Abstract
Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.
Highlights
The walls of a tube are described with complete membrane model
Models that describe waves in elastic tubes are of great interest for technical and biological applications
Equations based on the hyperelastic model and the complete membrane model are analyzed
Summary
Models that describe waves in elastic tubes are of great interest for technical and biological applications. Equations based on the hyperelastic model and the complete membrane model are analyzed. Such equations were derived in [1] and analytically investigated in [2] and [3]. The equations of wave motion of the walls of an elastic incompressible cylindrical tube with fixed internal and external pressure are given by [2]. V is the fluid velocity, ρ f is the fluid density
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
