Exact Solutions of the Free Vibration of a Nonlinear System with a Quadratic Spring : Expressions of the Solution and Trial Methods for the Fourier Coeflicients

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概要

• 論文の詳細を見る

• Using an elliptic function, an exact solution of the free vibration in an oscillatory system with one degree of freedom having a quadratic spring is determined. The system is presumed to be a typical model of the nonlinear system having an asymmetrical spring, in which chaotic phenomena may occur. Few discussions of the problem have been attempted, especially concerning its precise numerical computation, since Duffing presented a remarkable paper in which the symmetrical (cubic spring) case was fully analysed, but less so the quadratic one. For a given frequency, a transcendental equation must be solved to obtain a modulus parameter of the elliptic function. The parameter governs all coefticients of the Fourier expansion of the solution. Three algolithms of the trial method are developed which roughly correspond to the cases of the quasi-linear small vibration, strongly nonlinear slow vibration and the intermediate one. Some numerical results of the solution are presented.

• 一般社団法人日本機械学会の論文
• 1990-12-15

著者

• Tamura Hideyuki

  Department Of Mechanical Engineering For Power Faculty Of Engineering Kyushu Urliversity

• Tamura Hideyuki

  Department Of Biological And Environmental Sciences Faculty Of Agriculture Yamaguchi University

• Li Xiaomin

  Department Of Mechanical Engineering For Power Faculty Of Engineering Kyushu Urliversity

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• Exact Solutions of the Free Vibration of a Nonlinear System with a Quadratic Spring : Expressions of the Solution and Trial Methods for the Fourier Coeflicients

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