Summary
A method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is described. The method is a combination of a Galerkin projection and invariant manifold techniques and is applied to a class of distributed parameter vibratory systems. In this paper the general theory for a class of conservative systems is outlined and applied to determine the nonlinear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation.
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Communicated by Jerrold Marsden
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Shaw, S.W. An invariant manifold approach to nonlinear normal modes of oscillation. J Nonlinear Sci 4, 419–448 (1994). https://doi.org/10.1007/BF02430640
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DOI: https://doi.org/10.1007/BF02430640