Skip to main content
    • Aa
    • Aa

Flutter of long flexible cylinders in axial flow

  • E. DE LANGRE (a1) (a2), M. P. PAÏDOUSSIS (a2), O. DOARÉ (a3) and Y. MODARRES-SADEGHI (a2)

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the upstream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite-difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear and nonlinear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. Comparison is also made to existing experimental data, and a simple model for the behaviour of long cylinders is proposed.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. K. Bhattacharyya , C. P. Vendhan & K. Sudarsan 2000 The finite element method for hydroelastic instability of underwater towed cylindrical structures. J. Sound Vib. 237, 119143.

O. Doaré & E. de Langre 2002 The flow-induced instability of long hanging pipes. Eur. J. Mech. A/Solids 21, 857867.

G. T. S. Done & A. Simpson 1977 Dynamic stabilty of certain conservative and non-conservative systems. IMechE J. Engng Sci. 19, 251263.

A. P. Dowling 1988 The dynamics of towed flexible cylinders. Part 1. Neutrally buoyant elements. J. Fluid Mech. 187, 507532.

T. S. Lee 1981 Stability analysis of the Ortloff–Ives equation. J. Fluid Mech. 110, 293295.

M. J. Lighthill 1960 Note on the swimming of slender fish. J. Fluid Mech. 9, 305317.

J. L. Lopes , M. P. Païdoussis & C. Semler 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 2. The equations of motion. J. Fluids Struct. 16, 715737.

C. R. Ortloff & J. Ives 1969 On the dynamic motion of a thin flexible cylinder in a viscous stream. J. Fluid Mech. 38, 713720.

M. P. Païdoussis 1966 Dynamics of flexible slender cylinders in axial flow. Part 2. Experiments. J. Fluid Mech. 26, 737751.

M. P. Païdoussis 1973 Dynamics of cylindrical structures in axial flow. J. Sound Vib. 29, 365385.

M. P. Païdoussis , E. Grinevich , D. Adamovic & C. Semler 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 1. Physical dynamics. J. Fluids Struct. 16, 691713.

H. P. Pao 1970 Dynamics stability of a towed thin flexible cylinder. AIAA J. Hydronaut. 4, 144150.

L. Schouveiler , C. Eloy & P. Le Gal 2005 Flow-induced vibrations of high mass ratio flexible filaments freely hanging in a flow. Phys. Fluids 17, 047104.

C. Semler , J. L. Lopes , N. Augu & M. P. Païdoussis 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 3. Nonlinear dynamics. J. Fluids Struct. 16, 739759.

Y. Sugiyama & H. Kawagoe 1975 Vibration and stability of elastic columns under the combined action of uniformly distributed vertical and tangential forces. J. Sound Vib. 38, 341355.

G. S. Triantafyllou & C. Chryssostomidis 1984 Analytical determination of the buckling speed of towed slender cylindrical beams. Trans. ASME J. Energy Resources Technol. 106, 247249.

G. S. Triantafyllou & C. Chryssostomidis 1985 Stability of a string in axial flow. Trans. ASME J. Energy Resources Technol. 107, 421425.

J. Zhang , S. Childress , A. Libchaber & M. Shelley 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835839.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 40 *
Loading metrics...

Abstract views

Total abstract views: 160 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st September 2017. This data will be updated every 24 hours.