A new analytical approach to the Duffing-harmonic oscillator

This Letter presents a new approach to solving the nonlinear Duffing-harmonic oscillator. It addresses the significant drawback in the classical harmonic balance method. By combining the linearization of the governing equation with the method of harmonic balance, we construct analytical approximations to the oscillation periods and periodic solutions for the oscillator. These analytical representations give excellent approximations to the exact solutions for the whole range of values of oscillation amplitude. The new approach also avoids the necessity of numerically solving sets of equations with very complex nonlinearities as in the classical harmonic balance method. © 2003 Elsevier Science B.V. All rights reserved.