, for example, space-based radar antennae, space robotic systems, and space station, etc. The flexibility of these space structures results in problems of structural vibration and shape deformation, etc. Active control methods have to be developed to suppress structural vibration and improve the performance of these flexible structures. In this current study, the main focus is to analyze the effect of Lead Zirconium and Titanate (PZT) in vibration control over GFRP composite and aluminium structures. Also, the position of PZT along with the length of the structure is studied with various input voltage and control gains. The settling time of the structures with the above parameters has also been studied. 4.2 PIEZOELECTRIC MATERIAL Piezoelectric materials are active materials generally with high bandwidths. The two properties that piezoelectric materials have are the direct effect
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36
CHAPTER 4
PIEZOELECTRIC MATERIAL BASED VIBRATION
CONTROL 4.1 INTRODUCTION
This chapter focuses on the development of smart structure using
piezoelectric patches in order to control the vibration actively. More advanced
technology and materials in industry lead to the implementation of lightweight
components for miniaturization and efficiency. Lightweight components and
certain materials, however, are susceptible to vibrations. (Autur KK 1997) The
flexible structures that make up these systems pose a great problem to vibration
control. Flexible structures are extensively used in many space applications, for
example, space-based radar antennae, space robotic systems, and space station,
etc. The flexibility of these space structures results in problems of structural
vibration and shape deformation, etc. Active control methods have to be
developed to suppress structural vibration and improve the performance of
these flexible structures.
In this current study, the main focus is to analyze the effect of Lead
Zirconium and Titanate (PZT) in vibration control over GFRP composite and
aluminium structures. Also, the position of PZT along with the length of the
structure is studied with various input voltage and control gains. The settling time
of the structures with the above parameters has also been studied.
4.2 PIEZOELECTRIC MATERIAL
Piezoelectric materials are active materials generally with high
bandwidths. The two properties that piezoelectric materials have are the direct effect
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and the converse effect. The direct effect of a piezoelectric material is an electric
polarization that occurs as the material is stressed by producing an electrical charge
at the surface of the material. The converse piezoelectric effect results in a strain in
the material when placed within an electric field. These properties make
piezoelectric materials the most popular smart materials. Lead Zirconium Titanate
(PZT) and Polyvinylidene Fluoride (PVDF) are two piezoelectric materials that are
most widely used in actuation and sensing. Differences in the composition of these
materials allow them to be used as actuators and sensors, respectively. PZT is
roughly 4 times as denser, 40 times stiffer and has a relative permittivity of 100
times greater as that of PVDF. The rigidity of PZT makes this material a perfect
candidate for actuators and, on the other hand, the flexibility and extreme sensitivity
of PVDF makes it a perfect candidate for sensing. In this current study, PZT has
been used for vibration control of cantilever structures. The specifications of PZT
are presented in Table 4.1.
Table 4.1 Specification of PZT patch
Length (mm) 76.2 Width (mm) 25.4 Thickness (mm) 2
modulus (GPa) 63 Density (kg/m3) 7500
0.28 Damping constants
Max. Input voltage (V) 270
4.3 MODELING OF THE STRUCTURE
In this study, the GFRP composite of (0°/0°/0°)s ply orientation and
aluminium cantilever beams have been taken for analysis of vibration control.
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The size of the beam is 500 mm x 50 mm x 2mm. The properties of the beams are
shown in Table 4.2.
Table 4.2 Properties of aluminium and GFRP
Property Aluminium GFRP Density (kg/m3) 2700 1800
Pa) 70 38.6 0.32 0.28
Figure 4.1 shows the cantilever beam modelled using ANSYS. The PZT
patches have been placed at various positions along the length of the beam such as
50 mm, 250 mm and 450 mm from the fixed end. The influences of these positions
over the settling time of the beams have been studied.
