|
|
|
Nonlinear waves in a fluid-filled thin viscoelastic tube |
| Zhang Shan-Yuan(张善元) and Zhang Tao(张涛)† |
| Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China |
|
|
|
|
Abstract In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin–Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid–liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent $\alpha$ of the perturbation parameter in Gardner–Morikawa transformation according to the order of viscous coefficient $\eta$, three kinds of evolution equations with soliton solution, i.e. Korteweg–de Vries (KdV)–Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
|
Received: 03 March 2010
Revised: 07 May 2010
Accepted manuscript online:
|
|
PACS:
|
47.35.Fg
|
(Solitary waves)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10772129). |
Cite this article:
Zhang Shan-Yuan(张善元) and Zhang Tao(张涛) Nonlinear waves in a fluid-filled thin viscoelastic tube 2010 Chin. Phys. B 19 110302
|
| [1] |
Yang H L, Song J B, Yang L G and Liu Y J 2007 Chin. Phys. 16 3589
|
| [2] |
Lighthill J 1978 Waves in Fluids (Cambrige: Cambrige University Press) p231
|
| [3] |
Hashizume Y 1985 J. Phys. Soc. Japan 54 3305
|
| [4] |
Demiray H 2002 Appl. Math. Comput. 133 29
|
| [5] |
Demiray H 2008 Int. J. Non-linear Mech. 43 241
|
| [6] |
Duan W S, Wang B R and Wei R J 1997 Phys. Rev. E 55 1773
|
| [7] |
Zhang T and Zhang S Y 2009 Mech. Engineer. 31 25 (in Chinese)
|
| [8] |
Fung Y C 1997 Biomechanics: Circulation (New York: Spinger-Verlag) p108
|
| [9] |
Yao R X, Jiao X Y and Lou S Y 2009 Chin. Phys. B 18 1821
|
| [10] |
Zhang H P, Li B, Chen Y and Huang F 2010 Chin. Phys. B 19 020201
|
| [11] |
Pedley T J 1980 The Fluid Mechanics of Large Blood Vessels (London: Cambridge University Press)
|
| [12] |
Olson R M 1968 J. Appl. Phys. 24 563
|
| [13] |
McDonald D A 1974 Blood Flow in Arteries (London: Edward Amold) p259 endfootnotesize
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
