Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 59, Issue 2, 1997, Pages 165-181

  Demiray, Hilmi ^a  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES;

INCOMPRESSIBLE INVISCID FLUID; PRESTRESSED THIN ELASTIC TUBES; SCHRODINGER EQUATION;

AMPLITUDE MODULATION;

EID: 0031250680     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/59.2.165     Document Type: Article

References (22)

1. PEDLEY, T. J. 1980. The Fluid Mechanics of Large Blood Vessels. Cambridge: University Press.
2. FUNG, Y. C. 1984. Biodynamics: Circulation. New York: Springer.
3. WOMERSLEY, J. R. 1955. Oscillatory motion of a viscous liquid in a thin walled elastic tube I: The linear approximation for long waves. Phil. Mag. 46, 199-219.
4. RACHEV, A, I. 1980. Effects of transmural pressure and muscular activity on pulse waves in arteries. J. Biomech. Engng ASME 102, 119-123.
5. DEMIRAY, H. 1992. Wave propagation through a viscous fluid contained in a prestressed thin elastic tube. Int. J. Engng Sci. 30, 1607-1620.
6. RUDINGER, G. 1970. Shock waves in mathematical models of the aorta. J. Appl. Mech. 37, 34-37.
7. ANLIKER, M., ROCKWELL, R. L. & OGDEN, E. 1971. Nonlinear analysis of flow pulses and shock waves in arteries. Z. angew. Math. Phys. 22, 217-246.
8. TAIT, R. J. & MOODIE, T. B. 1984. Waves in nonlinear fluid filled tubes. Wave Motion 6, 197-203.
9. JOHNSON, R. S. 1970. A nonlinear equation incorporating damping and dispersion. J. Fluid Mech. 42, 49-60.
10. HASHIZUME, Y. 1985. Nonlinear pressure waves in a fluid filled elastic tube. J. Phys. Soc. Japan 54, 3305-3312.
11. YOMOSA, S, 1987. Solitary waves in large blood vessels. J. Phys. Soc. Japan 56, 506-520.
12. ERBAY, H. A., ERBAY, S. & DOST, S. 1992. Wave propagation in fluid filled nonlinear viscoelastic tubes. Acta Mech. 95, 87-102.
13. DEMIRAY, H. 1996. Solitary waves in prestressed elastic tubes. Bull. Math. Biology 58, 939-955.
14. KARPMAN, V. I. 1975. Non-Linear Waves in Dispersive Media. New York: Pergamon Press.
15. RAVINDRAN, R. & PRASAD, P. 1979. A mathematical analysis of nonlinear waves in a fluid-filled viscoelastic tube. Acta Mech. 31, 253-280.
16. ERBAY, H. A. & ERBAY, S. 1994. Nonlinear wave modulation in fluid filled distensible tubes. Acta Mech. 104, 201-214.
17. SCOT, A. C., CHU, F. Y. F. & MCLAUGHLIN, D. W. 1973. Soliton: A new concept in science, Proc. IEEE 61, 1443-1483.
18. LAMB, G. L., JR. & MCLAUGHLIN, D. W. 1980. Aspect of soliton physics. In Solitons (ed. R. K. Bullough & P. J. Caudrey). Berlin: Springer.
19. DEMIRAY, H. 1972. On the elasticity of soft biological tissues. J. Biomech. 5, 309-311.
20. FUNG, Y. C. 1972. Stress-strain history relation of soft tissues in simple elongation, in Biomechanics: Its Foundations and Objectives (ed. Y. C. Fung, N. Peronne & M. Anliker). Prentice Hall: Englewood Cliffs.
21. DEMIRAY, H. 1976. Large deformation analysis of some basic problems in biophysics. Bull. Math. Biology 38, 701-711.
22. SIMON, B. R., KOBAYASHI, A. S., STRADNESS, D. E. & WIEDERHIELM, C. A. 1972. Re-evaluation of arterial constitutive laws. Circulation Research 30, 491-500.