Development of Perturbations in a Fluid-Conveying Pipe with Non-uniform Elastic Properties

We consider bending oscillations of a pipe conveying fluid and lying on an elastic foundation with a non-uniform elasticity coefficient. Despite the absence of local absolute instability, there exists a global growing mode, whose structure is associated with the presence of the turning points (Kulikovskii in J Appl Mech Math, 1993). In the present study, we perform numerical modeling of the development of an initial disturbance of the pipe. In a linear formulation, we demonstrate how a disturbance is transformed into a growing eigenmode. In the nonlinear formulation, we show that the growth of the disturbance is limited, while the oscillations become quasi-chaotic, but do not leave the region bounded by the turning points, which are governed by the linearized problem.