Motion due to fundamental singularities in finite depth water with an elastic solid cover

Motion due to fundamental line and point singularities with time-dependent strengths submerged in water with an elastic solid cover is investigated assuming linear theory. The cover is of very small thickness and uniform area density. The problems are formulated as initial value problems and the Laplace transform technique is employed to obtain their solutions. For time-harmonic source strength, the steady-state development of the potential functions demonstrates the existence of outgoing progressive waves of any frequency under the solid cover. Alternative forms of the functions for their numerical evaluations are also obtained. Graphs of some particular integrals appearing in the representations of the potential functions are presented, which confirms that the expressions thus derived are suitable for numerical computation for all possible combinations of the positions of the field point and the source point.