Thermoelastic damping analysis of size-dependent nano-resonators considering dual-phase-lag heat conduction model and surface effect

摘要

Thermoelastic damping (TED) is one of the main energy dissipation sources of high performance resonators at room temperature, however, the classical TED model fails at the nano-scale due to the influence of small scale effect. In this paper, a novel TED model is proposed to estimate the impact of both mechanical and thermal small scale effects on TED of nano-resonators. The surface elastic theory and the dual-phase-lag heat conduction model (DPL model) are first combined to establish the TED model. Analytical expression of the TED model is derived, which can reduce to the classical TED model. In numerical simulations, a critical thickness is proposed to identify the influence of small scale effect on TED. Small scale effect significantly improves TED of resonators within the critical thickness, which however can be neglected as the resonator thickness is greater than the critical thickness. Moreover, surface effect has stronger effect than non-Fourier heat conduction on improving TED of nano-resonators. Additionally, influences of the other key factors on TED are examined in detail. This paper provides a more reasonable theoretical approach to estimate TED in the design of high performance nano-resonators.