This paper shows the mechanism of instability and chaos in acantilevered pipe conveying steady fluid. The pipe underconsideration has added mass or a nozzle at the free end. TheGalerkin method is used to transform the...This paper shows the mechanism of instability and chaos in acantilevered pipe conveying steady fluid. The pipe underconsideration has added mass or a nozzle at the free end. TheGalerkin method is used to transform the original system into a setof ordinary differential equations and the standard methods ofanalysis of the discrete system are introduced to deal with theinstability. With either the nozzle parameter or the flow velocityincreasing, a route to chaos can be observed very clearly: the pipeundergoing buckling (pitchfork bifurcation), flutter (Hopfbifurcation), doubling periodic motion (pitchfork bifurcation) andchaotic motion occurring finally.展开更多
基金the National Key Projects of China under grant No.PD9521907Science Foundation of Tongji University under grant No.1300104010
文摘This paper shows the mechanism of instability and chaos in acantilevered pipe conveying steady fluid. The pipe underconsideration has added mass or a nozzle at the free end. TheGalerkin method is used to transform the original system into a setof ordinary differential equations and the standard methods ofanalysis of the discrete system are introduced to deal with theinstability. With either the nozzle parameter or the flow velocityincreasing, a route to chaos can be observed very clearly: the pipeundergoing buckling (pitchfork bifurcation), flutter (Hopfbifurcation), doubling periodic motion (pitchfork bifurcation) andchaotic motion occurring finally.
