Title page for ETD etd-06222010-020244

Type of Document Master's Thesis
Author Gentry, Jeanette J.
URN etd-06222010-020244
Title Nonlinear oscillations under multifrequency parametric excitation
Degree Master of Science
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Mook, Dean T. Committee Co-Chair
Plaut, Raymond H. Committee Co-Chair
Nayfeh, Ali H. Committee Member
  • Structural dynamics
Date of Defense 1988-11-05
Availability restricted

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 ~q, 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 ~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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