二次曲線ばね非線形系における自由振動の厳密解 : その2, 準線形微小振動と強非線形低周波振動

概要

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The present study discusses better solutions, as an extension of the previous paper in which the existence of the solution in terms of an elliptic function and three algorithms to obtain the modulus parameter by the trial scheme were proposed. For a quasi-linear case, the modulus is now solved explicitly in terms of the given frequency by using the reversion of power series. For strongly nonlinear case, an algorithm for a high speed trial solution is developed to determine the Fourier characteristic parameter by applying the so-called q-expansion theory. The application also makes it possible to treat the ultra low frequency range for which no usually available formulae overcome the computer difficulty. The numerical results are demonstrated, in which in particular the solutions composed of the pulse train for the strongly nonlinear slow vibration are included. Results due to five different methods are mutually compared to estimate their respective accuracy / optimal territories in the frequency region.
社団法人日本機械学会の論文
1989-04-25