Solution of cubic-quintic Duffing oscillators using harmonic balance method

In this study, Harmonic Balance Method (HBM) is applied to determine approximate analytic solutions of strongly nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. Mainly, a set of nonlinear algebraic equations is solved in this method. The new method avoids the necessity of numerically solving sets of algebraic equations with very complex nonlinearities. Numerical comparisons between the HBM and the exact solutions reveal that the HBM is a promising tool for strongly nonlinear oscillator’s problems