An examination of a subsurface impact on a floating ice sheet

An examination was made of the influence that various parameters impose upon the structural dynamics of a floating ice sheet due to the initial impact of a large mass. The Ritz method was employed to formulate a simple shape function to approximate a solution of the plate equation, representing the static displacement of a floating ice sheet and obtaining a spring stiffness associated with bending. The fundamental frequency of the plate-fluid system was obtained by the principle of minimum potential energy utilizing the simple shape function. The fluid inertia was incorporated in the kinetic energy of the system by assuming the mass of a hemispherical volume of fluid, associated with the effective radius of the displaced shape would be distributed as a function of the displaced shape of the plate. The effective mass of the entire plate-fluid system was then obtained by equating the fundamental frequency to the circular frequency of a single degree-of-freedom spring-mass system.; A dynamic formulation of a two degree-of-freedom system was made with a simplification of the local contact subsystem involving a linear approximation for the local crushing behavior of underside of the ice plate due to contact with an impact structure. Speculation that the fluid inertia influence will completely dominate the dynamic behavior of the ice plate, creating a huge disparity between the two masses, lead to effectively splitting the proposed 2 degree-of-freedom spring-mass system into two separate 1 degree-of-freedom systems. Each of these two separate systems provided solutions for different issues of the study.; An inelastic collision between the effective plate-fluid mass and that of the impact structure, a submarine in this particular study, represents the global impact loading that influences the general bending of the ice plate. The influence of the local crushing deformation on the underside of the ice plate was found by both a Hertz contact solution, the case of a spherical radius contacting a massive plane surface, and the linear approximation for the single degree-of-freedom spring-mass contact where the plate-fluid system is the ground.