Acta Mechanica Solida Sinica

, Volume 21, Issue 2, pp 170–176

# Nonlinear Responses of a Fluid-Conveying Pipe Embedded in Nonlinear Elastic Foundations

Article

## Abstract

The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method discretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.

## Key words

fluid-conveying pipe nonlinear elastic foundation chaotic motion bifurcation differential quadrature method discretization (DQMD)

## References

1. [1]
Païdoussis, M.P., Flow-induced instabilities of cylindrical structures. Applied Mechanics Review, 1987, 40: 163–175.
2. [2]
Tang, D.M. and Dowel, E.H., Chaotic oscillations of a cantilevered pipe conveying fluid. Journal of Fluids and Structures, 1988, 2: 263–283.
3. [3]
Païdoussis, M.P. and Moon, F.C., Non-linear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid. Journal of Fluids and Structures, 1988, 3: 567–591.
4. [4]
Païdoussis, M.P., Li, G.X. and Moon, F.C., Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. Journal of Sound and Vibration, 1989, 135: 1–19.
5. [5]
Païdoussis, M.P., Li, G.X. and Rand, R.H., Chaotic motions of a constrained pipe conveying fluid: comparison between simulation, analysis and experiment. Journal of Applied Mechanics, 1991, 58: 559–565.
6. [6]
Païdoussis, M.P., Cusumand, T.P. and Copeland, G.S., Low-dimensional chaos in a flexible tube conveying fluid. Journal of Applied Mechanics, 1992, 59: 196–205.
7. [7]
Ni, Q. and Huang, Y.Y., Nonlinar dynamic analysis of a viscoelastic pipe conveying fluid. China Ocean Engineering, 2000, 14(3): 321–328.Google Scholar
8. [8]
Jin, J.D., Stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 1997, 208: 427–439.
9. [9]
Wang, L. and Ni, Q., The nonlinear dynamic vibrations of a restrained pipe conveying fluid by differential quadrature method. Journal of Dynamics and Control, 2004, 2(4): 56–61 (in Chinese).Google Scholar
10. [10]
Wang, L. and Ni, Q., A note on the stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 2006, 296: 1079–1083
11. [11]
Ni, Q., Wang, L. and Qian, Q., Chaotic transients in a curved fluid conveying tube. Acta Mechanica Solida Sinica, 2005, 18(3): 207–214.Google Scholar
12. [12]
Ni, Q., Wang, L. and Qian, Q., Bifurcations and chaotic motions of a curved pipe conveying fluid with non-linear constraints. Computers & Structures, 2006, 84: 708–717.
13. [13]
Païdoussis, M.P. and Issid, N.T., Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration, 1976, 33: 267–294.
14. [14]
Ni, Q. and Huang, Y.Y., Differential quadrature method to stability analysis of pipes conveying fluid with spring support. Acta Mechanica Solida Sinica, 2000, 13: 320–327.Google Scholar