Abstract
Based on Hamiltonian principle and a modified couple stress theory, a nonlinear differential equation of motion of electrostatically actuated microbeams is presented. The method of Galerkin–Bubnov decomposition is employed to convert the established system into reduced discrete modal equation. The analytical approximate solution to nonlinear free vibration is obtained by means of the optimal auxiliary functions method. The influence of internal material length scale parameter and outer diameter on the dynamic behavior is considered. The proposed procedure is effective, convenient and does not require linearization or small parameters assumption. The main advantage of this technique consists in that it provides a convenient way to control the convergence of the approximate solution in a very rigorous way.
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