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Generalization of the Rayleigh Theorem to Non-Linear and Parametrically Excited Systems

✍ Scribed by A.A. Zevin

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 277 KB
Volume: 171
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1994.1135

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✦ Synopsis

The behavior of natural frequencies of linear systems under an increase of rigidity or inertia is established by the classical Rayleigh theorem [1]. In the first part of this paper the analogous problem is investigated for free oscillations frequencies of non-linear Hamiltonian systems with fixed total energy. It is shown that the Rayleigh theorem cannot be entirely extended to such systems even having one degree of freedom. However, for certain values of the total energy an assertion similar to the Rayleigh theorem actually can be made (Theorem 1). In the second part of the paper linear parametrically excited systems are treated. It is proved that the Rayleigh theorem can be fully generalized to the critical values of a frequency of parametric excitation corresponding to the boundaries between stable and unstable regions.

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