Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators

This paper deals with effects of residual and axial stresses on thermoelastic damping (TED) in micro-beam resonators. Equations of coupled thermoelastic case for a capacitive micro-beam resonator have been governed using two dimensional non-Fourier heat conduction model based on continuum theory frame. A Galerkin based finite element formulation has been used to analyze TED for the first mode of vibration of the micro-beam resonator with both ends clamped and isothermal. Effect of axial stresses owing to stretching of the micro-beam on the TED ratio has been investigated. As results illustrate, this effect gets importance only when the resonator is vibrating about a large static deflection due to a bias DC voltage close to the pull-in voltage of the resonator, otherwise it can be neglected in calculations. Effect of compressive and tensile residual stresses has been also studied. The results show that compressive (tensile) residual stresses increase (decrease) the TED ratio considerably. The residual stresses effect has been also studied for various values of the micro-beam thicknesses. The results illustrate that the effect of residual stress on the TED ratio decreases by increasing the thickness of the micro-beam. The results show that, applying DC voltages near the pull-in voltage increases energy dissipation due to the TED considerably, therefore, there is a limitation for applied DC voltage for resonators, since residual stresses change the pull-in voltage of the resonator, hence, existing residual stresses can change the interval of the applied voltage limitation.