技術者教育のための工学数理の力学教材の改定(7): 斜めに取り付けられたバネによる物体と振子の非線形強制振動とカオス

概要

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We study numerically a mechanical model of nonlinear forced oscillations, following after the work byKoizumi & Oosone (Transactions of the Japan Society of Mechanical Engineers. C 69, pp.1197-1202). In the model, abody (cart) moves horizontally due to a sinusoidal, external forcing, being attached to a horizontal damper and a spring.This spring works as a double well type of restoring potential with geometrical nonlinearity. Here is taken into account aconstant force for which the symmetry of the oscillator may be changed. It is found from the Poincar´e map obtained thatthe route to chaos in this dissipative system is the period doubling and the chaotic motion may occur in a wider range ofparameter values. Including a tuned pendulum damper, the chaotic motion may become dispersive, so that the pendulumacts to suppress the oscillation. Bubbles (antimonotonicity) and hysteresis effects are found to arise.
沼津工業高等専門学校の論文
2009-01-31