Iterative Homotopy Harmonic Balance Approach for Determining the Periodic Solution of a Strongly Nonlinear Oscillator

A novel approach about iterative homotopy harmonic balancing is presented to determine the periodic solution for a strongly nonlinear oscillator. This approach does not depend upon the small/large parameter assumption and incorporates the salient features of both methods of the parameter-expansion and the harmonic balance. Importantly, in obtaining the higher-order analytical approximation, all the residual errors are considered in the process of every order approximation to improve the accuracy. With this procedure, the higher-order approximate frequency and corresponding periodic solution can be obtained easily. Comparison of the obtained results with those of the exact solutions shows the high accuracy, simplicity, and efficiency of the approach. The approach can be extended to other nonlinear oscillators in engineering and physics.