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Abstract
In this paper, two new analytical techniques named max–min approach (MMA) and iteration perturbation method (IPM) are applied for solving nonlinear equations of two oscillatory systems. One case consists of a mass grounded by linear and nonlinear springs in series and the other case is the rigid rod rocks on a circular surface. The main aim of the work is obtaining highly accurate analytical solutions for nonlinear free vibration of conservative oscillations and investigates the dynamic behavior of the systems. Results reveal that the nonlinear frequency of oscillatory systems remarkably affected with the initial conditions. In contrast to the time marching solution results, the present analytical methods are effective and convenient. It is predictable that the MMA and the IPM can apply for various problems in engineering specially vibration equations.
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