Nonlocal dual-phase-lagging thermoelastic damping in rectangular and circular micro/nanoplate resonators

摘要

Accurately estimating thermoelastic damping (TED) is of significance for the design of micro/nano-resonators with high quality factor. This work aims at providing new investigation of TED with considering the non-Fourier heat conduction (NFHC) effect and the size-dependent effects in the thermal and mechanical fields. Analytical models of TED in rectangular and circular micro/nanoplate resonators are firstly developed in the theoretical frameworks of nonlocal dual-phase-lagging (DPL) model and the modified couple stress (MCS) model. The governing equation of coupled thermoelasticity is modeled by adopting the nonlocal DPL theory, and the solution of dilatation temperature is solved by utilizing the trial-function method. The energy-definition approach is used to obtain TED expressions, in which the maximum stored energy includes the classical elastic potential energy and the MCS potential energy. Two representative materials involving the semiconductor silicon and the metal gold with typical thermal and mechanical length parameters and DPL times are selected in simulation. The influences of material intrinsic parameters on TED spectra, which include the DPL times, the MCS length parameter, and the nonlocal thermal length parameter referring to the mean free path, are investigated. TED spectra obtained by the classical models are also plotted for comparison. The results indicate that TED in micro/nanoplate resonators depends significantly on the DPL-NFHC effect and the nonlocal thermal size-dependent effect. Moreover, TED can be reduced by the MCS size-dependent effect resulting in improving the quality factor.