In this paper, one analytical technique named Frequency-Amplitude Formulation Method (FAF) isused to obtain the behavior and frequency of theelectrostatically actuated microbeams. The main aim of the work is obtaining highly accurate analytical solution for nonlinear free vibration of a microbeam and investigates the dynamic behavior of the system. Results reveal that the nonlinear frequency of oscillatory system remarkably affected with the initial conditions. In contrast to the time marching solution results, the present analytical method is effective and convenient. It is predictable that the FAF can apply for various problems in engineering specially vibration equations.
In this paper, Newton Harmonic Balancing Method (NHBM) is applied to scrutinize free vibration analysis of the nonlinear oscillatory systems. This method is combined by the Harmonic Balance and Newton's methods. Two classical cases are used to illustrate the applicable of NHBM and results compared by other analytical methods and ODE solver built in MATLAB. The results of the NHBM are shown that the solution quickly convergent and does not need to complicated calculations. So it is applied for various problems in engineering specially vibration equations.
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