Thermoelastic damping analysis model of transversely isotropic micro/nano-resonators based on dual-phase-lag heat conduction model and surface effect

Thermoelastic damping (TED) is one of the key factors for lowering the quality factor (Q-factor) of micro/nano-resonators. However, due to a complex small-scale effect and governing equations of non-homogeneous isotropic materials, the existing TED models usually focus on homogeneous isotropic micro/nano-resonators. In this paper, a closed-form TED model is derived to estimate the influence of the small-scale effect on TED of transversely isotropic micro/nano-resonators. The surface effect and the dual-phase-lag model are included to distinguish the influence of mechanical and thermal small-scale effects on TED, respectively. The obtained TED model is theoretically verified. The results indicate that TED values are underestimated if the classical TED model is employed. Moreover, a critical thickness can be determined by the frequency shift curve is proposed. The small-scale effect results in higher TED values within the critical thickness. However, since the small-scale effect has a weak influence on TED, it can be neglected when the resonator thickness is higher than the critical thickness. Additionally, the surface effect plays a dominant role in improving the TED of nano-resonators. In this paper, a more reasonable theoretical approach for estimating TED in transversely isotropic micro/nano-resonators is provided.