Thermoelastic damping in rectangular micro/nanoplate resonators by considering three-dimensional heat conduction and modified couple stress theory

Thermoelastic damping (TED) has been confirmed as an intrinsic energy loss and determines the upper limit of the quality factor of micro/nanoelectromechanical system (M/NEMS) resonators. A framework for determining the TED in the full clamped (C-C-C-C), clamped-free-clamped-free (C-F-C-F), and cantilever (C-F-F-F) rectangular microplate resonators operating in the fundamental mode by considering three-dimensional heat conduction in conjunction with modified couple stress theory (MCST) is proposed in this article. Then by using Rayleigh's method, three analytical models expressed by Fourier series for TED are derived, respectively. The difference between the present TED model and the previous one-dimensional (1-D) MCST model and 3-D classical model are comprehensively investigated. The comparison results indicate that the size effect on TED decreases to be ignorable as the thickness increases to h/l >= 50. In the case of h/l <= 50, the size effect cannot be ignored. The corresponding critical thicknesses for TED peaks are independent of the size effect. TED behaviors vary significantly under different structural support types.