Nonlinearity in micromechanical free–free beam resonators: modeling and experimental verification

In this paper, we present a systematic characterization and modeling technique for the micromechanical free–free beam resonator to analyze its nonlinear vibration behavior. Different from the conventional FEM-based approach whose simulation accuracy is usually limited around 60–70%, the proposed modeling method is able to accurately identify both the mechanical and electrostatic nonlinear parameters from just a few preliminary experimental observations. The nonlinear equation of motion is then numerically solved, demonstrating both the spring hardening and softening effects in the system. The simulated nonlinear behavior of the resonator under different driving conditions is validated by comparing them with the experimental data. In addition, based on the verified nonlinear model, design guidelines such as the nonlinearity cancellation are also highlighted. Although this work focuses on the free–free beam resonators, the proposed modeling approach can be applied to any other electrostatically driven microresonator to reveal different intrinsic nonlinear properties of the device.