Global residue harmonic balance method for large-amplitude oscillations of a nonlinear system

A new approach, namely global residue harmonic balance method, was used to deal with large-amplitude oscillations of a nonlinear system with inertia and static nonlinearities. Unlike other harmonic balance methods, all the former residual errors are introduced in the present approximation to improve the accuracy. Comparison of the result obtained using this approach with the exact one and existing results reveals that the high accuracy, simplicity and efficiency of the proposed procedure. The methods are valid for small as well as large amplitudes of oscillation, and can be easily extended to other strongly nonlinear oscillators.