Wave Resistance Caused by a Point Load Steadily Moving on the Surface of a Floating Viscoelastic Plate

Abstract

The wave resistance caused by a point load steadily moving on an infinitely extended viscoelastic plate floating on an inviscid fluid is analytically studied, which can be used to describe the response due to the motion of amphibious air-cushion vehicles on the continuous ice sheet on the ocean. The action of concentrated and distributed point loads are both considered. Under the assumptions that the fluid is incompressible and homogeneous and the motion of the fluid is irrotational, the Laplace equation is taken as the governing equation. For the floating plate, the Kelvin–Voigt viscoelastic model is employed. At the plate–fluid interface, linearized boundary conditions are used when the wave amplitude generated is less than its wavelength. The Fourier integral transform is performed to achieve the formal solution. The residue theorem is applied to derive the response of flexural–gravity wave resistance. It is indicated that for a point load with a uniform rectilinear motion, the wave resistance shows a sharp decrease with the increase in the moving speed when the load velocity is greater than the minimum phase velocity. There is no steady wave resistance when the load velocity is smaller than the minimum phase velocity. The effects of different parameters are obtained. Wave resistance decreases with the increasing plate thickness, viscoelastic parameter, and Poisson’s ratio, especially for a small value of viscoelastic parameter.