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Nonlinear oscillations under multifrequency parametric excitation

A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub>, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w<sub>r</sub><u>~</u>3w<sub>q</sub> on the resonance λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub> is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ<sub>s</sub> + λ<sub>t</sub>. / Master of Science

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/43402
Date22 June 2010
CreatorsGentry, Jeanette J.
ContributorsEngineering Mechanics, Nayfeh, Ali H., Mook, Dean T., Plaut, Raymond H.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeThesis, Text
Formatvi, 58 leaves, BTD, application/pdf, application/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationOCLC# 19289568, LD5655.V855_1988.G467.pdf

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