Lukomsky D. Hydroelastic instability in elastic liquid-filled tube under pressure pulse wave propagation

The thesis deals with a theoretical analysis of the instability phenomenon which appears in a liquid-filled elastic cylindrical tube, which is preliminary stressed, in the case of pulse pressure wave propagation. Nonlinear models "liquid-shell" and "liquid-hyperelastic isotropic body", applied in the thesis, describe the propagation of a real heart-generated pulse wave in vessels of a living organism. The instability is found to appear after exceeding of the certain threshold value by a stationary uniform (transmural) pressure. This fact is in correspondence with known experimental data obtained on mammals. In the framework of the model "liquid-shell" the dispersion law for a pressure wave is obtained in analytical form. Also such basic parameters of the instability as a characteristic length, a threshold value for the transmural pressure and a corresponding wavelength are obtained in explicit form. As for the more general model "liquid-hyperelastic isotropic body", used for thicker tubes as compared to shells, the existence of two instability domains relative to the transmural pressure is revealed. The first domain has characteristic lengths for each value of the transmural pressure. The second domain is characterized by the presence of waves with a negative group velocity. It is shown that a limiting process to the shell theory leads to disappearance of the first domain. This means that the less general shell theory is able to describe only one domain, which is characterized by a negative group velocity. The numerical estimate of the results based on real hydroelastic parameters of a blood-vascular system is conducted. It is revealed that the instability is absolutely real phenomenon during heart-generated pulse wave propagation in arteries of a mammal's cardiovascular system. Also strong dependence of a velocity of long pulse wave propagation on the transmural pressure is obtained in the domain of high pressures, which has an effect on blood circulation in the cases of hypertonia.