Parametric excitation in non-linear dynamics |
| |
Authors: | T Bakri R Nabergoj F Verhulst |
| |
Institution: | a Mathematics Institute, Utrecht University, PO Box 80.010, Utrecht, TA 3508, The Netherlands b Department of Naval Architecture, Ocean and Environmental Engineering, Via Valerio Trieste 10, I-34127, Italy c Zborovská 41, Praha 5 CZ-15000, Czech Republic |
| |
Abstract: | Consider a one-mass system with two degrees of freedom, non-linearly 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 find 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. |
| |
Keywords: | Dynamical systems Neimark-Sacker bifurcation Averaging method and tori |
本文献已被 ScienceDirect 等数据库收录! |
|