Collaborative Research: Improving Capabilities of Micro-scale Vibratory Systems by Embracing and Accounting for Large-Amplitude Responses

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This project considers the development of techniques to assist in the design and optimization of micro-electro-mechanical-systems (MEMS) that utilize resonant vibrations. These micro-scale devices are important elements in many consumer electronics and products including wireless telephones, automobiles, and entertainment devices. The capabilities of these systems are often limited by a number of factors that restrict their range of operation, such as their maximum amplitude of vibration. This research pursues a fundamental understanding of these limitations and developing systematic tools for improving the performance of these devices. The broader impact of this project includes outreach, mentoring and training, inclusion of students from underrepresented groups, development of classroom materials motivated by the research, and dissemination of results. This project will result in multidisciplinary training of students, who benefit from the close collaboration and integrated theoretical and experimental research approach of the PIs. Also, the PIs and their graduate students will continue their longstanding participation in summer outreach programs to middle- and high-school students, and the inclusion of undergraduate research assistants. The PIs also plan to create an alumni mentoring program for graduate students, in which current graduate students will be connected with alumni who will offer professional advice and support.Most commercial devices that employ vibratory MEMS are designed so that the resonant elements operate in their linear range and the designer can rely on simple models to analyze their response. However, this sets limits on their operating range that do not take full advantage of their potential. There have been recent efforts demonstrating significantly improved performance when nonlinear effects are systematically included in the MEMS design process. The focus of this project is to embrace nonlinear behavior in resonators, to develop an understanding of the attendant limits, and to develop and experimentally demonstrate design methods that allow one to optimize performance in this realm. The research focus is on MEMS that operate with one or two fundamental vibratory modes that can be described by weakly nonlinear models so that analytical methods, namely perturbation techniques, and the theory of normal forms, are applicable. These models are linked with multi-physics computational tools and optimization techniques, using normal forms to formulate objective functions for the applications of interest. Devices developed with these tools will be fabricated, characterized, and tested to validate the approach. Applications will include frequency generation, frequency conversion, and inertial sensing.