ANALYSIS OF A FORCED STRONGLY NON-LINEAR TWO-DEGREE-OF-FREEDOM SYSTEM BY MEANS OF THE POWER-SERIES METHOD

A power-series solution is presented for the periodic motion of an undamped strongly non-linear two-degree-of-freedom system excited by harmonic forces. The analysis is facilitated by transforming the time variable into an harmonically oscillating time. The frequency of the new time variable is determined by observing the equality between the rate of change of dynamical energy and the power delivered by the forces. The results show good agreement with the modified Lindstedt–Poincaré method and the incremental harmonic balance method.