Three-dimensional Bending grativational Waves Generated by moving pertubrations

The fluctuations of the floating ice cover on the surface of which the load moves are considered. The vibrations of the floating ice sheet are based on linearized equations of hydromechanics and linear classical theory of plate vibrations. The ice cover is modeled by a thin elastic isotropic plate taking into account the hydrodynamic pressures on the lower surface of the ice. When moving along the surface of the load plate, waves are formed. Of interest is studying the impact on the movement of load velocity on the amplitudes of created waves. This model is consistent with the results which where obtained by Kobeko P. P. and co-authors during the study and definition of dangerous (critical) velocity and optimal intervals of car movement. And also with the theory of the behavior of the ice cover under load, which was developed in the works of Heisin D. E. It is also consistent with the theory of behavior of ice under load, developed in the works by Heisin D. E. The original problem is to solve the Laplace equation for the speed potential of $\varphi$. Using the Fourier transform on horizontal (spatial) variables, an integral representation for plate bending is obtained. The analysis of the amplitudes of the three-dimensional bending-gravitational waves formed in this case is carried out. If the velocity of the load is $v_{0}<v<v_{1}$, then one system of bending-gravitational waves is formed. These waves cover the entire surface of the plate. The amplitude of the waves propagating ahead of the load is less than the amplitude of the waves behind the load. At $v_{1}<v<(gH)^{\frac{1}{2}}$, three wave systems are formed - transverse, longitudinal and elastic waves. Transverse and longitudinal waves propagate behind the source and have the character of gravitational ship waves. Elastic waves are caused by the elastic forces of the plate and do not form in its absence. The amplitude of elastic waves is greater than the amplitude of transverse and longitudinal waves. Transverse waves have the smallest amplitude. At $v>(gH)^{\frac{1}{2}}$, longitudinal and elastic waves are formed. Transverse waves are not formed. There is an angular zone behind the source in which waves with a attenuation amplitude of $R^{-\frac{1}{2}}$ are not formed. The amplitude of the elastic wave is greater than the amplitude of the longitudinal wave. With an increase in the velocity of the source of disturbances and the thickness of the ice cover, the amplitude of the waves formed decreases.