半無限弾性体上の円板の動的コンプライアンス問題 : その1.軸対称鉛直振動

Abstract

Vertical simple harmonic oscillation of a circular disc on an elastic half-space is investigated theoretically. The theory is then examined numerically. This problem, dynamic compliance of a circular disc, has not yet been solved in general form ; rigorous formulation is only known in case of a rigid disc. In this paper an extension of this theory is presented. The new theory is derived from an investigation of the elastic medium alone. As a consequence, the result obtained is valid against any deformable discs such as elastic plates. The theory brings eventually a basic relation between the vertical displacement of the disc and the normal stress at the contact surface. It is a linear integral transformation. Its integral kernel, which is obtained explicitly for the first time in the present paper, is expressed as a definite integral of some higher functions which are easily calculated numerically. By solving simultaneously the basic equation presented here and the equation of motion of the disc, one can readily take the dynamical interaction between the disc and the elastic medium into account. The present theory is examined numerically, too, by applying to the case of a rigid disc whose result is known. In spite of the quite different formulation, the present theory surely gives identical solutions.