Viscothermoelastic vibrations in micro-scale beam resonators with linearly varying thickness

Abstract

In this paper the closed form expressions for the transverse vibrations of a homogenous, isotropic, thermally conducting, Kelvin–Voigt type viscothermoelastic thin beam with variable thickness, based on Euler–Bernoulli theory have been derived. The effects of relaxation times, thermomechanical coupling, surface conditions, and beam dimensions on energy dissipation induced by thermoelastic damping in microelectromechanical systems resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in the case of silicon nitride have also been presented. The computer simulated results with respect to the damping factor and frequency shift have been presented graphically.