El-Bassiouny, A. F. Parametrically excited nonlinear systems: A comparison of two methods. (English) Zbl 1012.65141 Int. J. Math. Math. Sci. 32, No. 12, 739-761 (2002). 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. Cited in 1 Document MSC: 65P30 Numerical bifurcation problems 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 37M20 Computational methods for bifurcation problems in dynamical systems Keywords:comparison of methods; subharmonic resonance; two-degree-of-freedom systems; multiple scales; generalized synchronization; stability PDFBibTeX XMLCite \textit{A. F. El-Bassiouny}, Int. J. Math. Math. Sci. 32, No. 12, 739--761 (2002; Zbl 1012.65141) Full Text: DOI EuDML