Nonlinear dynamical analysis of some microelectromechanical resonators with internal damping

In this paper, a new Kelvin-Voigt type beam model of a microelectromechanical resonator made of power-law materials taking into account internal strain-rate damping is proposed and the corresponding lumped-parameter model is derived. Analytical formulas of the lumped parameters in the model are presented. And the pull-in solution is analyzed based on the lumped-parameter model. It is demonstrated analytically and numerically that the internal damping plays an important role in the pull-in solution as well as in determination of the amplitudes and frequencies of the resonator. The hysteresis loops are provided for this model with initial conditions using numerical simulations. The approximation of the electrostatic force in the lumped-parameter model can describe the relations between amplitudes and frequencies with different values of the stiffness and damping coefficients quite well.