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Parametrically excited nonlinear systems: A comparison of two methods. (English) Zbl 1012.65141
Summary: Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters. The results obtained by the two methods are in excellent agreement. Numerical solutions are carried out and graphical representations of the results are presented and discussed.

65P30 Numerical bifurcation problems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
37M20 Computational methods for bifurcation problems in dynamical systems
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