Waves generated by moving loads on ice plates: Viscoelastic approximations

Abstract

The paper investigates waves generated by the moving loads on ice plates floating on an incompressible fluid. Two different viscoelastic approximations are considered for the ice cover: A model depending on the strain-relaxation time, and a model including a hereditary delay integral. The problem is formulated in terms of the exact dispersion relation and the Dirichlet–Neumann operator connected to the fluid motion. Weakly nonlinear and linear approximations are derived by truncating the Dirichlet–Neumann operator. The Laplace transform is used to find the exact solutions of the linearized problems for the two viscoelastic models considered.