Investigation on the effects of versatile deformating bed on a water wave diffraction problem

A hydroelastic model is considered to examine the proliferation of water waves over little deformation on a versatile seabed. The versatile base surface is modelled as a thin large plate and depends upon Euler-Bernoulli beam equation. In such circumstances, two different modes of time-harmonic proliferating waves exist rather than one mode of proliferating waves for any particular frequency. The waves with smaller wavenumber proliferate along the free-surface and the other with higher wavenumber spreads along the versatile base surface. The expression for first and second-order potentials and, henceforth, the reflection and transmission coefficients upto second-order for both modes are acquired by the strategy in view of Green's function method. A fix of sinusoidal swells is considered for instance to approve the scientific outcomes. It is seen that when the train of occurrence waves engenders because of the free-surface unsettling influence or the flexural wave movement in the fluid, we generally acquire the reflected and transmitted vitality exchange from the free-surface wave mode to the flexural wave mode. Further, we understand that the practical changes in the flexural unbending nature on the versatile base surface have a remarkable effect on the issue of water wave proliferation over small bottom distortions.