Analytical Solution of Nonlinear Dynamics in Electrostatically Driven MEMS Scanning Mirrors

This paper presents an analytical solution for the nonlinear dynamics of electrostatically driven MEMS scanning mirrors. These mirrors are widely used due to their small size, low cost, and low power consumption. However, nonlinearities in MEMS mirror's amplitude-frequency response complicate control and design. Traditional numerical methods are time-consuming. This study uses a nonlinear approximation method and the averaging method to derive analytical solutions, improving design efficiency. Simulations and experiments validate these solutions, demonstrating good agreement for large amplitudes. The paper elucidates the origins of nonlinear phenomena such as threshold voltage, hysteresis in frequency response, and frequency shifts. An expression for the maximum vibration amplitude is derived, providing valuable insights for optimizing MEMS scanning mirrors. These findings provide a theoretical foundation for enhancing amplitude control, expediting the design process, and improving the performance of MEMS scanning mirrors. 2024-0128