Simple solutions to the wave problem on the surface of a fluid with the linear hydroelastic model

The problem of generation of waves on the surface of a water layer placed on an elastic base is considered. It is assumed that the generating source is located inside the elastic half-space. The Podyapolskii approach is used which is based on study of the solutions to the common linear system of equations of the theory of elasticity in the half-space and the theory of water waves linked at the interface by the corresponding boundary conditions. The previously obtained simplified dispersion relation for the water mode with account for the elastic base effect is used to derive a simple integral formula which associates the initial perturbation of a special kind in the elastic half-space and the amplitude of the surface water waves generated by this source. The obtained solutions are compared with the solutions based on the well-known piston model of long wave generation.