A generalized model for thermoelastic damping in beams with mid-plane stretching nonlinearity

Abstract

This work presents a general model to accurately capture thermoelastic damping in beams with mid-plane stretching nonlinearity. The model consists of a nonlinear Timoshenko beam model coupled with a two-dimensional heat conduction model. The heat conduction model accounts for heat transfer in both the transverse and the axial directions of the beam. Numerical solutions are obtained by discretizing the beam using spectral element method (SEM). Using the proposed model, the thermoelastic damping (QTED) quality factor is obtained for beams actuated by electrostatic force using the eigenfrequency analysis and the energy approach. The eigenfrequency analysis conducted on the beams under the electrostatic actuation showed significant difference from the results published in literature. A detailed numerical analysis is performed in order to understand the discrepancy. It is shown that the discrepancy primarily occurs due to the differences in the methods to couple the displacement and thermal fields, with the model presented in the paper being the more general one.