SOLITARY WAVES IN A THICK-WALLED ELASTIC TUBE

In the present work, we studied the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible i nviscid fluid. The effects of wall inertia and shear deformation are t aken into account in determining the inner pressure-inner cross-sectio nal area relation. Using the reductive perturbation technique, the pro pagation of weakly nonlinear waves in the long wave approximation is i nvestigated and the Korteweg-de Vries equation is obtained as the evol ution equation. Due to dependence of the coefficients of the governing Korteweg-de Vries equation on the initial deformation, the material p arameters and the thickness ratio, it is observed that the solution pr ofile changes with these parameters. The numerical calculations indica te that for engineering materials (small alpha) the wave profile gets steepened with increasing thickness ratio, whereas for soft biological tissues the wave profile is not so sensitive to the thickness ratio b ut it is quite sensitive to the material nonlinearity characterized by the coefficient alpha. This shows that for biological tissues the mat erial nonlinearity is more important than the geometrical nonlinearity . (C) 1998 Elsevier Science Inc. All rights reserved.