Thermoelastic damping in anisotropic piezoelectric microbeam resonators

Abstract

In this paper, an analytical model for thermoelastic damping in an anisotropic piezoelectric microbeam is investigated based on the thermal energy approach. The charge in the microbeam is distributed along the width and thickness directions, while the thermal conduction is along the width and length directions. The maximum elastic strain energy stored in the piezoelectric beam has an additional component that refers to the electric field due to the piezoelectric effect. The analytical model is a function of the piezoelectric constants of the quartz. The results obtained by the proposed model agree well with the experimental data reported in previous works. In addition, the proposed model can reduce to the model for isotropic non-piezoelectric microbeams. The convergence rate of the proposed model in the width direction is faster than that in the length direction. The width and length of the beam have a significant effect on thermoelastic damping. Moreover, the critical width and length with maximum damping can be calculated by the normalized dimension, and the convergence rate of the proposed model is also dependent on the value of the normalized dimension. The increment of excitation voltage will lead to the increment of the displacement and fluctuating temperature. The fluctuating temperature due to the vibration is much smaller than the equilibrium temperature.