Homoclinic orbits in the dynamics of articulated pipes conveying fluid
- 1 August 1991
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 4 (3) , 747-774
- https://doi.org/10.1088/0951-7715/4/3/007
Abstract
A model is considered representing an elastically jointed pair of articulated pipes conveying fluid. The motion is described by a four-component system of autonomous ordinary differential equations. Numerical techniques are used to investigate changes in the dynamics as two parameters are varied. These parameters represent the fluid flow-rate and a form of symmetry-breaking. Evidence is found that the global bifurcation picture is surprisingly complicated, involving chaos and two types of homoclinic behaviour: namely, Sil'nikov homoclinic orbits to a saddle-focus stationary point, and homoclinic tangencies to periodic orbits. Local theory respective to each type of homoclinicity is reviewed and compared with the numerical results.Keywords
This publication has 26 references indexed in Scilit:
- Shilnikov Dynamics in a Passive Q -Switching LaserEurophysics Letters, 1988
- Asymptotic chaosPhysica D: Nonlinear Phenomena, 1985
- Interactions Between Self and Parametrically Excited Motions in Articulated TubesJournal of Applied Mechanics, 1984
- On the rate of approach to homoclinic tangencyPhysics Letters A, 1982
- Bifurcations in Three-Dimensional Motions of Articulated Tubes, Part 1: Linear Systems and SymmetryJournal of Applied Mechanics, 1982
- Parallel Flow-Induced Vibrations and Instabilities of Cylindrical StructuresThe Shock and Vibration Digest, 1974
- Instabilities of a Spatial System of Articulated Pipes Conveying FluidJournal of Fluids Engineering, 1974
- The Dynamic Behavior of Articulated Pipes Conveying Fluid With Periodic Flow RateJournal of Applied Mechanics, 1974
- Dynamics of a system of articulated pipes conveying fluid - II. ExperimentsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1961
- Dynamics of a system of articulated pipes conveying fluid - I.TheoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1961