Nonlinear normal modes of structural systems via asymptotic approach

An asymptotic approach, based on the method of multiple scales, is employed to construct the nonlinear normal modes (NNM's) of self-adjoint structural systems with arbitrary linear inertia and elastic stiffness operators, general cubic inertia and geometric nonlinearities. The methodology employed for constructing the approximate invariant manifolds of individual NNM's-away from internal resonances-and of the resonant modes-near three-to-one internal resonances-attempts to generalize previous studies based on asymptotic techniques. The theory is applied to a hinged-hinged uniform elastic beam carrying a lumped mass and undergoing axis stretching. Depending on the lumped mass relative to the beam mass and on its position along the span, different classes of nonlinear normal modes and their stability are investigated. (C) 2004 Elsevier Ltd. All rights reserved.