Nonlinear Vibration of Electrostatically Actuated Microbeam

In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate analytical solutions of an electrostatically actuated micro-beam. To illustrate the applicability and accuracy of the method, a high level of accuracy was established for the analytical solutions by comparing the results of the solutions with the numerical solution as well as the already published literature, such as the variational approach (VA), Hamiltonian approach (HA), energy balance method (EBM), and homotopy analysis method (HAM). It is shown that the GRHB method can be easily applied to nonlinear problems and provides solutions with a higher precision than existing methods. The obtained analytical expressions are employed to study the effects of axial force, initial gape, and electrostatic load on nonlinear frequency.