Thermoelastic damping in the size-dependent micro/nanobeam resonator with nonlocal dual-phase-lag heat conduction

Abstract

Precisely calculating quality factor based on thermoelastic damping (TED) is of great importance for the design and optimization of micro/nano-resonators. With the consideration of size-dependent effects in the thermal and mechanical fields and the non-Fourier (NF) heat conduction effect, analytical expressions of TED in the micro/nanobeam resonator are proposed by adopting the theories of the modified-couple-stress (MCS) model and the nonlocal dual-phase-lag (DPL) model. TED models expressed in the series form and the explicit form are both developed basing on the energy-definition approach. The differences among TED models are discussed. In the simulation, silicon and gold, which are two representative materials with typical intrinsic length-scale quantities and phase-lag times, are selected for illustration. Additionally, the nonlocal thermal length-scale parameter refers to the mean-free-path (MFP) of energy carriers, and the MCS mechanical length-scale parameter is not constant but proportional to the beam thickness. TED results obtained by the classical model and the previous DPL model are also shown for comparison. The peak phenomena of TED spectra including the peak damping and the peak frequency are investigated according to the present simple model. Results reveal that TED in micro/nanobeam resonators is of dependence observably on the effect of nonlocal DPL-NF heat conduction associated with the thermal field, and the quality factor is improved by the MCS mechanical size-dependent effect.