Application of two-dimensional approach in mechanical systems subject to longitudinal loadings

The survey of literature carried out from the point of view of the application possibilities of two-dimensional approach in mechanical systems subject to longitudinal loadings is in the paper. The exact theory as well as the approximate ones, and problems formulated for semi-infinite and finite circular cylinders are considered. These problems reduce to analysis of two equations of motion in two spatial variables according to the exact theory, and to the discussion of equations in a simplified form according to suitable approximate theories. The two-dimensional approach reflects better the physical phenomena in a cylinder than the one-dimensional approach, however appropriate methods for its application in discrete-continuous mechanical systems consisting of several rigid bodies and elastic cylindrical elements have not been elaborated yet. Many mathematical difficulties are overcome in the one-dimensional wave approach. So, in the final part of the paper an effective method based on the utilization of the one-dimensional longitudinal waves is described.