球殼振動時の一般解 : その1・理論式誘導と厳正解

概要

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This paper is concerned with the general solutions of spherical shell in state of free vibrations. First of all, setting on the general equations of spherical shell, which contain all necessary solutions with the introduction of following functions, on the basis of displacement components, [numerical formula] [numerical formula] authers got general solutions of free vibrations of spherical shell. But for the convenience of practical uses, expression method with stress function is considered for this state, secondarily. After the explanation that the expression with stress function does not give all necessary solutions even in static state, that expression was expanded to kinematic state. Comparing this expression with X, Y-expression, authers compensate lacked solutions from solutions of X, Y-exp. Setting stress resultants with stress functions as follows, [numerical formula] [numerical formula] [numerical formula] authers get[numerical formula] as necessary condition, but in this case compatibility condition is identically sufficed and it becomes as follows, [numerical formula] Therefore the lack of two solutions is apparently expected. Then from the comparison with X, Y-expression solutions, solutions(X=0, Y≠0) where Y: solutions of [numerical formula] must be compensated. Here all general solutions of spherical shell in state of free vibrations are shown as the expression of Legendre Bi-Function.
社団法人日本建築学会の論文
1963-03-30