A non-Fourier and couple stress-based model for thermoelastic dissipation in circular microplates according to complex frequency approach

Abstract

This research tries to render an unconventional model for thermoelastic dissipation or thermoelastic damping (TED) in circular microplates by accommodating small-scale effect into both structure and heat transfer fields. To accomplish this purpose, the modified couple stress theory (MCST) and Guyer−Krumhansl (GK) heat conduction model are utilized for providing the coupled thermoelastic equations of motion and heat conduction. The equation of heat conduction is then solved to acquire the closed-form of temperature profile in the circular microplate. By placing the extracted temperature profile in the equation of motion, the size-dependent frequency equation influenced by thermoelastic coupling is established. By conducting some mathematical manipulations, the real and imaginary parts of damped frequency are obtained. In the next stage, with the help of the description of TED based upon the complex frequency (CF) approach, an explicit single-term relation consisting of structural and thermal scale parameters is derived for making a size-dependent estimation of TED value in circular microplates. For evaluating the precision and veracity of the proposed model, the results obtained through the presented solution are compared with the ones available from the literature. In addition, by way of several examples, the pivotal role of length scale parameter of MCST and thermal nonlocal parameter of GK model in the magnitude of TED is assessed. Various numerical results are also given to place emphasis on the impact of some parameters such as boundary conditions, geometrical features, material and ambient temperature on TED value. The formulation and results provided in this study can be used as a benchmark for optimal design of microelectromechanical systems (MEMS).