Thermoelastic damping in circular microplate resonators based on fractional dual-phase-lag model and couple stress theory.

• The size-dependent thermoelastic damping of a circular microplate is determined. • Fractional dual-phase-lag (DPL) incorporating the couple stress theory is put forward. • An analytical expression for thermoelastic damping of a circular microplate is given. • Effects of the fractional order, relaxation time, and characteristic length on the inverse quality factor are analyzed. 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. [ABSTRACT FROM AUTHOR]