Thermoelastic damping in moderately thick microplate resonators based on the fractional heat conduction model

Thermoelastic damping is a fundamental mechanism for intrinsic energy loss in resonators operating at room temperature. Accurate prediction of thermoelastic damping is of paramount importance for the design and manufacture of high-performance micro-resonators. In this study, thermoelastic dissipation in relatively thick micro-plate resonators is investigated. A new first-order shear deformation plate theory, or the simplified Mindlin plate theory (SMPT), and fractional-order Fourier heat conduction are utilized to establish an analytical model for thermoelastic micro-plates. By employing the complex frequency approach (CFA) and energy ratio approach (ERA), an analytical expression for the inverse quality factor $Q^{-1}$ of rectangular micro-plates is derived. To validate the present model, the numerical results for fully clamped thin plates and SMPT are compared, and those for fully simply supported thick plates using CFA and ERA are also compared. Emphasis is focused on analyzing the effects of shear deformation and rotary inertia of the section, subdiffusion, normal diffusion, and superdiffusion on thermoelastic damping in moderately thick micro-plate resonators. The effect of geometry, vibration modes, boundary constraints, and ambient temperatures on thermoelastic dissipation is also discussed. The numerical results indicate that shear deformation should be considered while the rotary inertia may be neglected in the analysis of thermoelastic damping in vibrating relatively thick plates for the fundamental mode.