二次曲線ばね非線形系における自由振動の厳密解 : その3, フーリエ係数を決定する超越方程式の陽な解表示

概要

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Improved solutions are sought as an extension of the previous papers in which an exact solution as well as its precise numeration of the free vibration in a quadratic spring system are considered. A characteristic parameter, which is a function of the given frequency and governs all the Fourier coefficients, must be determined by solving a transcendental equation usually by employing a trial scheme. Two polynomials are proposed here to give explicitly the characteristic parameter; these formulae are asymptotically exact in cases of a quasi-linear small vibration and of a strongly nonlinear slow vibration. They are obtained by applying the reversion of power series and cover the entire frequency range with a relative error of less than 10^<-14>. Some numerical results are demonstrated and the waveform of the strongly nonlinear slow vibration is composed of a pulse train standing on the unstable equilibrium point. Formulae of reversed power series up to the 15th order are derived and listed.
社団法人日本機械学会の論文
1990-05-25