Energy balance method and amplitude frequency formulation based simulation of strongly non-linear oscillators

Abstract

The Energy Balance Method (EBM) and Amplitude Frequency Formulation (AFF) have been applied to derive the approximate analytical solution for motion of two mechanical oscillators. In first problem both methods yield the same result but in the second problem, the results which are obtained from Amplitude Frequency Formulation and Energy Balance Method are different. In comparison with the forth order Runge-Kutta method, the results show that these methods are very convenient for solving non-linear equations and also can be used for strong non-linear oscillators.