The Nonlinear Dynamics of a MEMS Resonator with a Triangular Tuning Comb

Abstract

The nonlinear dynamic response of a MEMS resonator with a triangular tuning comb is studied. The motion equation with dis-smooth tuning electrostatic force is derived according to Newton’s second law. The analytical solution of the periodic response is obtained using the harmonic balance method and section integral method. The singularity theory is then applied to investigate the bifurcation of the periodic response of the untuned system. The transition sets on the DC-AC voltage plane dividing the planes into several persistent regions are obtained. The bifurcation diagrams’ topological structures and jump phenomena corresponding to different parameter regions are analyzed. We explore the effects of tuning voltage on the response. This demonstrates that the amplitude–frequency curves present more hardening characteristics with increased tuning voltage. Many twists, bifurcation points, and unstable solutions appear, leading to complicated jump phenomena. Two bifurcation points exist on the response curves: the smooth and dis-smooth bifurcation points, with the latter occurring on the switching plane of non-uniform fingers.

Keywords

• nonlinear dynamics
• MEMS resonator
• triangular tuning comb
• periodic solution
• dis-smooth tuning force