Internal Resonances in Microelectromechanical Resonators

Abstract: Internal Resonances inMicroelectromechanical Resonators1 2PIs: Oriel Shoshani and Steven W. ShawDepartment of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, IsraelDepartment of Mechanical and Civil Engineering, Florida Institute of Technology, Melbourne, USAApplication No. 2018041Internal resonances are manifested by strong interactions and the exchange of energy betweenvibrational modes that arise when modal frequencies are rationally related. Micro-electro-mechanical-system (MEMS) resonators are an ideal platform for studying these phenomena,from both fundamental and application points of view, due to their versatile tunability and theability to develop physics-based models that are amenable to systematic methods for predictingand manipulating system response. The modes of interest are affected by nonlinearity andcoupling from electro-mechanical sources, plus coupling to the environment, resulting in a widerange of nonlinear and noisy dynamic behaviors. We seek to develop a thorough understandingof these features and their influence on the system response. In particular, the bifurcationstructures of two coupled modes for common internal resonances will be thoroughly explored,along with their attendant noise properties, with an eye towards applications. A successfulachievement of these goals will pave new avenues for the identification, characterization, andperformance enhancement of MEMS-based resonators, including those used for timekeepingand inertial sensing.

An integrated theoretical-computational study is proposed, accompanied by experimentsfor demonstrations of feasibility. The focus will be on modeling and theory, with particularattention given to weakly-nonlinear systems where the dynamics can be investigated usinganalytical and computational tools. The proposed research will theoretically complement awider ongoing effort on nonlinear dynamics in MEMS that is supported by the US NSF.