The response of ice cover to a load moving along a frozen channel

Abstract

Deflections and stresses in an ice cover of a frozen channel caused by a load moving with a constant speed along the channel are studied. The channel is of rectangular cross section. The ice cover is isotropic and clamped to the walls of the channel. The fluid in the channel is inviscid and incompressible. The external load is modeled by a localized smooth pressure distribution moving along the central line of the channel. The ice cover is modeled as a viscoelastic plate. Deflection of the ice and strains in the ice plate are independent of time in the coordinate system moving together with the load. The effect of the channel walls on the ice response is studied. This effect can be significant in experiments with loads moving in ice tanks. The linear hydroelastic problem is solved by using the Fourier transform along the channel and the method of normal modes across the channel. It is found that the presence of the vertical walls of the channel reduces the ice deflection but increases the elastic strains in the ice plate. The effects of the load speed, width and depth of the channel on the hydroelastic response of the ice cover are studied in detail. In contrast to the problem of a load moving on ice sheets of infinite extent, there are infinitely many critical speeds of hydroelastic waves in a frozen channel. Correspondingly, there are many values of the speeds of a moving load at which the stresses in the ice cover are amplified. The obtained deflections and strains in the canned ice cover are compared with the corresponding solutions for the infinite ice plate and with the solutions of simplified problems without account for the dynamic component of the liquid pressure. It is shown that the models of ice response without hydrodynamic component of the pressure provide correct stresses in the ice sheet only for very low speeds of the moving load.