(a) 50 mm from the fixed end
(b) 250 mm from the fixed end
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(c) 450 mm from the fixed end
Figure 4.1 Position of PZT from the fixed end of the beam
The typical finite element used in the modeling and analysis of
piezoelectric crystal was (SOLID5), which has piezoelectric capacity in three
dimensional couple field problem. Like other structural solid elements, this
element has three displacement degrees of freedom per node. In addition to this
degree of freedom, the element has also potential degree for analysing of the
anisotropic and yield three-dimensional spatial vibration in their response to the
piezoelectric actuation.
The models developed for the passive portion includes consistent
degree of freedom at the location where these elements interface.
For modeling the passive portion of the smart structure solid element used is
(SOLID45). The passive portion is made of aluminum and GFRP.
4.4 MODAL ANALYSIS AND DEVELOPMENT OF CONTROL
LAWS
Modal analysis was performed on both the aluminium and GFRP beam
to find out the natural frequency of the structure. The analysis was furthur carried
out for both passive and active structures. Table 4.3 presents the first four natural
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frequencies of aluminium and composite beams or structures. From this table, it
can be inferred that the addition of PZT patch increases both the mass and stiffness
of the system. But the increase was not proportional, causing the natural frequency
to increase. If they had proportionally increased, the natural frequency would have
remained constant. The natural frequency of the beams can be validated
analytically by using the Equation 4.1(Rao SS 2002).
Table 4.3 Natural frequencies of aluminium and GFRP beams
Modes
Natural frequency of aluminium (Hz)
Natural frequency of GFRP (Hz)
Passive Beam
Active Beam
Passive Beam
Active Beam
First Mode 6.65 6.63 5.982 5.76
Second Mode 41.18 41.12 37.456 36.09
Third Mode 115.5 114.4 112.56 111.3
Fourth Mode 226.28 225.2 225.4 224.64
, f = (4.1)
The harmonic response analysis was used to determine the steady
response of the linear structure under the harmonic loads. Under normal
circumstances, the PZT patches were actuated by a sine-wave power from the
power supply. This kind of PZT-structure coupled analysis accorded with the
conditions of the harmonic response analysis. Figure 4.2 shows the response of
harmonic analysis of the aluminium and composite beams. It can be noticed that
the peak occurs in the frequencies corresponding to the frequencies found by using
modal analysis.
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(a) Aluminium beam
(b) GFRP beam
Figure 4.2 Harmonic response of cantilever beam
From these figures, it can be inferred that only the vibration modes
corresponding to first, second and fourth modes have been obtained. This is due to
the fact that they correspond to the bending loads, since bending load is only
applied. Vibration modes corresponding to the third and fifth natural
frequencies would rise while applying the torsion loads. Only, when bending
loads are applied, their corresponding natural frequencies are validated.
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Closed loop simulation for active vibration control in smart structure
has been performed by using ANSYS. Control actions have been incorporated into
the finite element model by using APDL (ANSYS Parametric Design Language)
codes. Ks, Kc and Kv are the sensor, control and power amplification factors,
respectively. Ks and Kv are taken as 100 and Kc is changed in the analyses by
selecting the values starting from 10 with the step increase of 10. Only the
proportional control has been applied. The multiplication of Ks, Kc and Kv is the
proportional constant for the actuator voltage Va. Therefore, changing the values of
Ks, Kc and Kv and keeping the same multiplication do not seem to affect the results. In this control system, the controller used is that of a proportional
controller with a displacement feedback. The strain rate feedback control has also
been used for vibration control. From the literatures reviewed, displacement
feedback seems to enable better controlling action with higher actuation voltages
when compared to strain rate feedback. Modal analysis have been performed to find the undamped natural
as 1/(20fh), where fh is the highest frequency. In the transient analysis, the
0.0001
which taken in this study. The displacement has been calculated at the tip of the
beam and it is multiplied by Ks and then subtracted by zero. The zero value is the
reference input value. The difference between the input reference and the sensor
signal is called the error signal. The error value is multiplied by Kc and Kv to
determine Va at a time step. The part of the macro which enables the calculations for the closed loop