EFFECTS OF INITIAL DEFORMATION IN THIN TUBES ON WAVE REFLECTION AND TRANSMISSION AT MECHANICAL MISMATCH

The aim of this paper is to investigate the reflection and transmissio n of deformations and stress waves in two initially deformed thin diss imilar orthotropic elastic tubes joined longitudinally and containing pulsatile fluid flow. In the undeformed state the tubes have the same radius. In the initially deformed state, the area of the cross-section around the joint varies with axial distance, but far upstream and dow nstream of the joint the cross-sections are essentially uniform. The s egment of joined tube with varying cross-section is approximated as a discontinuous change of the cross sectional area when the wavelength i s long enough compared to the diameter of the tubes. Then superpositio n of two Womersley solutions for a single frequency is used in each tu be, and continuity conditions for both the fluid and the tubes are use d. The effects of the initial stretch ratios on reflection and transmi ssion are illustrated for a blood pulse in a natural artery joined wit h an artificial graft. Numerical calculations for the amplitudes of re flected and transmitted waves at the joint are made, and also for the corresponding energy flow rates. It appears that only the faster of th e two incident waves considered leads to a significant mixing of wave types at the joint. The theoretical approach is justified since it wou ld be extremely difficult to find the stresses at the joint experiment ally. (C) 1995 Academic Press Limited