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Abstract

The method of reverberation-ray matrix proposed by Pao et al. is applied to analyze the transient response of a multi-span pipe conveying fluid. The pipe under transverse vibration is considered as Timoshenko beam conveying axial flow. In the process of analysis, fast Fourier transform is used to convert the partial differential equation into ordinary differential equation. The support points of the pipe are chosen as the elements’ nodes. The transient wave motions at each node are divided into incident and reflected wave. By virtue of continuity and balance condition, the scattering relation is established between the above wave motions. The transient response is obtained by inverse fast Fourier transform. In the examples, the natural frequencies are calculated for single- and multi-span pipe conveying fluid with different fluid velocity, and great agreement is shown with the published literature. And then the transient responses, such as deformation, velocity, shear force and bending moment are obtained for a two-span pipe conveying fluid under different fluid velocity.

Keywords

Fast Fourier transform multi-span pipe conveying fluid transient response

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References

Beale

Accorsi

(1995) Power flow in two- and three-dimensional frame structures. Journal of Sound and Vibration 185(4): 685–702.

Chang

Lee

(2009) Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model. Physics Letters A 373(10): 982–985.

Doyle

(1989) Wave Propagation in Structures: An FFT-Based Spectral Analysis Methodology, SpringerNew York.

Guo

Zhang

Paidoussis

(2010) Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles. Journal of Fluids and Structures 26(5): 793–803.

Guo

Chen

(2007) Dynamic analysis of space structures with multiple tuned mass dampers. Engineering Structures 29(12): 3390–3403.

Guo

Chen

Pao

(2008) Dynamic analysis of space frames: the method of reverberation-ray matrix and the orthogonality of normal modes. Journal of Sound and Vibration 317(3-5): 716–738.

Housner

(1952) Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics 19(6): 205–208.

Jung

Chung

Andre

(2008) Dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid. Journal of Sound and Vibration 315(1–2): 100–117.

Knudsen

Sorokin

(2010) Modelling of linear wave propagation in spatial fluid filled pipe systems consisting of elastic curved and straight elements. Journal of Sound and Vibration 329(24): 5116–5146.

10.

Olivier

(2010) Dissipation effect on local and global stability of fluid-conveying pipes. Journal of Sound and Vibration 329(1): 72–83.

11.

Paidoussis

(1998) Fluid–Structure Interactions: Slender Structures and Axial Flow Vol. 1, London: Academic Press.

12.

Paidoussis

(2004) Fluid–Structure Interactions: Slender Structures and Axial Flow Vol. 2, London: Elsevier Academic Press.

13.

Paidoussis

(1993) Pipes conveying fluid: a model dynamical problem. Journal of Fluids and Structures 7: 137–204.

14.

Pao

Chen

(2009) Elastodynamic theory of framed structures and reverberation-ray matrix analysis. Acta Mechanica 204: 61–79.

15.

Pao

Keh

Howard

(1999) Dynamic response and wave propagation in plane trusses and frames. AIAA Journal 37(5): 594–603.

16.

Stephanie

Sairam

Srikar

Paidoussis

(2010) Dynamics of microscale pipes containing internal fluid flow: damping, frequency shift, and stability. Journal of Sound and Vibration 329(8): 1081–1088.

17.

Tan

Kang

(1999) Free vibration of axially loaded, rotating Timoshenko shaft systems by the wave-train closure principle. International Journal of Solids and Structures 36(26): 4031–4049.

18.

Thomsen

Jonas

(2010) Analytical predictions for vibration phase shifts along fluid-conveying pipes due to Coriolis forces and imperfections. Journal of Sound and Vibration 329(15): 3065–3081.

19.

Vedula NL (1999) Dynamics and stability of parametrically excited gyroscopic systems. PhD Thesis, University of Missouri, India.

20.

Shih

(2001) The dynamic analysis of multispan fluid-conveying pipe subject to external load. Journal of Sound and Vibration 239(2): 201–215.

21.

Guo

(2010) Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method. Computers & Mathematics with Applications 60(3): 520–527.

22.

Wen

Zhao

Liu

Wen

(2008) Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. Journal of Sound and Vibration 318(1–2): 193–205.

Transient response analysis of multi-span pipe conveying fluid

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