Nonlinear Pressure Waves in a Fluid-Filled Elastic Tube

Abstract

The nonlinear pressure wave propagation in a straight thin elastic tube containing an inviscid incompressible fluid is considered using the shell theories which are extended to the second order of magnitude of deformations. The nonlinear effects being taken into account are due to the convective motion of fluid, nonlinear strains and stress-strain relations. Though our problems are considerably simplified by the shell theories, the resultant equations for the displacements of the middle surface are still complicated. Therefore, further considerations are confined to the asymptotic state in which the system of equations can be reduced to the Korteweg-de Vries (K-dV) equation and the relation between the multi-soliton solutions and peaking and steepening phenomena is discussed.