衝突振動系における周期解の厳密な大域表現 : 切り換え時刻のみをパラメータとした陽表示(<小特集>機械系における非線形力学と解析法)

概要

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This paper gives exact and global representation of all periodic solutions appering in 1-DOF vibro-impacting system. The previously derived form of periodic solution by authors can be represented as superposition of periodic solution for linearized system and finite number of continuous periodic functions which is evaluated by equivalent impulsive responses caused by nonlinearity. However, it is not practical, because determination of impact velocities characterising periodic solutions includes infinite product and summation procedures in the form. To avoid this difficulties, relation between two types of representation of periodic solutions, traditional and newly one by authors, is reconsidered. As a result, it is clarified that transcendental equations for periodic connecting conditions in these representations can be mutually transformed by a pair of linear transfomations. According to apply this fact, the finite product and summation scheme determining impact velocities of periodic solutions is derived.
一般社団法人日本機械学会の論文
2007-04-25