A generalized theory of viscous and inviscid flutter

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 466, Issue 2113, 2010, Pages 141-156

  Mandre, Shreyas ^a   Mahadevan, L ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

1 : 1 resonance; Fluid structure interaction; Flutter

Indexed keywords

COMPLEXATION; FLEXIBLE STRUCTURES; FLUID DYNAMICS; FLUID STRUCTURE INTERACTION; FLUIDS; HYDRODYNAMICS; RESONANCE; VISCOUS FLOW;

CRITICAL FLOW; ELASTIC DISPLACEMENTS; ELASTIC MODES; EXTREME CASE; FLUIDELASTIC INSTABILITY; GENERALIZED THEORY; HYDRODYNAMIC COUPLING; HYDRODYNAMIC FORCES; INVISCID FLOWS; PROBLEM PARAMETERS; TIME-SCALES; UNCONFINED FLOW; UNIFIED THEORY;

FLUTTER (AERODYNAMICS);

EID: 73949153226     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0328     Document Type: Article

References (41)

1. Alben, S. 2008 The flapping-flag instability as a nonlinear eigenvalue problem. Phys. Fluids 20, 104106. (doi:10.1063/1.3000670)
2. Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. USA 102, 1829-1834. (doi:10.1073/pnas.0408383102) (Pubitemid 40261971)
3. Balmforth, N. J., Craster, R. V. & Rust, A. C. 2005 Instability in flow through elastic conduits and volcanic tremor. J. Fluid Mech. 527, 353-377. (doi:10.1017/S0022112004002800)
4. Batchelor, G. K. 1967 An introduction to fluid mechanics. Cambridge, UK: Cambridge University Press.
5. Benjamin, T. B. 1960 Effects of flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513-532. (doi:10.1017/S0022112060001286)
6. Bertram, C. D. & Pedley, T. J. 1982 A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39-50. (doi:10.1016/0021-9290(82) 90033-1)
7. Billah, K. Y. & Scanlan, R. H. 1991 Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks. Am. J. Phys. 59, 118-124. (doi:10.1119/1.16590)
8. Bisplinghoff, R. L. & Ashley, H. 1962 Principles of aeroelasticity. Mineola, NY: Dover.
9. Bisplinghoff, R. L., Ashley, H. & Halfman, R. L. 1955 Aeroelasticity. Cambridge, MA: Addison-Wesley.
10. Chang, Y. B. & Moretti, P. M. 2002 Flow-induced vibration of free edges of thin films. J. Fluid Struct. 16, 989-1008. (doi:10.1006/jfls.2002.0456) (Pubitemid 36017289)
11. Chouet, B. 1985 Excitation of a buried magma pipe: a seismic source model for volcanic tremor. J. Geophys. Res. 90, 1881-1893. (doi:10.1029/ JB090iB02p01881)
12. Dowell, E. H. (ed.) 2004 A modern course in aeroelasticity. Dordrecht, The Netherlands: Kluwer Academic.
13. Eggert, M. D. & Kumar, S. 2004 Observations of instability, hysteresis, and oscillation in low-Reynolds-number flow past polymer gels. J. Colloid Int. Sci. 278, 234-242. (doi:10.1016/ j.jcis.2004.05.043)
14. Fletcher, N. H. 1993 Autonomous vibration of simple pressure-controlled valves in gas flows. J. Acoust. Soc. Am. 93, 2172-2180. (doi:10.1121/1.406857)
15. Fung, Y.-C. 2002 An introduction to the theory of aeroelasticity. Mineola, NY: Dover Publications.
16. Grotberg, J. B. & Jensen, O. E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Flu. Mech. 36, 121-147. (doi:10.1146/annurev.fluid.36.050802. 12198)
17. Happel, J. & Brenner, H. 1983 Low Reynolds number hydrodynamics: with special applications to particulate media. Dordrecht, The Netherlands: Kluwer Academic (Print on demand).
18. Huang, L. 1998 Reversal of Bernoulli effect and channel flutter. J. Fluids Struct. 12, 131-151. (doi:10.1006/jfls.1997.0131)
19. Huang, L. 2001 Viscous flutter of a finite elastic membrane in Poiseuille flow. J. Fluids Struct. 15, 1061-1088. (doi:10.1006.jfls.2001.0392)
