Boundary value problem for fluid-filled elastic tubes

A realistic boundary value problem designed to study wave propagation in thin-walled cylindrical tubes containing inviscid and incompressible fluids is here analysed. One end of the tube is held fixed while the fluid in its interior is subjected to a sudden rise in mean pressure. This pressure increase is applied at the fixed end and is of finite duration. A membrane shell theory for the tube is employed and a detailed analysis of the propagating dispersive pressure pulse is carried out. Both asymptotic and numerical methods are used. The large time asymptotic results, when compared with those obtained from the exact solution by numerical procedures, are shown to give excellent agreement if two terms in the asymptotic expansion are employed.