Equivalent network representation for thickness vibration modes in piezoelectric plates with an exponentially graded parameter

Equivalent network representation is derived for thickness vibration modes in piezoelectric plates having an exponentially graded parameter. The network is composed of a transmission line of length corresponding to the plate thickness and an electrical port with two capacitors which is linked to the line at both its ends via two ideal transformers. The ratios of the two transformers are different from each other and frequency dependent. The two capacitors are also frequency dependent and have the same value but opposite sign. The frequency characteristic of the input electric admittance of the resonator, which shows the unique feature of the functionally graded piezoelectric plate, is demonstrated by equivalent network analysis.