Title page for ETD etd-06222010-020244
|Type of Document
||Gentry, Jeanette J.
||Nonlinear oscillations under multifrequency parametric excitation
||Master of Science
|Mook, Dean T.
|Plaut, Raymond H.
|Nayfeh, Ali H.
|Date of Defense
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, λs + λt ~2ωq, is
examined. Second, the influence of an internal resonance, ωq~3ωr, on the previous
case is studied. Finally, the effect of the internal resonance wr~3wq on the resonance
λs + λt ~2ωq 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 λs + λt.
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