Nonlinear dynamic analysis of MEMS switches by nonlinear modal analysis

A nonlinear modal analysis approach based on the invariant manifold method proposed earlier by Boivin et al. [10] is applied in this paper to perform the dynamic analysis of a micro switch. The micro switch is modeled as a clamped-clamped microbeam subjected to a transverse electrostatic force. Two kinds of nonlinearities are encountered in the nonlinear system: geometric nonlinearity of the microbeam associated with large deflection, and nonlinear coupling between two energy domains. Using Galerkin method, the nonlinear partial differential governing equation is decoupled into a set of nonlinear ordinary differential equations. Based on the invariant manifold method, the associated nonlinear modal shapes, and modal motion governing equations are obtained. The equation of motion restricted to these manifolds, which provide the dynamics of the associated normal modes, are solved by the approach of nonlinear normal forms. Nonlinearities and the pull-in phenomena are examined. The numerical results are compared with those obtained from the finite difference method. The estimate for the pull-in voltage of the micro device is also presented.