Thermoelastic damping analysis of size-dependent piezoelectric nano-beam resonators under driving voltage
摘要
Thermoelastic damping (TED) has been studied for years for the purpose of designing high performance resonators. In this paper, a TED model for size-dependent piezoelectric resonators is established based on the surface elastic theory and the dual-phase-lag heat conduction model (DPL model) to evaluate the influence of both mechanical and thermal small scale effects on TED. Due to the existence of surface effect and piezoelectric effect, the energy dissipation caused by the irreversible heat flow during heat transfer and the maximum elastic energy stored in the piezoelectric resonators have an additional component, which refers to the surface stress and surface electric displacement. Analytical solution of the TED model is derived by thermal energy approach. The TED model is theoretically verified. The numerical validation is presented. A critical thickness is proposed to distinguish the influence region of small scale effect. Rapid reduction of TED under overload driving voltage is observed. The influence of other key factors such as surface effect, material constants, and phase-lags of heat flux and temperature gradient on TED is analyzed in detail. This paper provides a new theoretical approach to evaluate TED of size-dependent piezoelectric micro/nano-resonators.