Interaction of a Flexural-Gravity Wave with a Vertical Rigid Plate Built in a Floating Elastic Plate

Abstract

The linear two-dimensional problem of interaction between an hydroelastic wave propagating along an elastic floating ice plate with built-in vertical rigid plate is studied. The fluid under the ice is inviscid and incompressible. The fluid depth is finite. The deflection of the ice plate is described by the linear theory of thin elastic plates. The flow under the ice is potential. The total velocity potential is decomposed into the potential of the incident wave, even potential caused by the vertical motion of the rigid plate, and an odd potential caused by the rotation of the rigid plate. The vertical mode method is used. The third potential is obtained by solving a mixed boundary-value problem numerically using Chebyshev polynomials. The solution is validated by analysis of its convergence. The first and second potentials, and the corresponding deflections and strains of the ice plate, are obtained analytically. The motions of the rigid plate, as well as deflection and strains in the floating plate, are numerically analyzed. It is shown that the rotation of the rigid plate due to the incident wave is the main factor of increasing strains in the ice plate.