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DOI: 10.23671/VNC.2017.1.5822

Building the Solution of the Lame Problem for a Cylinder with a Spiral Anisotropy and its Applications in Hemodynamics of Arterial Vessels

Portnov E. N. , Ustinov Yu. ј.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 1.
Abstract:
A cylinder with spiral anisotropy may be presented, in particular, as a result of spiral wrapping of a cylindrical surface by layers of thin threads of rigid material with simultaneous covering by a polymer material. Thus, there will be locally transversely isotropic composite material with a symmetry axis directed tangentially to helical spirals; in order to determine its elastic characteristics, one can use homogenization methods. To construct a mathematical model of propagation of sphygmic"pressure waves'' in arterial vessels whose walls possess spiral anisotropy, we give a description of the method to calculate a radial stiffness and phase velocity of a certain wave. In the same way, we present a comparative analysis of radial stiffness values, various theories and calculation results illustrating the dependency of rigidity and phase velocity on geometric parameters.
Keywords: wave pressure, helical anisotropy, radial stiffness, the phase velocity.
Language: Russian Download the full text  
For citation: Portnov E. N., Ustinov Yu. ј. Building the Solution of the Lame Problem for a Cylinder with a Spiral† Anisotropy and its Applications in Hemodynamics of Arterial Vessels. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp.3-11. DOI 10.23671/VNC.2017.1.5822
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