Demiray, H.; Antar, N. Effects of initial stresses and wall thickness on wave characteristics in elastic tubes. (English) Zbl 0887.73057 Z. Angew. Math. Mech. 76, No. 9, 521-530 (1996). 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. Cited in 2 Documents 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 Keywords:human arteries; large initial static deformations; harmonic waves; power series method; reaction of fluid; dispersion relation; thickness parameter PDFBibTeX XMLCite \textit{H. Demiray} and \textit{N. Antar}, Z. Angew. Math. Mech. 76, No. 9, 521--530 (1996; Zbl 0887.73057) Full Text: DOI References: [1] : Pulsatile blood flow. Mc Graw-Hill, New York 1964. [2] : Blood flow in arteries. The Williams and Wilkins Co., Baltimore 1966. [3] : Biodynamics: Circulation. New York, Springer-Verlag 1984. [4] Lambossy, Helv. Physiol. Acta 9 pp 145– (1951) [5] : Wave propagation in blood flow. In Biomechanics symposium (Ed.: ). American Soc. Mech. Engr. N. Y., 1966, pp. 20–40. [6] : Über erzwungene Wellenbewegungen zäher, inkompressibler Flüssigkeiten in elastischen Rohren. Inaugural-Dissertation, University of Bern 1914. [7] Morgan, J. Acoust. Soc. Am. 26 pp 323– (1954) [8] : An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteris. W. A. D. C. Technical Report, TR 56-614 (1957). [9] Atabek, Biophys. J. 7 pp 480– (1966) [10] Mirsky, Biophys. J. 7 pp 165– (1967) [11] Rachev, J. Biomechanical Engng. ASME 102 pp 119– (1980) [12] Kuiken, J. Fluid Mech. 141 pp 289– (1984) [13] Fung, Am. J. Physiol. 11 pp 620– (1979) [14] Cox, J. Biomech. 8 pp 293– (1975) [15] Demiray, J. Biomech. 5 pp 309– (1972) [16] Demiray, Bull. Math. Biology 38 pp 701– (1976) · Zbl 0334.92012 · doi:10.1007/BF02458644 [17] ; : Theoretical elasticity. Clarendon Press, Oxford 1968. · Zbl 0155.51801 [18] ; : Elastodynamics. Vol. I. Academic Press, New York 1974. [19] Rubinow, J. Fluid Mech. 88 pp 181– (1978) [20] Simon, Circulation Research 30 pp 491– (1972) · doi:10.1161/01.RES.30.4.491 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.