INTERMITTENCY ROUTE TO CHAOS OF A CANTILEVERED PIPE CONVEYING FLUID WITH A MASS-DEFECT AT THE FREE END

Citation
C. Semler et Mp. Paidoussis, INTERMITTENCY ROUTE TO CHAOS OF A CANTILEVERED PIPE CONVEYING FLUID WITH A MASS-DEFECT AT THE FREE END, Journal of applied mechanics, 62(4), 1995, pp. 903-907
Citations number
29
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanics
ISSN journal
0021-8936
Volume
62
Issue
4
Year of publication
1995
Pages
903 - 907
Database
ISI
SICI code
0021-8936(1995)62:4<903:IRTCOA>2.0.ZU;2-2
Abstract
The nonlinear equations for planar motions of a vertical cantilevered pipe conveying fluid are modified to take into account a small lumped mass added at the free end. The resultant equations contain nonlinear inertial terms; by discretizing the system first and inverting the ine rtia matrix, these terms are transferred into other matrices. In this paper, the dynamics of the system is examined when the added mass is n egative (a mass defect), by means of numerical computations and by the software package AUTO. The system loses stability by a Hopf bifurcati on, and the resultant limit cycle undergoes pitchfork and period-doubl ing bifurcations. Subsequently, as shown by the computation of Floquet multipliers, a type I intermittency route to chaos is followed-as ill ustrated further by a Lorenz return map, revealing the well-known norm al form for this type of bifurcation. The period between ''turbulent b ursts'' of nonperiodic oscillations is computed numerically as well as Lyapunov exponents. Remarkable qualitative agreement, in both cases, is obtained with analytical results.