THE PROBLEM ON THE DYNAMICS OF A HOLLOW PRISM OF A RECTANGULAR CROSS SECTION

In the article, the process of propagation of non-stationary waves in hollow rectangular semi-infinite prisms is studied for the first time. It is believed that in all 8 sides there are mixed boundary conditions, and impact is made on the end face of this prism. In the papers (1-3), using the integral transformations and replacing the sought values (three displacement components) through new successfully chosen functions (wave potentials), the system of three-dimensional Lame equations is reduced to the system of Bessel equations. On the other hand, it is well known that the selected mixed conditions on the surface of the body allow us to separate the values of different waves (longitudinal and transverse) on the same surface, i.e. all these waves propagate independently of each other. These two circumstances make it possible to obtain a new boundary value problem for each potential- function, separately. Solutions of these boundary-value problems for a whole prism are obtained, and for the selected boundary conditions of this article (sliding contact conditions). A kind of method was used that made it possible to generalize the resulting solution for the entire prism in the case of a hollow prism.