Gentry, Jeanette J.2014-03-142014-03-141988-11-05etd-06222010-020244http://hdl.handle.net/10919/43402A 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_s + λ_t <u>~</u>2Ï _q, 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_r<u>~</u>3w_q on the resonance λ_s + λ_t <u>~</u>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 λ_s + λ_t.vi, 58 leavesBTDapplication/pdfIn CopyrightLD5655.V855 1988.G467Nonlinear oscillationsStructural dynamics -- Mathematical modelsThesishttp://scholar.lib.vt.edu/theses/available/etd-06222010-020244/