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A direct method for non-linear normal modes

✍ Scribed by Richard H. Rand


Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
234 KB
Volume
9
Category
Article
ISSN
0020-7462

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πŸ“œ SIMILAR VOLUMES


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✍ M.I. Qaisi πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 171 KB

A power series method is presented for the computation of normal modes and frequencies of an elastic beam resting on a non-linear foundation. The equation of motion is first discretized by using the Galerkin procedure. The time-dependent generalized co-ordinates are obtained by transforming the time

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✍ W.C. XIE; H.P. LEE; S.P. LIM πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 156 KB

Non-linear modal analysis approach based on invariant manifold method proposed earlier by Shaw and Pierre (Journal of Sound and <ibration 164, 85}124) is utilized here to obtain the non-linear normal modes of a clamped}clamped beam for large amplitude displacements. The results obtained for the fund

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A method based on the power series technique is developed for the computation of normal modes and frequencies of a non-linear conservative lumped parameter system. The power series analysis is facilitated upon transforming the time variable into an harmonically oscillating time. Recurrence relations

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✍ X. MA; M.F.A. AZEEZ; A.F. VAKAKIS πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 224 KB

The Karhunen}Loeve (K}L) decomposition procedure is applied to a system of coupled cantilever beams with non-linear grounding sti!nesses and a system of non-linearly coupled rods. The former system possesses localized non-linear normal modes (NNMs) for certain values of the coupling parameters and h

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✍ A.Y.T. Leung; T. Ge πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 468 KB

For a strongly non-linear multi-degree-of-freedom system, in general, one cannot consider one mode at a time as in linear modal analysis. In the absence of external excitation, the natural vibration often involves more than one mode at a time resulting in quasi-periodic or multi-periodic (toroidal)