Impedance Analysis of Piezoelectric Film with Periodic Electrodes
Date Issued
2009
Date
2009
Author(s)
Tseng, Yi-I-Che
Abstract
This thesis bring up with a matrix-structured theorem to solve the wave propagation problem in piezoelectric material with periodic electrode distribution which combines plane wave expansion method and Stroh formalism. Starting with piezoelectric constitutive equation, governing equation can be derived from Newton’s motion equation and Gauss’s law. Then presuming that displacement and electrical potential are periodic function with the concept of Floquet theory. An eigen-value problem is obtained after substituting the assumed field into governing equation. Summing all eigen-vector of corresponding eigen-value with different coefficient to be determined to fulfill the general solution in the piezoelectric domain. The boundary condition of the electrode patch is represented by first order approximation of the electrode thickness. The dispersion relation of both open and short circuit is presented. The relation between impedance and frequency is also discussed. On the numerical, this thesis introduces a non-dimensionlize to the detail. And a quick approach to the dispersion relation using a method to continualize the dispersion function is introduced. Besides, this thesis differentiate the wave-propagate property of different situation with slowness and eigen-value.
Subjects
Floquet theory
plane wave expansion method
Stroh formalism
dispersion relation
impedance analysis
slowness relation
Type
thesis
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