Abstract
In the present work, thermoelastic damping in a micro-resonator operating in vacuum as a vibrating size-dependent circular thin plate is studied. To better describe the heat conduction process, a generalized thermoelasticity theory of fractional dual-phase-lag (DPL) incorporating the couple stress theory is put forward to capture the experimentally observed small-scale effect of thermoelastic dissipation. The complex frequency of the micro-plate is obtained through Laplace transform technique. Finally, Lifshitz and Roukes’s complex frequency method is employed to derive an analytical expression for thermoelastic damping. The influences of the parameters including fractional order, phase-lag time, and internal characteristic length on the inverse quality factor Q−1 are analyzed. The obtained results show that the influences of these parameters on thermoelastic damping are pronounced. These results are helpful to the design of micro-/nano-resonators with high-performance.
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