Generalization of the Lighthill problem for the viscous fluid filled tubes with complicated wall rheology
A generalization of the Lighthill model of the plane waves propagation along fluid-filled viscoelastic tubes is proposed. The rheological relation of the wall has two relaxation times for strains and stresses. The equations of the generalized model for the averaged pressure, velocity and the cross-sectional area of the tube are obtained. The solution of the equations in the form of the running waves and the dispersion relation are obtained and compared to those for the Lighthill and Shapiro problems, and the viscoelastic Kelvin-Voigt model for the wall material. Numerical calculations for the model parameters corresponded to human circulation system have been carried out. It is shown, the complicated properties of the material allow accounting for both Young and Lame wave modes, and stabilization the modes that were unstable in the case of simpler rheology. The developed model is helpful in performing the numerical calculations on complex models of arterial vasculatures at lower computation time and resources.
Key words: viscoelastic tubes, pulse waves, mathematical modeling, wave dispersion.
Pages of the article in the issue: 67 - 70
Language of the article: Ukrainian
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