Analysis of thermoelastic damping in microresonators by considering the stretching effect

In this paper, the previous theory for obtaining the quality factor of thermoelastic damping in microresonators has been modified. Here, the stretching term for the neutral axis of bending is considered, which has been neglected in previous work. The Taylor expansion of electric actuation has described the static position of microbeam, which is more accurate than previous work that extends it about the straight position of a microbeam. Also, the theory of this work may be used for two layered microresonators without this assumption that the length of two layered electrically actuated microresonators may be obtained, for the first time. To obtain this complete theory firstly the equations of motion coupled with thermal effects are obtained in a two layered microbeam where the second layer is deposited on a part of the first layer length. Then, the quality factor of thermoelastic damping of the system, i.e. the half of the ratio of the real part of the free vibration resonance frequency to its imaginary part, has been obtained by solving the free vibration equation using the strained parameter perturbation method. It has been shown that neglecting the stretching of neutral axis of bending and expanding the electrostatic actuation about the straight position of the microbeam considered in previous researches cause an error that is not negligible for the voltage larger than 30% of the pull-in voltage. Also, it is shown that the quality factor of thermoelastic damping in two layered microresonators depends on the value of length, thickness and the kind of material of the deposited layer.