High-order energy balance method to nonlinear oscillators (Q1760720)

Summary: 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.