Analysis of 2:1 Internal Resonance in MEMS Applications

Micromachined resonators are typically used within their linear range of operation. Recently, there has been an increasing interest in understanding nonlinearities and potentially employing them to improve the performance of resonance-based devices. The focus of this thesis is to study the nonlinear mode coupling at 2:1 internal resonance both experimentally and analytically. It is shown that quadratic nonlinearities can couple two vibrational modes of a micro-resonator with a 2:1 ratio between two of its mode frequencies. This nonlinear coupling of modes can lead to the transfer of energy between these two modes through internal resonance. To study the phenomenon, a modified T-beam structure is proposed, and a simplified mathematical model of operation including the nonlinearities is developed for this system. Perturbation solutions of the mathematical model, along with finite element and reduced-order method analysis are used to describe the nonlinear behaviour of the system. Experiments are performed on a modified micro T-beam structure with 2:1 ratio between its resonance frequencies. Nonlinear modal interactions between vibrational modes, jump and saturation phenomena, and bandwidth enhancement are also observed both in experiments and numerical simulations. The effect of damping on the behaviour of the system is also studied. Some of the potential applications of internal resonance in sensing are also proposed and discussed throughout the thesis.