Nonlinear regimes of variation of the shape of an elastic tube containing a flowing fluid

Abstract

A linear and nonlinear analysis of the distributed oscillations of an elastic tube with a fluid flowing in it is developed. The critical flow velocity and the wavelength and oscillation frequency in the tube-flow system at loss of stability are found. The geometrical and physical nonlinearities, the latter related to increase in the Young’s modulus of the tube wall material with increasing strain, are considered. It is shown that four characteristic regimes of change of tube shape are possible: local dilatation, collapse, flexure, and distributed auto-oscillations. The tube oscillations are analyzed numerically for the nonaxisymmetric case. The conditions of existence of these effects in blood vessels are examined.