技術者教育のための工学数理の力学教材の改定(18):斜めに取り付けられたバネによる物体の非線形振動の特異摂動法による解析

概要

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We studied numerically a simple mechanical model of nonlinear forced oscillations, following after the workby Koizumi & Oosone (Transactions of the Japan Society of Mechanical Engineers. C 69 (2003), pp.1197-1202). Theyshowed first that chaotic oscillations yield in the model, where a body moves horizontally due to a sinusoidal, externalforcing, being attached to a horizontal damper and a spring. This spring inclined, another end of which is attached to anupper wall fixed, gives rise to nonlinear effects just as a double well type of restoring potential. Nonlinear effects of theinclined spring in free oscillations is evaluated here by numerical solving of initial value problem, numerical integrationof mechanical energy and by means of He's modified Lindstedt-Poincar´e method. The results obtained in the respectivemethods are shown to give sufficient accuracy and consistency in oscillation periods. More detailed analysis by He'smethod in higher orders will be made in a forthcoming paper.
2011-01-31