Summary
In a previous paper the present authors developed a model describing wave propagation in liquid filled distensible tubes and tested it against impulse experiments involving water filled latex rubber tubes. This model incorporates both dissipative and dispersive mechanism which are absent from the commonly employed linear long wave-length (LLW) theory of haemodynamics. This higher order theory is here employed to study propagation of an impulse in a semi infinite tube, reflection of an impulse from the distal end of a finite length tube, and reflection and transmission of impulses impinging on a function connecting dissimilar liquid filled tubes. Both open and closed type reflections are treated and numerical results presented graphically. To the best of our knowledge this is the first time that such a higher order theory has been employed to treat reflection and transmission of waves in tube systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Newman, D. L., Greenwald, S. E., Denyer, H. T.: Impulse propagation in normal and stenosed vessels. Cardiovasc. Res.15, 190 (1981).
Greenwald, S. E., Newman, D. L.: Impulse propagation through junctions. Med. a. Biol. Eng. a Comput.20, 343 (1982).
Newman, D. L., Greenwald, S. E., Moodie, T. B.: Reflection from elastic discontinuities. Med. a. Biol. Eng. a. Comput.21, 697 (1983).
Greenwald, S. E., Newman, D. L., Moodie, T. B.: Impulse propagation in rubber tube analogues of arterial stenoses and aneurysms. Med. a. Biol. Eng. a. Comput.23, 150 (1985).
Moodie, T. B., Barclay, D. W., Greenwald, S. E., Newman, D. L.: Waves in fluid filled tubes: theory and experiment. Acta Mechanica54, 107–119 (1984).
Young, T.: Hydraulic investigations, subserviant to an intended Croonian lecture on the motion of the blood. Philos. Trans. Roy. Soc. London98, 164 (1808).
Lighthill, M. J.: Waves in fluids. Cambridge University Press 1978.
Pedley, T. J.: The fluid mechanics of large blood vessels. Cambridge University Press 1980.
Moodie, T. B., Barclay, D. W., Greenwald, S. E.: Impulse propagation in liquid filled distensible tubes: theory and experiment for intermediate to long wavelengths. Acta Mechanica59, 47–58 (1986).
Barclay, D. W., Moodie, T. B., Tait, R. J.: Impulse propagation in liquid filled distensible tubes: a two dimensional analysis. Utilitas Mathematica26, 17 (1984).
Crump, K. S.: Numerical inversion of Laplace transforms using a Fourier series approximation. J. ACM23, 89 (1976).
Moodie, T. B., Mainardi, F., Tait, R. J.: Pressure pulses in fluid filled distensible tubes. Meccanica20, 33 (1985).
Author information
Authors and Affiliations
Additional information
With 8 Figures
Rights and permissions
About this article
Cite this article
Moodie, T.B., Barclay, D.W. Wave propagation and reflection in liquid filled distensible tube systems exhibiting dissipation and dispersion. Acta Mechanica 59, 139–155 (1986). https://doi.org/10.1007/BF01181661
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01181661