Analysis of linear free and forced vibrations of microbeams with thermoelastic damping

Abstract

Thermoelastic damping is a crucial mechanism of energy dissipation in microbeams and has been widely considered by microelectromechanical systems (MEMSs) researchers. However, more research is required on the connections between microbeam parameters and thermoelastic vibrations. In this paper, we investigate the effects of the coefficient of thermal expansion (CTE) and the thermal conductivity (TC) on the microbeam's linear free and forced vibrations through the partial differential equations (PDEs), which include a scale-dependent microbeam model and the Fourier transport equation. First, the ordinary differential equations (ODEs) are obtained by applying the Galerkin method to the PDEs at the first-order bending and heat transport modes. Then, the precise analytical solutions of the ODEs are obtained to illustrate the relationships of the bending and temperature vibrations. The solutions reveal three significant results: (1) The mechanical energy dissipation in free vibrations increases with the increment of the CTE and the TC; (2) The CTE's augmentation decreases amplitudes of the bending vibrations but increases the amplitudes of temperature vibrations under forced vibrations. (3) The amplitudes of bending and temperature vibrations decrease with the TC's increment; simultaneously, the TC does not change the load's frequency corresponding to the most vibration amplitude under the forced vibrations.