Size dependent dynamic behavior of electrostatically actuated microbridges

In this paper, based on the size dependent theories, an accurate investigation for nonlinear dynamic analysis of electrostatically actuated microbridges is presented by using the nonlinear finite element formulation, analytical method and numerical approach. The microbridge used as a microresonator, is driven by simultaneously applied DC and AC voltages. In the framework of modified couple stress theory (MCST), the nonlinear equation of dynamic motion for this system is derived using extended Hamilton's principle. Thereupon, the nonlinear partial differential equation is converted to the nonlinear ordinary equation by Galerkin's method and solved by analytical and numerical techniques. The analytical solution for nonlinear vibration of the microresonators is obtained by perturbation theory. Findings show that the numerical and analytical results are in good agreement with each other. In order to make further verification of the analytical expression, a nonlinear nonclassical finite element formulation for dynamic deformation of the system is presented to calculate the time history results. The good agreement observed between the results of analytical method and nonlinear finite element simulation demonstrates that the procedures used in the analytical method such as Taylor expansion, one mode analysis and perturbation expansion in multiple scale approach are appropriate. By determining the frequency-response curves, the effects of size dependency on the amplitude of vibration and frequency position of the peak response are studied. Results show that considering the size dependent theory leads to notable decreasing of the amplitude of nonlinear vibration and approaching the frequency value of peak response to linear resonance frequency.