技術者教育のための工学数理の力学教材の改定(12):斜めに取り付けられたバネによる物体の3D強制非線形振動系の解析

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Linear spring yields force ¡kx where k is the spring constant and x denotes the displacement from equilibriumstate; x > 0 for stretch and x < 0 for contraction. When the two ends of spring are placed in a complicated way, thedisplacement is given by a nonlinear function of the ends' coordinates, which is referred to as "geometrical nonlinearity."We study here some oscillation problems with this nonlinearity, by means of numerical computations. Chaotic solutionshave been found when a damper and an external excitation are taken into account in the one dimensional (1D) problemwith a spring of geometrical nonlinearity. Free oscillation, parametric excitation and external forcing are solved for someinitial value problems of the 2D/3D systems with two and four springs, and the resulting oscillation patterns are reported.The system with multi springs may be formulated to give rise to hybrid nonlinear oscillations.
沼津工業高等専門学校の論文
2009-01-31