The nonlinear analysis of elastic wave of piezoelectric crystal plate with perturbation method

•We analyze the piezoelectric solid nonlinear effect using Tiersten and Sinha’s perturbation theory.•We study the elastic constants influences on the frequency of the anti-symmetric thickness vibration plate.•We obtain the A–F relation caused by nonlinear stress and strain.•We calculate the amplitude–frequency relationship with the cut angle of quartz numerically.

When investigating or designing acoustic wave sensors, the behavior of piezoelectric devices is supposed to be linear. However, if the sensors are subjected to a strong elastic field, the amplitude of the elastic strain induced in the piezoelectric material is so large that the nonlinearity, which affects the stability and performance of the piezoelectric sensors, can no longer be ignored. In this paper, we perform a theoretical analysis on nonlinear anti-symmetric thickness vibration of thin-film acoustic wave resonators made from quartz. Using Green’s identity, under the usual approximation of neglecting higher time harmonics, a perturbation analysis is performed from which the resonator frequency–amplitude (A–F) relation is obtained. Numerical calculations are made. Furthermore, the validity of the method is examined.