Analytical solution of the forced Duffing's oscillator

This paper presents an analytical approach based on the power series method for determining the periodic solutions of the forced undamped Duffing's oscillator. The time variable is first transformed into a new harmonically oscillating time which transforms the governing differential equation into a form suitable for power series analysis. Hamilton's principle for non-conservative systems is then used to determine the frequency of the oscillating time. The formulation is applied to a number of periodic solutions and excellent agreement is obtained with numerical solutions. The potential of the method is highlighted by comparing the results for a periodic response with perturbation and harmonic balance solutions. (C) 1996 Academic Press Limited