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Elliptic balance solution of two-degree-of-freedom, undamped, forced systems with cubic nonlinearity

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Abstract

The solution of a system of two coupled, nonhomogeneous undamped, ordinary differential equations with cubic nonlinearity and sinusoidal driving force is obtained by the use of Jacobian elliptic functions and the elliptic balance method. To assess the accuracy of our proposed solution, we consider an example that arises in the study of the finite amplitude, nonlinear vibration of a simple shear suspension system. It is shown that the analytical results exhibit good agreement with the numerical integration solutions even for moderate values of the system parameters.

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Authors and Affiliations

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

    Alex Elías-zúñiga

  2. Department of Engineering Mechanics, University of Nebraska – Lincoln, Lincoln, NE, 68588–0526, USA

    Millard F. Beatty

Authors
  1. Alex Elías-zúñiga
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  2. Millard F. Beatty
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Correspondence to Alex Elías-zúñiga.

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Elías-zúñiga, A., Beatty, M.F. Elliptic balance solution of two-degree-of-freedom, undamped, forced systems with cubic nonlinearity. Nonlinear Dyn 49, 151–161 (2007). https://doi.org/10.1007/s11071-006-9119-8

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  • DOI: https://doi.org/10.1007/s11071-006-9119-8

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