Probabilistic reliability of micro-resonators with thermoelastic coupling

Analyzing the probabilistic reliability of micro-resonators is essential for the design of microelectromechanical systems (MEMS). In order to investigate more complex structures and take into account the random variation of the design parameters, an efficient thermoelastic Finite Element (FE) formulation is derived from Hamilton's variational principle. A generalized eigenvalue equation can be obtained through the formulation. The effects of thermoelastic coupling and the randomness of parameters on the natural frequency are studied by using a non-symmetric block Lanczos algorithm combined with the right and left eigenproblem. Considering the influence of thermoelastic coupling on temperature is little, the thermoelastic coupling term in heat conduction equation can be negligible, thus the heat conduction equation is simplified based on linearization. Depending on the eigenproblem for temperature field and thermal stress in micro-resonators, further analysis is conducted on the randomness of temperature and stress in micro-resonators. For reliability analysis, a method which considering both strength and frequency is proposed. The strength failure criterion is set based on fracture mechanics, and frequency reliability is taken into account the probabilistic of resonators when the natural frequency is close to the excitation frequency. With a simply supported model of micro-resonators as an example, the numerical solutions of quality factor have shown little difference with the analytical solutions proposed by Zener and Lifshitz, verifying the correctness of the model calculations. Finally, the natural frequency shift and the probabilistic reliability with temperature are calculated.