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Free vibrations of a thin elastica by normal modes

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Abstract

In this work we investigate the existence, stability and bifurcation of periodic motions in an unforced conservative two degree of freedom system. The system models the nonlinear vibrations of an elastic rod which can undergo both torsional and bending modes. Using a variety of perturbation techniques in conjunction with the computer algebra system MACSYMA, we obtain approximate expressions for a diversity of periodic motions, including nonlinear normal modes, elliptic orbits and non-local modes. The latter motions, which involve both bending and torsional motions in a 2:1 ratio, correspond to behavior previously observed in experiments by Cusumano.

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Authors and Affiliations

  1. College of Engineering, Cornell University, 14853, Ithaca, NY, U.S.A.

    C. H. Pak, R. H. Band & F. C. Moon

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  1. C. H. Pak
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  2. R. H. Band
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  3. F. C. Moon
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Pak, C.H., Band, R.H. & Moon, F.C. Free vibrations of a thin elastica by normal modes. Nonlinear Dyn 3, 347–364 (1992). https://doi.org/10.1007/BF00045071

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  • DOI: https://doi.org/10.1007/BF00045071

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