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
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/43402 |
| Date | 22 June 2010 |
| Creators | Gentry, Jeanette J. |
| Contributors | Engineering Mechanics, Nayfeh, Ali H., Mook, Dean T., Plaut, Raymond H. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis, Text |
| Format | vi, 58 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 19289568, LD5655.V855_1988.G467.pdf |
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