Multi-Physical Fields Coupling Nonlinear Dynamics Of Micro-Plate

As an important driving mode, electrostatic drive is widely applied to micro electromechanical products, and micro-plate is a typical structural element in MEMS product design. The nonlinear characteristics generated by electromechanical coupling or electromechanical fluid coupling between electrostatic field force and micro components deformationes exist in the operation of MEMS devices. At present, the related calculation methods and design theoretics cannot satisfy application requirements yet, it is the bottleneck which slows down the step of research and industrialization of the MEMS products. Based on the theories of nonlinear dynamics, electrostatic field, elasticity and fluid mechanics, the problems of multi-physical fields coupling nonlinear dynamics in electrostatically driven micro-plate are investigated.Based on the small deflection theory and electrostatics theory, the electromechanical coupling dynamics model is established, analytical formulas of the static and dynamic electric field force are derived, Moreover, the basic differential equation of lateral vibration is established by using elasticity theory. On the basis of linear analysis, considering the nonlinear characteristic of electrostatic force, the analytical formula for nonlinear electrostatic force is derived, and the differential equation about weakly nonlinear dynamics of the electromechanical coupling micro-plate is established. By using perturbation method, the periodic solutions and amplitude frequency responses which meet the accuracy requirements are given. On the basis of the nonlinear dynamics research, the multi-physical fields coupling nonlinear dynamics model is eshtablished which involves nonlinear damping factor and the nonlinear electrostatic force simultaneously. Based on two dimentional Leinuo equation, the approximate analytical formulas of damping coefficient and fixed damping coefficient inside the parallel micro-plates are derived. Furthermore, nonlinear dynamics differential equation which involves nonlinear damping factor is founded. Using KBM method, nonlinear dynamics and electric field, pressure field responses in micro-plate system of multi-physical fields coupling are researched. Take three typical boundary conditions of the micro-plates as examples, the system parameters are optimized rationally, frequency characteristics, time responses, amplitude frequency responses, electric field and pressure field responses are caculated with the aid of simulation to achieve the systemic analysis and design, which provides theoretical basis for optimizing the system parameters, improving the ability to resist interferences and increase the reliability.Based on the small capacitance detection principle, electrostatically actuated micro-plate dynamics test system is designed, fretting test platform is developed which realizes the detection of high resonance frequencies. The test proves that theoretical analysis is correct.