Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation

A variety of microelectromechanical (MEM) oscillators is governed by a version of the Mathieu equation that harbors both linear and cubic nonlinear time-varying stiffness terms. In this paper, chaotic behavior is predicted and shown to occur in this class of MEM device. Specifically, by using Melnikov's method, an inequality that describes the region of parameter space where chaos lives is derived. Numerical simulations are performed to show that chaos indeed occurs in this region of parameter space and to study the system's behavior for a variety of parameters. A MEM oscillator utilizing noninterdigitated comb drives for actuation and stiffness tuning was designed and fabricated, which satisfies the inequality. Experimental results for this device that are consistent with results from numerical simulations are presented and convincingly show chaotic behavior.