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A General Solution of the Duffing Equation

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Abstract

In this paper, we describe the application of the elliptic balance method (EBM) to obtain a general solution of the forced, damped Duffing equation by assuming that the modulus of the Jacobian elliptic functions are slowly varying as a function of time. From this solution, the maximum transient and steady-state amplitudes will be determined for large nonlinearities and positive damping. The amplitude–time response curves obtained from our elliptic balance approximate solution are in good agreement with those obtained from the numerical integration solution over the selected time interval.

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  1. Departamento de Ingeniería Mecánica, Instituto Tecnológico y de Estudios Superiores de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, NL, México

    Alex Elías-Zúñiga

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  1. Alex Elías-Zúñiga
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Correspondence to Alex Elías-Zúñiga.

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Elías-Zúñiga, A. A General Solution of the Duffing Equation. Nonlinear Dyn 45, 227–235 (2006). https://doi.org/10.1007/s11071-006-1858-z

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  • DOI: https://doi.org/10.1007/s11071-006-1858-z

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