Transformation of a Pressure Pulse in a Fluid-Filled Cylindrical Elastic Shell

The influence of a tubular elastic insert of finite length in a fluid-filled elastic shell on the propagation of a pressure pulse generated at a certain distance from the insert is investigated. The Laplace integral transform is used to solve the corresponding mathematical problem. Analytical solutions are first obtained in each separate domain of the hydroelastic system, subject to the coupling boundary conditions, and then the Laplace transforms are inverted numerically. The influence of the geometrical parameters of the insert and the shell on the pressure distribution in the fluid, the radial displacement, the bending moments, and the shearing forces are analyzed in detail both quantitatively and qualitatively. It is shown that the transmission of the pressure pulse in the junctions of the insert with the shell is accompanied by highly localized stress concentration there, which is several orders of magnitude greater than in the homogeneous shell.