An application of the inch algebraization to the stability of non-linear normal vibration modes

A normal vibration mode stability in conservative non-linear systems is investigated. The algebraization by Ince (transition from linear equations with periodic coefficients to equations with singular points) is used. The normal mode stability in homogeneous systems, whose potential is an even homog...

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Bibliographic Details
Published in:International journal of non-linear mechanics 1997-03, Vol.32 (2), p.393-409
Main Authors: Mikhlin, Yu.V., Zhupiev, A.L.
Format: Article
Language:English
Subjects:
bifurcation
Ince algebraization
normal vibration mode
stability
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Summary:A normal vibration mode stability in conservative non-linear systems is investigated. The algebraization by Ince (transition from linear equations with periodic coefficients to equations with singular points) is used. The normal mode stability in homogeneous systems, whose potential is an even homogeneous function of the variables and systems close to the homogeneous one, is investigated. Eigenvalues and eigenfunctions are obtained. Conditions when a number of instability zones in a non-linear system parameters space are finite (finite zoning or finite-gap conditions) are also obtained.
ISSN:0020-7462
1878-5638
DOI:10.1016/S0020-7462(96)00047-9