衝突振動系の動的挙動に関する研究 : 1/n次分数調波解の分岐現象とカオス的挙動

抄録

Taking a simpified mechanical model of the vibro-impact motions as a typical nonlinear system, dynamic behaviour was studied by using a numerical simulation method. First, 1/n harmonic and subharmonic motions are investigated by means of the Poincare mapping technique, and stability analysis is carried out for these motions. In particulary, a symmetric solution and its bifurcation sets are obtained in an explicit form for the system parameters. Second, in order to investigate a qualitative behaviour of 1/n subharmonic motions in the unstable condition, global analysis is carried out by digital simulation. In addition to regular bifurcation, singular bifurcation phenomena based upon discontinuity of mapping can be recognized. Also, transient chaotic behaviour in which the chaotic attractor disappears can be observed.