Effect of thermoelastic damping in nonlinear beam model of MEMS resonators by differential quadrature method

Abstract

This paper presents a nonlinear model of a clamped-clamped microbeam actuated by an electrostatic load with stretching and thermoelastic effects. The frequency of free vibration is calculated by discretization based on the Differential Quadrature (DQ) Method. The frequency is a complex value due to the thermoelastic effect that dissipates energy. By separating the real and imaginary parts of frequency, the quality factor of thermoelastic damping is calculated. Both the stretching and thermoelastic effects are validated by the referenced papers. This paper shows that the main nonlinearity of this model is voltage, which makes the difference between linear and nonlinear models. The variation of thermoelastic damping (TED) versus geometrical parameters, such as thickness, gap distance and length, is investigated and these results are compared by linear and nonlinear models in high voltages. This paper also shows that in high voltages the linear model has a large margin of error for calculating thermoelastic damping (TED) and thus the nonlinear model should be used.