直接数値積分法による非線形系の周期解の求解 : 運動方程式に不連続関数を含む場合

概要

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The direct numerical integral method (D.N.I.) which is a kind of shooting method, is presented for determining the periodic solutions of nonlinear systems with discontinuous characteristics. The present method is applied to a system with Coulomb's frictions, a system with bilinear stiffness and damping, and a system with preloaded compliance. By comparing the results of this method and the analytical method, it is found that this method yields very accurate results. In the system with Coulomb's frictions, many kinds of periodic solutions, i.e., slip, stick-slip and lockup solutions are obtained. In the other two systems, superharmonic vibrations, subharmonic vibrations and ultra-subharmonic vibrations are obtained by the D.N.I. Moreover, Liapunov numbers are calculated by applying the algorithm to integrate the corresponding variational equation in the D.N.I.
一般社団法人日本機械学会の論文
1993-05-25