Micro Resonator Nonlinear Dynamics Considering Intrinsic Properties


Department of Mechanical Engineering,Sharif University of Technology


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.