Parametric Excitation in Nonlinear Dynamics
نویسنده
چکیده
Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution may emerge, there are also cases where the trivial solution is stable and co-exists with a stable periodic solution; if both the trivial solution and the periodic solution(s) are unstable we nd an attracting torus with large amplitudes by a Neimark-Sacker bifurcation. The results of the harmonic balance method and averaging are compared, as well as the results on the Neimark-Sacker bifurcation obtained by the numerical software package CONTENT and by averaging. In all cases we have good agreement.
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