Stochastic dynamic behavior of electrostatically actuated clamped–clamped microbeams with consideration of thermal field

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Environment perturbation and structure vibration can lead to the change of the thermal field, which may have certain effects on intrinsic frequency and dissipation mechanism for small-scale mechanical resonators. This article aims to theoretically investigate static and stochastic dynamic behavior of electrostatically actuated microbeams via a low dimensional model. Considering thermoelastic damping and thermal residual stress, an improved single degree of freedom model to describe microbeam-based resonators is obtained by using Hamilton’s principle and Galerkin method. Through static behavior analysis, the influence of temperature field and electric field on the natural frequency and thermoelastic damping of the system is theoretically derived. The results show that the perturbation of environment temperature can significantly change the natural frequency and quality factor of the system. The following, a random frequency perturbation parameter is introduced to describe the perturbation of the environment temperature. An efficient approximation method is proposed to qualitatively study nonlinear stochastic dynamic behavior under small perturbation of stochastic parameter. It is found that the randomness of environment temperature suppresses nonlinear behavior and reduces the possibility of large amplitude vibration. Typically, the environment temperature disturbance reduces the resonance frequency of the system. Finally, the numerical method is put forward to not only verify the validity of the theoretical method but also quantitatively give the effects of noise strength and correlation rate on the nonlinear dynamic behavior. The present work provides theoretical framework for analyzing the effects of the perturbation of temperature field on nonlinear system response.