A POWER-SERIES SOLUTION FOR A STRONGLY NON-LINEAR TWO-DEGREE-OF-FREEDOM SYSTEM

A power-series method is presented for the analysis of a conservative strongly non-linear two-degree-of-freedom (d.o.f.) system with cubic non-linearity. The method is based on transforming the time variable into an harmonically oscillating time whereby the governing differential equations become well conditioned for power-series analysis. The oscillating time frequency is obtained by enforcing Rayleighʹs energy principle. The results show good agreement with those obtained using the Lindstedt–Poincaré method.