区分線形振動系の一般解の大域構造 : 退化した場合の大域表現

概要

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In the previous paper, a global formulation method was proposed for representing the general response solution of piecewise linear oscillator system. In this paper, the method is expanded to further generalized systems such as those whose solutions are contracting with the boundary region or having trapping behaviour. First, after giving the definition of "degenerative" solution, it was made clear that only the acceleration can be discontinuous on the boundary region among the other differentials of those solutions. Secondly, by use of Filippov's definition for the expanded solutions, following specific characteristics regarding the solutions were obtained. (1) While "bounded leap" is keeping positive on the discontinuous point of restoring function, singular local trapping solutions appear which can not be given through ordinal linear solutions. (2) By regarding contact of the solution with the boundary region as non-transeverse crossing in wide sense, proposed global expressions are available even for the contact case. Finally, discussions are devoted to the development of this global formulation. And it leads to unified expression for both of trapping and non-trapping solutions whereby local trapping solutions within the crossing interval are replaced by local "constant" solutions.
一般社団法人日本機械学会の論文
2000-12-25