Development and Characterization of an H-Shaped Microresonator Exhibiting 2:1 Internal Resonance

This paper reports on the design and characterization of an H-shaped microresonator exhibiting nonlinear modal interactions due to 2:1 internal resonance. This has been made possible through careful design of the structure with attention to the limits of microfabricated devices. The intended nonlinear dynamics rely on the continuous transfer of energy between the anti-phase motions of two H-like proof masses of the device to a mode along the orthogonal direction. Finite element and reduced order models of the structure were developed and used to design the devices with two desired flexural modes in a ~2:1 frequency ratio. The microresonator was fabricated in a commercial foundry process. Extensive experiments and transient simulations were conducted to verify the desired nonlinear responses and the models. It was demonstrated that the low-frequency mode of the device was excited through auto-parametric excitation of the higher frequency mode when the excitation level exceeded a specific threshold as expected. The device design methodologies can be employed to fabricate various sensors, including nonlinear Coriolis vibratory gyroscopes incorporating 2:1 internal resonance.