Iterative homotopy harmonic balancing approach for conservative oscillator with strong odd-nonlinearity

A new approach that the iterative homotopy harmonic balancing is presented for charactering and predicting analytical approximations of conservative oscillator with strong odd-nonlinearity in the paper. The new technique does not depend upon small parameter assumption and incorporates the salient features of both methods of the parameter-expansion and the harmonic balance. The results of applying this procedure to the studied examples that the cubic–quintic Duffing equation and Duffing-harmonic equation show the high accurate, simplicity and efficiency of the approach. The approach can be easily extended to other nonlinear oscillators.