技術者教育のための工学数理の力学教材の改定(4) : 斜めに取り付けられたバネによる物体の非線形強制振動とカオス

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In this paper, we study numerically a simple mechanical model of nonlinear forced oscillations, following after the work by Koizumi & Oosone (Transactions of the Japan Society of Mechanical Engineers. C 69 (2003), pp.1197-1202). They showed first that chaotic oscillations yield in the model, where a body moves horizontally due to a sinusoidal, external forcing, being attached to a horizontal damper and a spring. This spring inclined, another end of which is attached to an upper wall fixed, gives rise to nonlinear effects just as a double well type of restoring potential. The forcing is modified to include a constant force for which the symmetry of the oscillator may be changed. It is found from the Poincare map obtained for some cases that the route to chaos in this dissipative system is the period doubling and the chaotic motion may occur in a wider range of parameter values. In addition to these, basin boundary problems are solved, so that the chaotic motion is found to depend strongly upon initial conditions given.
沼津工業高等専門学校の論文
2008-01-31