A generalized methodology for thermoelastic damping in axisymmetric vibration of circular plate resonators covered by multiple partial coatings. (May 2021) - Yang, Longfei; Li, Pu; Fang, Yuming; Ge, Xiao
Abstract: Microresonators used for microelectromechanical systems (MEMS) are becoming more and more complex in terms of structural geometry and mode shapes. Accompanying this increase in complexity is the challenge to develop an accurate analytical method to evaluate the thermoelastic damping (TED). This paper firstly presents a generalized methodology for TED in axisymmetric vibration of circular plate microresonators covered by multiple partial coatings. The frequency and mode shape function of plates are solved by the Kirchhoff–Love plate theory. The thermoelastic temperature fields are acquired by solving the one-way coupled heat conduction along the thickness direction with Green's function method, accordingly obtaining the effects of partial coating on the microplate. The present model can reduce to that of the fully covered bilayer plates, and is validated by finite element model (FEM). This methodology produces an explicit model for TED in the form of one infinite series with rapid converge, and a simple model is given by retaining the first term. The accuracy and practicality of the simple model are investigated. The results suggest that SiO2 coating with thermally perfect interfaces can reduce the TED at the fundamental mode. However, SiO2 coating significantly increases TED values with thermally imperfect interfaces. Three distinctive peaks of TED spectra in Si/DLC/SiO2 plates are observed. This work can be utilized to optimize the TED in the composite circular microplates and gain more insights into the intrinsic dissipation. Highlights: A theoretical framework for TED in circular plates covered by n ( n ⩾ 1 ) partial coatings is proposed firstly. As for f h 1 ≤ 0 . 01 or f r 1 = 0 . 2 for all cases, the simple model can be adopted to calculate the TED with excellent accuracy at low frequencies. To minimize the TED, Si substrate should be fully covered by SiO2 coating. SiO2 coating significantly increases TED values with thermally imperfect interfaces. Three Debye peaks of plates covered by two partial coatings are presented.