The response of two-degree-of-freedom systems with quadratic and cubic non-linearities to multifrequency parametric excitations

Abstract The response of two d.o.f. systems with quadratic and cubic non-linearities to multi-frequency parametric excitations is determined by using the method of multiple scales. Four first-order ordinary differential equations are derived to describe the modulation of the amplitudes and the phases when principal parametric resonances of both modes and combination resonances of the additive and difference type occur simultaneously. In all cases the steady state solutions and their stability are determined. Numerical results depicting the various resonances are presented.

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