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Wave propagation through a viscous fluid contained in a prestressed thin elastic tube. (English) Zbl 0764.73065
Summary: A theoretical analysis is presented for the wave propagation through a viscous incompressible fluid contained in a prestressed thin elastic tube. The fluid is assumed to be incompressible and Newtonian, whereas the tube material is considered to be incompressible, isotropic and elastic. Such an elastic tube is subjected to a mean pressure ${P}_{i}$ and the axial force $N$ (or, stretch ratio $\lambda$). Assuming that the disturbance added on this initial deformation is small, the governing differential equations are obtained for the elastic tube and the fluid. A harmonic wave type of solution is sought for these field equations, and the dispersion relation is obtained. Various special cases as well as the general case are throughly investigated, and the present formulation is compared with previous works on the same subject.
##### MSC:
 74L15 Biomechanical solid mechanics 74F10 Fluid-solid interactions 76D33 Waves in incompressible viscous fluids 76Z05 Physiological flows