The transmission of a flexural-gravitational wave through several straight obstacles in a floating plate

Periodic wave processes in a thin elastic plate floating on the surface of an incompressible fluid of finite depth are studied. The plate completely covers the fluid surface and executes flexural oscillations under the action of gravitational waves in the fluid. The system of free oscillations in the plate is disrupted along a set of parallel lines. Rigid clamping of the plate, a sliding fastening and an infinitesimally narrow slit are considered as such disruptions. The apparatus used to construct the solution is quite general, and other disruptions in the elastic properties of a plate or its reinforcement, that are realized with linear boundary-contact conditions, can be treated in a similar way. The transmission and reflection of a harmonic flexural-gravitational wave, that is orthogonally incident on the inhomogeneities in the plate, are studied. Exact analytical representations of the wave fields in the plate and in fluid are obtained and the transmission and reflection coefficients for the incident flexural-gravitational wave are determined. The forces developed in the fastenings are found.