Harmonic balance method for solving a large-amplitude oscillation of a conservative system with inertia and static non-linearity

In this paper, an analytical approximate technique based on harmonic balance method (HBM) is presented to obtain the approximate frequencies and the corresponding periodic solutions of a conservative oscillator having inertia and static non-linearity. The results of the present paper are valid for small and large amplitudes of oscillation. In previous articles, the first and second approximations were determined for the same oscillator; but the results were not close to the exact result. On the contrary, the new results of this paper are very close to the exact result. (C) 2016 Published by Elsevier B.V.