20. Jensen, O. E. & Heil, M. 2003 High-frequency self-excited oscillations in a collapsible-channel flow. J. Fluid Mech. 481, 235-268. (doi:10.1017/S002211200300394x) (Pubitemid 36632357)
21. Julian, B. R. 1994 Volcanic termor: nonlinear excitation by fluid flow. J. Geophys. Res. 99, 11859-11 877. (doi:10.1029/93JB03129)
22. Kelvin, W. T. & Tait, P. G. 1912 Treatise on natural philosophy. Cambridge, UK: Cambridge University Press.
23. Korotkoff, N. S. 1905 On the subject of methods of determining blood pressure. Bull. Imperial Mil. Med. Acad 11, 356-367.
24. Kumaran, V. & Muralikrishnan, R. 2000 Spontaneous growth of fluctuations in the viscous flow of flow past a soft interface. Phys. Rev. Lett. 84, 3310-3313. (doi:10.1103/physrevlett.84.3310)
25. Landahl, M. 1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 607-632. (doi:10.1017/ S002211206200097X)
26. Lemaitre, C. & de Langre Hémon, E. P. 2007 Thin water film around a cable subject to wind. J. Wind Eng. 95, 1259-1271. (doi:10.1016/j. jweia.2007.02.007) (Pubitemid 47308535)
27. Luo, X.-Y. & Pedley, T. J. 1998 The effects of wall inertia on flow in a two-dimensional collapsible channel. J. Fluid Mech. 363, 253-280. (doi:10.1017/S0022112098001062)
28. Miyata, T. 2003 Historical view of long-span bridge aerodynamics. J. Wind Eng. Ind. Aerodyn. 91, 1393-1410. (doi:10.2471/BLT.06.037671)
29. Müller, C., Schlindwein, V., Eckstaller, A. & Miller, H. 2005 Singing icebergs. Science 310, 1299-1299 (doi:10.1126/science.1117145) (Pubitemid 41698855)
30. Paidoussis, M. P. 1998 Fluid-structure interactions: slender structures and axial flow. San Diego, CA: Academic Press.
31. Pedley, T. J. 1990 Fluid mechanics of large blood vessels. Cambridge, UK: Cambridge University Press.
32. Pines, S. 1958 An elementary explanation of the flutter mechanism. In Proc. National Specialists Meeting on Dynamics and Aeroelasticity, pp. 52-58. New York, NY: Institute of Aeronautical Sciences.
33. Pironneau, O., Hecht, F. & Morice, J. 2009 Freefem++. See http://www.freefem.org/ff++.
34. Rocard, Y. 1957 Dynamic instability: automobiles, aircraft, suspension bridges. New York, NY: F. Ungar Publication.
35. Rust, A. C., Mandre, S. & Balmforth, N. J. 2007 The feasibility of generating low-frequency volcano seismicity by flow through a deformable channel. Geological Society of London Special Publications, 307, pp. 45-56. London, UK: Geological Society of London.
36. Tarnopolsky, A. Z., Fletcher, N. H. & Lai, J. C. S. 2000 Ocillating reed valves-an experimental study. J. Acoust. Soc. Am. 108, 400-406. (doi:10.1121/1.429473) (Pubitemid 30459083)
37. Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. Technical Report no. 496. National Advisory Commitee for Aeronautics (NACA). Also available online at http://ntrs.nasa.gov.
38. Titze, I. R. 1988 The physics of small-amplitude oscillation of the vocal folds. J. Acoust. Soc. Am. 83, 1536-1552. (doi:10.1121/1.395910)
39. Watanabe, Y., Isogai, K., Suzuki, S. & Sugihara, M. 2002a A theoretical study of paper flutter. J. Fluid Struct. 16, 543-560. (doi:10.1006/jfls.2001.0436) (Pubitemid 34853908)
40. Watanabe, Y., Suzuki, S., Sugihara, M. & Sueoka, Y. 2002b An experimental study of paper flutter. J. Fluid Struct. 16, 529-542. (doi:10.1006/jfls.2001.0435) (Pubitemid 34853907)
41. Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835-839. (doi:10.1038/ 35048530) (Pubitemid 32016089)