Abstract
In this work a theoretical analysis is presented for wave propagation ina thin-walled prestressed elastic tube filled with a viscous fluid. Thefluid is assumed to be incompressible and Newtonian, whereas the tubematerial is considered to be incompressible, isotropic and elastic.Considering the physiological conditions that the arteries experience, sucha tube is initially subjected to a mean pressure Pi and anaxial stretch λz. If it is assumed that in the course ofblood flow small incremental disturbances are superimposed on this initialfield, then the governing equations of this incremental motion are obtainedfor the fluid and the elastic tube. A harmonic-wave type of solution issought for these field equations and the dispersion relation is obtained.Some special cases, as well as the general case, are discussed and thepresent formulation is compared with some previous works on the samesubject.
Similar content being viewed by others
References
D.A. McDonald, Blood Flow in Arteries, Baltimore: Williams and Wilkins (1966) pp. 496.
Y.C. Fung, Biodynamics: Circulation. New York: Springer Verlag (1984) pp. 404.
P. Lambossy, Aperçu et historique sur le probléme de la propagation des ondes dans un liquide compressible enfermé dans un tube élastique. Helv. Physiol. Acta 9 (1951) 145–161.
R. Skalak, Wave propagation in blood flow. In: Biomechanics Symposium, Y. C. Fung (ed.), pp. 20–46, ASME, New York (1966).
K. Witzig, Über erzwungene Wellenbewegungen Zaher, inkompressibler Flüssigkeiten in elastischen Rohren. Inaugural Dissertation, University of Bern (1914).
G.W. Morgan and J.P. Kiely, Wave propagation in a viscous liquid contained in a flexible tube. J. Acoust. Soc. Am. 26 (1954) 323–328.
J.R. Womersley, Oscillatory motion of a viscous liquid in a thin walled elastic tube. I: The linear approximation for long waves. Phil. Mag. 46 (1955) 199–219.
H.B. Atabek and H.S. Lew, Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube. Biophysical J. 6 (1966) 481–503.
I. Mirsky, Wave propagation in a viscous fluid contained in an orthotropic elastic tube. Biophysical J. 7 (1967) 165–186.
H.B. Atabek, Wave propagation through a viscous fluid contained in a tethered, initially stressed orthotropic elastic tube. Biophysical J. 8 (1968) 626–649.
A.I. Rachev, Effect of transmural and muscular activity on pulse waves in arteries. J. Biomech. Engng 102 (980) 119–123.
G.D.C. Kuiken, Wave propagation in a thin walled liquid-filled initially stressed tube. J. Fluid Mech. 141 (1984) 289–308.
H. Demiray, Stresses in ventricular wall. J. Appl. Mech., Trans. ASME 98 (1976) 194–197.
R.H. Cox, Anisotropic properties of the canine carotid artery in vitro. J. Biomechanics 8 (1975) 293–300.
B.R. Simon, A.S. Kobayashi, D.E. Strandness and C.A. Wiederhielm, Re-evaluation of arterial constitutive laws. Circul. Res. 30 (1952) 491–500.
A.E. Green and W. Zerna, Theoretical Elasticity. Oxford: Clarendon Press (1968) pp. 457.
A.C. Eringen and E.S. Şuhubi, Elastodynamics, Vol. I. New York: Academic Press (1974) pp. 341.
H.F. Bauer, S.T. Metten and J. Seikmann, Dynamical behavior of distensible fluid lines carrying a pulating incompressible liquid. ZAMM 60 (1980) 221–234.
H.A. Erbay, S. Erbay and H. Demiray, Effect of prestress on pulse waves in arteries. ZAMM 67 (1987) 473–485.
H. Demiray and A. Ercengiz, Wave propagation in a prestressed elastic tube filled with a viscous fluid. Int. J. Engng. Sci 29 (1991) 575–585.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Demiray, H., Antar, N. Harmonic waves in a prestressed thin elastic tube filled with a viscous fluid. Journal of Engineering Mathematics 32, 305–320 (1997). https://doi.org/10.1023/A:1004250431638
Issue Date:
DOI: https://doi.org/10.1023/A:1004250431638