An invariant manifold approach to nonlinear normal modes of oscillation

Steven Shaw (1)

1 Department of Mechanical Engineering and Applied Mechanics

A method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is de· scribed. 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.

Mots clés: nonlinear vibrations; nonlinear oscillations; invariant manifolds; normal modes; Galerkin

Domaines: Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Vibrations [physics.class-ph]

Steven Shaw. An invariant manifold approach to nonlinear normal modes of oscillation. Journal of Nonlinear Science, 1994, 4, pp.419-448. ⟨10.1007/BF02430640⟩. ⟨hal-01354040⟩