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A new analytical approach to the Duffing-harmonic oscillator. (English) Zbl 1055.70009

Summary: We present 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 approximations to the exact solutions in the whole range of oscillation amplitude. The new approach also avoids the necessity of numerically solving equations with complex nonlinearities as in the classical harmonic balance method.

MSC:

70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
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