Dynamics of cantilevered pipes conveying fluid. Part 1: Nonlinear equations of three-dimensional motion

Journal of Fluids and Structures

Volumn 23, Issue 4, 2007, Pages 545-567

  Wadham Gagnon, M ^a   Paidoussis M P ^a   Semler, C ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

3D motions; Additional end mass; Additional intraspan spring support; Cantilevered; Hamilton's principle; Nonlinear equations; Pipe conveying fluid

Indexed keywords

COMPUTER SIMULATION; CONVEYING; EQUATIONS OF MOTION; FLUID DYNAMICS; GALERKIN METHODS; HAMILTONIANS; NONLINEAR EQUATIONS;

ADDITIOAL INTRASPAN SUPPORT; ADDITIONAL END-MASS; CANTILIVERED PIPES; PIPE CONVEYING FLUID;

PIPELINES;

COMPUTER SIMULATION; CONVEYING; EQUATIONS OF MOTION; FLUID DYNAMICS; GALERKIN METHODS; HAMILTONIANS; NONLINEAR EQUATIONS; PIPELINES;

EID: 34047264848     PISSN: 08899746     EISSN: 10958622     Source Type: Journal    
DOI: 10.1016/j.jfluidstructs.2006.10.006     Document Type: Article

References (25)

1. Bajaj A.K., and Sethna P.R. Flow induced bifurcations to three-dimensional oscillatory motions in continuous tubes. SIAM Journal of Applied Mathematics 44 (1984) 270-286
2. Benjamin T.B. Dynamics of a system of articulated pipes conveying fluid, I. Theory. Proceedings of the Royal Society A261 (1961) 457-486
3. Benjamin T.B. Dynamics of a system of articulated pipes conveying fluid, II. Experiments. Proceedings of the Royal Society A261 (1961) 487-499
4. Copeland G.S., and Moon F.C. Chaotic flow-induced vibration of a flexible tube with end mass. Journal of Fluids and Structures 6 (1992) 705-718
5. Feodos'ev V.P. Vibration and stability of a pipe when liquid flows through it. Inzhenernyi Sbornik 10 (1951) 169-170
6. Gregory R.W., and Pai{dotless}̈doussis M.P. Unstable oscillations of tubular cantilevers conveying fluid-I. Theory. Proceedings of the Royal Society A293 (1966) 512-527
7. Gregory R.W., and Pai{dotless}̈doussis M.P. Unstable oscillations of tubular cantilevers conveying fluid-II. Experiments. Proceedings of the Royal Society A293 (1966) 528-542
8. Housner G.W. Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics 19 (1952) 205-208
9. Lundgren T.S., Sethna P.R., and Bajaj A.K. Stability boundaries for flow induced motions of tubes with an inclined terminal nozzle. Journal of Sound and Vibration 64 (1979) 553-571
10. Modarres-Sadeghi, Y., Semler, C., Wadham-Gagnon, M., Pai{dotless}̈doussis, M.P., 2007. Dynamics of cantilevered pipes conveying fluid. Part 3: three-dimensional dynamics in the presence of an end-mass. Journal of Fluids and Structures 23, 589-603.
11. Pai{dotless}̈doussis M.P. The 1992 Calvin Rice Lecture: some curiosity-driven research in fluid-structure interactions and its current applications. ASME Journal of Pressure Vessel Technology 115 (1993) 2-14
12. Pai{dotless}̈doussis M.P. Fluid-Structure Interactions: Slender Structures and Axial Flow (1998), Academic Press, London
13. Pai{dotless}̈doussis M.P., and Li G.X. Pipes conveying fluid: a model dynamical problem. Journal of Fluids and Structures 7 (1993) 137-204
14. Pai{dotless}̈doussis M.P., and Luu T.P. Dynamics of a pipe aspirating fluid such as might be used in ocean mining. ASME Journal of Energy Resources Technology 107 (1985) 250-255
15. Pai{dotless}̈doussis M.P., and Semler C. Nonlinear dynamics of a fluid-conveying cantilevered pipe with an intermediate spring support. Journal of Fluids and Structures 7 (1993) 269-298
16. Pai{dotless}̈doussis M.P., and Semler C. Non-linear dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end. Journal of Non-Linear Mechanics 33 (1998) 15-32
17. Pai{dotless}̈doussis, M.P., Semler, C., Wadham-Gagnon, M., Saaid, S., 2007. Dynamics of cantilevered pipes conveying fluid. Part 2: dynamics of the system with intermediate spring support. Journal of Fluids and Structures 23, xxx-xxx.
18. Saaid, S., 1999. Nonlinear dynamics of a fluid-conveying cantilevered pipe with an intermediate nonlinear spring support. B.Eng. Honours Thesis, Department of Mechanical Engineering, McGill University, Montreal, Québec, Canada.
19. Semler C., Li G.X., and Pai{dotless}̈doussis M.P. The non-linear equations of motion of pipes conveying fluid. Journal of Sound and Vibration 169 (1994) 577-599
20. Semler C., Gentleman W.C., and Pai{dotless}̈doussis M.P. Numerical solutions of second order implicit non-linear ordinary differential equations. Journal of Sound and Vibration 195 (1996) 553-574
21. Steindl A., and Troger H. Flow induced bifurcations to 3-dimensional motions of tubes with an elastic support. In: Besserling J.F., and Eckhaus W. (Eds). Trends in Applications of Mathematics to Mechanics (1988), Springer, Berlin 128-138
22. Steindl A., and Troger H. Non-Linear Stability and Bifurcation Theory (1991), Springer, Berlin
23. Steindl A., and Troger H. Nonlinear three-dimensional oscillations of elastically constrained fluid conveying viscoelastic tubes with perfect broken O (2)-symmetry. Nonlinear Dynamics 7 (1995) 165-193
24. Steindl A., and Troger H. Heteroclinic cycles in the three-dimensional post-bifurcation motion of O (2)-symmetrical fluid conveying tubes. Applied Mathematics and Computation 78 (1996) 269-277
25. Wadham-Gagnon, M., 2004. Three-dimensional nonlinear dynamics of cantilevered pipes conveying fluid with nonlinear constraints. B. Eng. Honours Thesis, Department of Mechanical Engineering, McGill University, Montreal, Québec, Canada.