In-Plane Ice Structure Vibration Analysis by Two-Dimensional Elastic Wave Theory

Abstract

This paper presents a theoretical analysis of an in-plane ice sheet vibration problem due to a circular cylindrical structure moving in the plane of an infinite ice sheet, and computes the ice forces exerted on the structure as the motion occurs. The basic equations are derived from two-dimensional elastic wave theory for a plane stress or plane strain problem. The ice material is treated as a homogeneous, isotropic and linear elastic solid. The resulting initial and boundary value problems are described by two wave equations. One equation governs the ice motion associated with longitudinal wave propagation, and the other governs propagation of transverse waves. The equations are subject to 1) either a fixed or a frictionless boundary condition at the ice structure interface, and 2) a radiation condition at large distance from the structure to ensure the existence of only outward traveling elastic waves. The governing equations are then solved by 1) Fourier transforms, or 2) Laplace transforms, depending on the problem. Closed-form solutions are obtained in terms of Bessel functions. Plots are provided for estimating the ice added mass, the damping, and the unit function response for a circular cylindrical structure vibrating in the horizontal plane of an infinite ice sheet.