Influence of narrow cylindrical cavities on the wave field excited by a concentrated force in an elastic space (Q1067827)

An elasticity problem is considered concerning the excitation of a wave field in a space weakened by a system of cylindrical cavities of small radius with rigid walls, with a concentrated force applied to a certain point of the space outside the shafts and varying sinusoidally. The solution of this problem is constructed by the principle of superposing the solutions of the following problems: the non-axisymmetric vibrations of an elastic space subjected to an oscillating concentrated force (problem 1); the wave field that occurs in an elastic space perforated by a system of narrow cavities vibrating under the effect of a sinusoidally varying stress applied to their walls (problem 2). We also apply the method elucidated to the investigation of the displacement field in an elastic space equipped with a system of elastic cylindrical inclusions of small diameter, or a system of cavities filled with liquid or a viscoelastic medium.