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In this study, the influences of the squeeze-film damping effect on the dynamic behavior of the microelectromechanical electrostatic actuators are investigated by the hybrid numerical scheme comprising the differential transformation method and the finite difference method. There are two types of actuators which including the circular micro-plate and the clamped-clamped micro-beam, relatively. The analyses take account of the axial stress effect, the residual stress and the fringing field effect within the micro actuators and explore the dynamic response of the plate/beam as a function of the magnitude of the AC driving voltage. The effectiveness of a combined DC/AC loading scheme in driving the micro actuators are examined. It is shown that the use of an AC actuating voltage in addition to the DC driving voltage provides an effective means of tuning the dynamic response of the micro actuators. Therefore, the results show that the hybrid method provides an accurate and computationally-efficient means of analyzing the nonlinear behavior of the micro-beam structures used in many of today’s MEMS-based actuator systems.

The dynamic behavior of micro circular plate electrostatic devices is not easily analyzed using traditional methods such as perturbation theory or Galerkin approach method due to the complexity of the interactions among the electrostatic coupling effect, the residual stress and the nonlinear electrostatic force. Accordingly, the present study proposes a approach for analyzing the dynamic response of such devices using a hybrid numerical scheme comprising the differential transformation method and the finite difference method. The feasibility of the proposed approach is demonstrated by modeling the dynamic response of a micro circular plate actuated by a DC voltage. The numerical results for the pull-in voltage are found to deviate by no more than 0.27 % from those derived in the literature using various computational methods. Thus, the basic validity of the hybrid numerical scheme is confirmed. Moreover, the effectiveness of a combined DC/AC loading scheme in driving the micro circular actuator is examined. It is shown that the use of an AC actuating voltage in addition to the DC driving voltage provides an effective means of tuning the dynamic response of the micro circular plate.

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.