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Effects of initial stresses and wall thickness on wave characteristics in elastic tubes. (English) Zbl 0887.73057

Summary: Employing the theory of small deformation superimposed on large initial static deformations, the propagation of harmonic waves in an initially stressed thick elastic tube filled with a viscous fluid is studied. Due to variability of the coefficients of the resulting differential equation of the tube, the field equations are solved by a power series method. Utilizing the properly posed boundary conditions that characterize the reaction of fluid with the tube wall, the dispersion relation is obtained as a function of initial deformations and geometrical characteristics. The dispersion equation is examined analytically, whenever it is possible, and numerically, and the results are depicted on some graphs. It is observed that wave speeds increase with thickness parameter.

MSC:

74L15 Biomechanical solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
92C10 Biomechanics
74J10 Bulk waves in solid mechanics
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References:

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