Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam

Analyzing the dynamic response of electrostatic devices is problematic due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect and the nonlinear electrostatic force. To resolve this problem, this study presents an efficient computational scheme in which the nonlinear governing equation of the electrostatic device is obtained in accordance with Hamilton’s principle and is then solved using a hybrid differential transformation/finite difference method. The feasibility of the proposed approach is demonstrated by modeling the dynamic responses of two micro fixed-fixed beams with lengths of 250 and 350 μm, respectively. The numerical results show that the pull-in voltage reduces as the beam length increases due to a loss in the structural rigidity. Furthermore, it is shown that the present results for the pull-in voltage deviate by no more than 0.75% from those derived in the literature using a variety of different schemes. Overall, the results presented in this study demonstrate that the proposed hybrid method represents a computationally efficient and precise means of obtaining detailed insights into the nonlinear dynamic behavior of micro fixed-fixed beams and similar micro-electro-mechanical systems (MEMS)-based devices.