High‐Order Energy Balance Method to Nonlinear Oscillators

Abstract

Energy balance method (EBM) is extended for high‐order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic‐quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first‐ and second‐order approximation, respectively. The third‐order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.