Non-linear vibration of curved microbeam under electrostatic actuation by using reduced order model and finite element simulation

In this research, the dynamic behavior and nonlinear vibration of a clamped-clamped initially curved microbeam under electrostatic step actuation is investigated. The initially curved microbeams under transverse loading may exhibit two different stable states and this is the basis of the emergence of bi-stable micro electro mechanical systems (MEMS). The equation of motion is derived based on energy method and Hamiltonian principle, and re-written in non-dimensional form by using appropriate non-dimensional parameters. The resultant equation of motion in non-dimensional form is discretized and converts to a system of nonlinear ordinary differential equations by using a reduced order model based on the Galerkin procedure. Runge-kutta method of order four is employed to solve the resulting system of nonlinear ordinary differential equations. COMSOL Multiphysics software is used for finite element simulation. Then, the effect of various parameters including voltage parameter, damping, initial midpoint elevation and gap length is investigated. It is concluded that the critical voltage of pull-in is decreased by increasing of the initial midpoint elevation. Also The results depict that by increasing of the damping parameter, the possibility of transition between two stable stats is eliminated.