自律性Duffing方程式の厳密解とその計算法 : 第3報,準線形振動に対する特性パラメータのべき級数解

概要

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A power series expansion of the characteristic parameter is obtained in terms of the natural frequency, which is defined as an implicit function in a transcendental equation. It plays a central role in calculating the Fourier coefficient of exact solutions. A general algorithm is proposed to obtain the solution in the power series x=Σ b_ny^n to the equation Σ c_nx^n=y. The method is particularly effective when m (the modulus parameter of elliptic functions) approaches zero, which corresponds with the quasi-linear small oscillations in those systems with a hard, a soft or snap-through (half-swing mode) spring. The accuracy of existing (simple) approximate solutions to the autonomous Duffing equation, i.e., the perturbation, the averaging and the (two-term) harmonic balance methods, is examined by comparison with the present exact solutions.
社団法人日本機械学会の論文
1987-11-25