Investigation of the Dynamic Behavior of Periodic Systems with Newton Harmonic Balance Method

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 Newtonʹs 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.