Micro Resonator Nonlinear Dynamics Considering Intrinsic Properties

Abstract

Abstract. One of the most important phenomena to a ect the motion behaviour of Micro Resonators is their thermal dependency. This has recently received the attention of researchers widely. A thermal phenomenon has two main e ects, the rst is damping, due to internal friction, and the second is softening, due to Young's modulus-temperature relationship. In this research work, some theoretical and experimental reported results are used to make a proper model, including thermal phenomena. Two Lorentzian functions are used to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal e ects, a nonlinear model of the MEMS, considering capacitor nonlinearity and mid-plane stretching, has been used. The responses of the system are developed by employing a multiple time scale perturbation method on a non-dimensionalized form of the equations. Frequency response, resonance frequency and peak amplitude are examined by varying the dynamic parameters of the modelled system. Finally, Fuzzy Generalized Cell Mapping (FGCM) is introduced and applied to the Micro Resonator's dynamical system behaviour. It is then concluded as to how the model uncertainties and di erent initial conditions can a ect the working domain of the system and/or make it pull in instabilities. At the end, it can be seen that FGCM is a useful method for monitoring the working regions of Micro Resonators, while varying system parameters.