Numerical simulation and analysis of the micro electrostatic device

In general, analysis of the electrostatic device is quite difficult and complicated due to the electrostatic coupling effect and the nonlinear electrostatic force. In this study, a hybrid method (H. M.) for the micro-structure system, which combines the differential transformation method (D. T. M.) and finite difference approximation techniques, is used to overcome the nonlinear electrostatic coupling phenomenon. The differential transformation employed is a transformed function based on the Taylor series that is effective in solving nonlinear problems with fast convergence. First, the natural frequencies of a micro fixed-fixed beam are derived as the solutions to a boundary value problem with prescribed boundary conditions by the differential transformation method. And then the nonlinear governing equation of a micro cantilever beam is solved by the hybrid method. The numerical results of the calculated pull-in voltage and natural frequencies are compared with other literatures using various computational methods and are found to be in good agreement. Overall, the results presented in this study show that the proposed hybrid method, provides an accurate and versatile means of analyzing the complex nonlinear behavior of a micro electrostatic devices.