三次元均質等方弾性体動問題の基本解とその応用 : Mindlin 問題その 1

抄録

The displacement potentials to have a new representative form are derived from dynamic governing equations of a three dimentional homogeneous, isotropic elastic medium. We discuss the relation between these potentials and well-known potentials. The fundamental solution in the case of an infinite elastic medium to be excited by a harmonic point load, or a point load with impulsive time dependence at the origin, is obtained and the solution to be called the Dynamic Kelvin solution, is investigated. The simple application, used the fundamental solutions in the harmonic case is performed, and it is discussed that the result is similar to that of the problem for a point load acting normally to the boundary in the interior of a semiinfinite medium. The other fundamental solutions, in impulsive loading, are presented in Fig.4-9, where the wave geometry of the propagation state with dilatational waves and equivoluminal waves are shown, and wave fronts are caught approximately. It has been described, in dfferent static cases, that the method, using the potential H and fundamental solutions, to analyze problems of a semi-infinite elastic medium subjected to a point load, has been general, While methods of synthesis and superposition, using fundamental solutions, need some skillful idea. This paper is the first part of our study, in which the former method is applied to the dynamic analysis of a three dimensional elastic medium.