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Non-linear normal modes and invariant manifolds

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

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