Transition from the Classical Biot Problem on Cylindrical Wave to the Case of Transversely Isotropic Medium

The problem of the surface harmonic elastic wave propagating along the free surface of a cylindrical cavity in the direction of the cavity axis is considered. In the case of isotropic medium, this problem is classical Biot’s problem of 1952. First, Biot’s pioneer work is described: the analytical part of Biot’s findings is shown in the main fragments. The features: using two potentials and representation of the solution by the Macdonald functions of different indexes. Then, the new direct generalization of Biot’s problem for the case of the transversely isotropic medium is proposed. It includes the new statement and new mathematical procedures. The transition to the transverse isotropy leads to the necessity of using the more complex representations of displacements through two potentials. As a result, the newly stated problem is solved in its analytical part.