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    Nonlinear oscillations under multifrequency parametric excitation

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    LD5655.V855_1988.G467.pdf (1.438Mb)
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    Date
    1988-11-05
    Author
    Gentry, Jeanette J.
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    Abstract

    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 ~2Ï q, is examined. Second, the influence of an internal resonance, Ï q~3Ï r, on the previous case is studied. Finally, the effect of the internal resonance wr~3wq on the resonance λs + λt ~2Ï q 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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    http://hdl.handle.net/10919/43402
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    • Masters Theses [19598]

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