WAVE-PROPAGATION IN FLUID FILLED NONLINEAR VISCOELASTIC TUBES

The present work considers one dimensional wave propagation in an infinitely long, straight and homogeneous nonlinear viscoelastic tube filled with an incompressible, inviscid fluid. In order to include the geometric dispersion in the analysis, the tube wall inertia effects are added to the pressure-area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long-wave approximation is examined. In the long-wave approximation, a general equation is obtained, and it is shown that by a proper scaling this equation reduces to the well-known nonlinear evolution equations. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained. In the absence of nonlinear viscoelastic effects all the equations reduce to those of the linear viscoelastic tube.