Theoretical Analysis and Experimental Measurement of ut-Plane Vibration and Characteristics for Piezoelectric Rectangular Plate
Date Issued
2009
Date
2009
Author(s)
Wu, Yi-Zhuang
Abstract
In this thesis first we will analyze the response frequencies and mode shapes of isotropic thin plate for out-plate displacement and then we could use the method to find out the dynamic characteristics of piezoelectric rectangular plate. So we use the equilibrium of mechanics to derive the governing equation of isotropic plate and mechanical conditions. The analytical solutions for out-plane displacement field with boundary conditions and response frequencies are obtained by superposition method. In this thesis the issues we consider the are completely free plate and cantilever plate. The analytical solution are compared with two methods to confirm the validity. One is the numerical computation from the finite element method (FEM), another is amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI) technique. Next we use the variation method to obtain the constitutive equations of piezoelectric plate. To find out the governing equation and the formulas of mechanics and electricity, Hamilton’s principle is the method we usually use. Then we could find out the governing equation and function of mechanics and electricity. The PZT plate is the transverse isotropic material, so it can be equivalent to isotropic plate. Then we could use the solution of isotropic plate to solve the out-plate displacement field and response frequencies for PZT plate. After getting the out-plane displacement field formula, we could obtain the mechanical and electric equations and comparing the result by FEM method, AF-ESPI and laser Doppler vibrometer (LDV) to confirm the validity. Finally we use the Maxwell equation to find out the equivalent magnetic flux, and observe the magnetic quantity distribution. In this thesis, we not only discuss the response frequencies and out-plane displacement, but use the relationship between mechanics and electricity to obtain the tendency of modal excitation. Then we could get more information of the relation between mechanical and electric coupling.
Subjects
sotropic rectangular plate
superposition method
piezoelectric rectangular plate
variation method
Hamilton’s principle
finite element method
response frequencies
AF-ESPI
LDV
Type
thesis
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