Abstract
A system of second order equations with weak quadratic and cubic non-linearities is considered. Simultaneous parametric and external (forcing) excitations act on the system, each including multiple harmonic components with independent amplitudes, frequencies and phases. Attention is focused on resonances involving two frequencies from one of the excitations and one frequency from the other. Results are obtained by the method of multiple scales. Figures are presented which illustrate the behavior of the steady state response amplitude as a function of the excitation amplitudes and the relative values of the excitation frequencies.
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