Forced Vertical Vibration of Rigid Discs with Arbitrary Embedment

Abstract

This paper is concerned with the investigation of the forced time‐harmonic vertical vibration of a rigid disc embedded at an arbitrary depth in a semi‐infinite medium. By virtue of transform methods, the generalized mixed boundary‐value problem is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. With the aid of contour integration, the governing integral equation is solved numerically. Selected results for the complex compliance are presented to illustrate the various effects of embedment on the dynamic response. In addition to furnishing a unified view of the static and dynamic solutions for zero and infinite embedments, the present analysis reveals a dynamic boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general.