Non-linear normal modes and invariant manifolds

Steven Shaw (1) , Christophe Pierre (2)

1 Michigan State University [East Lansing]
2 Department of Mechanical Science and Engineering

Small-amplitude motions of dynamic systems (structural, fluid, control, etc.) about an equilibrium state are modeled by linear differential equations which have constant coefficients. These are typically obtained by a Taylor series expansion of the forces about the equilibrium point. Under quite general circumstances these equations admit a set of special solutions, called normal mode motions, in which each system component moves with the same frequency and with a fixed ratio amongst the displacements of the components (for a conservative system; for a non-conservative system all displacements and velocities are linearly related to a single displacement/velocity pair).

Mots clés: modal analysis; nonlinear normal modes; nonlinear dynamics; invariant manifold

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Steven Shaw, Christophe Pierre. Non-linear normal modes and invariant manifolds. Journal of Sound and Vibration, 1991, 150 (1), pp.170-173. ⟨10.1016/0022-460X(91)90412-D⟩. ⟨hal-01310674⟩