Nonlinear hydroelastic waves traveling in a thin elastic plate floating on a two-layer fluid

Effects of the sharp stratification of fluid density on the nonlinear hydroelastic waves traveling in an infinite elastic plate floating on a two-layer inviscid fluid are analytically investigated with the aid of the homotopy analysis method. Under the assumptions that the upper and lower fluid layers with different constant densities are incompressible and the motion is irrotational, the problem is formulated within the frame of the potential flow theory. The convergent series solutions for the velocity potentials, the plate deflection and the interfacial elevation are derived, from which the interaction between surface hydroelastic waves and interfacial gravity waves is studied. The influences of different physical parameters, including the density ratio and the depth ratio of the fluid layers, Young's modulus and the thickness of the plate on the progressive waves are discussed. It is found that the increment of those plate parameters has slight influence on the interfacial wave elevation and apparently changes the plate deflection. A larger density ratio or depth ratio of the fluid layers can reduce the plate deflection and the interfacial wave elevation.