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Intermittency route to chaos of a cantilevered pipe conveying fluid with a mass defect at the free end. (English) Zbl 0861.73055

The aim is to propose and study a mathematical model describing motion of a cantilevered pipe conveying a fluid. In addition to a lumped end-mass, the authors assume a contribution to the kinetic and potential energies due to the presence of a mass at the free end of the pipe. The concentrated mass gives rise to a Dirac delta function term in a governing nonlinear beam equation. This equation is approximated by means of Galerkin procedure. Such an approximation provides a system of ODEs which the authors solve numerically. A careful bifurcation analysis shows a sequence of periodic doubling bifurcations leading to an intermittency route to chaos when the flow velocity is increased beyond a critical value.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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