Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

We present theoretical and experimental investigation of the nonlinear behavior of a clamped-clamped in-plane microelectromechanical systems (MEMS) arch when excited by a dc electrostatic load superimposed to an ac harmonic load. Experimentally, a case study of in-plane silicon micromachined arch is examined and its mechanical behavior is measured using the optical techniques. An algorithm is developed to extract the various parameters, such as the induced axial force and the initial rise, needed to model the behavior of the arch. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. In addition, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Dynamic snap-through behavior is also reported for the larger range of electric loads. Theoretically, a multi-mode Galerkin reduced order model is utilized to simulate the arch behavior. General agreement is reported among the theoretical and experimental data.