二次曲線ばね非線形系における自由振動の厳密解 : その1, 解の表示とフーリエ係数の試行解

概要

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An exact solution of the free vibration is determined using an elliptic function, sn , in an oscillatory system with one-degree-of-freedom having a quadratic spring. 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 on the problem have been attempted, especially in its precise numerical computations, after Duffing who studied the symmetrical case (cubic spring) fully but not the quadratic one. For the given frequency, a transcendental equation must be solved to obtain a modulus parameter of the elliptic function. The parameter governs all the coefficients of Fourier expansion of the solution. Three algorithms of the trial method are developed, which roughly correspond to the cases of the quasi-linear small vibration, strongly nonlinear slow vibration and the moderate one, respectively. Some numerical results of the solution are demonstrated.
社団法人日本機械学会の論文
1989-01-25