Mathematical Modeling and Analysis of Flutter in Bending-Torsion Coupled Beams, Rotating Blades, and Hard Disk Drives
This article has a reply.
VIEW THE REPLYPublication: Journal of Aerospace Engineering
Volume 17, Issue 2
Abstract
In this study I present a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability that occurs in a solid elastic structure interacting with a flow of gas or fluid, and consists of violent vibrations of the structure with rapidly increasing amplitudes. The focus of this review is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. The main objects of interest are analytical results on such models, which can be used for flutter explanation, its qualitative and even quantitative treatments. This paper does not pretend to be a comprehensive review of the enormous amount of engineering literature on analytical, computational, and experimental aspects of the flutter problem. I present a brief exposition of the results obtained in several selected papers or groups of papers on the following topics: (1) bending-torsion vibrations of coupled beams; (2) flutter in transmission lines; (3) flutter in rotating blades; (4) flutter in hard disk drives; (5) flutter in suspension bridges; and (6) flutter of blood vessel walls. Finally, I concentrate on the most well-known case of flutter, i.e., flutter in aeroelasticity. The last two sections of this review are devoted to the precise analytical results obtained in my several recent papers on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abrahamson, S. D., Chiang, C., and Eaton, J. K.(1991). “Flow structure in head-disk assemblies and implications for design.” Adv. Inf. Storage Syst., 1, 111–132.
Adam, C.(1999). “Forced vibrations of elastic bending-torsion coupled beams.” J. Sound Vib., 221(2), 273–287.
Adam, C., Heuer, R., and Druml, A.(1997). “Österreichische Ingenieur-und Architekten-Zeitschrift (ÖIAZ).” Biegedrillschwingungen elastischer kontinuirlicher Träger mit offenem, einfach symmetrischem Querschnitt,142, 175–179 (in German).
Banerjee, J. R.(1984). “Flutter characteristics of high aspect ratio tailless aircraft.” J. Aircr., 21, 733–736.
Banerjee, J. R.(1988). “Flutter modes of high aspect ratio tailless aircraft.” J. Aircr., 25, 473–476.
Banerjee, J. R.(1989). “Coupled bending-torsional dynamic stiffness matrix for beam elements.” Int. J. Numer. Methods Eng., 28, 1283–1298.
Banerjee, J. R., and Fisher, S. A.(1992). “Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements.” Int. J. Numer. Methods Eng., 33, 739–751.
Banerjee, J. R., and Price, W. G.(1997). “Coupled bending and twisting of a Timoshenko beam.” J. Sound Vib., 50, 469–477.
Bishop, R. E. D., Cannon, S. M., and Miao, S.(1989). “On coupled bending and torsional vibration of uniform beams.” J. Sound Vib., 131, 457–464.
Bouchard, G., and Talke, F. E.(1986). “Non-repeatable flutter of magnetic recording disks.” IEEE Trans. Magn., 17(5), 1019–1021.
Butler, R., and Banerjee, J. B.(1996). “Optimum design of bending-torsion coupled beams with frequence or aeroelastic constraints.” Comput. Struct., 60(5), 715–724.
Chonan, S., Jiang, Z. W., and Shyu, Y. J.(1992). “Stability analysis of disk drive system and the optimum design of the disk stabilizer.” J. Vibr. Acoust., 114, 283–286.
D’Angelo, C., and Mote, Jr., C. D.(1993a). “Aerodynamically excited vibration and flutter of thin disk rotating at supercritical speed.” J. Sound Vib., 168, 15–30.
D’Angelo, C., and Mote, Jr., C. D.(1993b). “Natural frequencies of a thin disk, clamped by thick collars with friction at the contacting surfaces, spinning at high rotation speed.” J. Sound Vib., 168, 1–14.
Dokumaci, E.(1977). “An exact solution for coupled bending and torsoin vibrations of uniform beam having single cross-sectional symmetry.” J. Sound Vib., 119, 443–449.
Dzygadlo, Z., and Sobieraj, W.(1977). “Natural flexural-torsional vibration analysis of helicopter rotor blades by the Finite Element Method.” J. Tech. Phys., 18(4), 443–454.
Eslimy-Isfahany, S. H. R., Banerjee, J. R., and Sobey, A. J.(1996). “Response of a bending-torsion coupled beam to deterministic and random loads.” J. Sound Vib., 195(2), 267–283.
Friberg, P. O.(1983). “Coupled vibration of beams—an exact dynamic element stiffness matrix.” Int. J. Numer. Methods Eng., 19, 479–493.
Friberg, P. O.(1985). “Beam element matricies derived from Vlasov’s theory of open thin-walled elastic beams.” Int. J. Numer. Methods Eng., 21, 1205–1228.
Friedmann, P. P.(1999). “Renaissance in aeroelasticity and its future.” J. Aircr., 36(1), 105–121.
Friedmann, P. P., and Straub, F.(1980). “Application of the finite element method to rotary-wing aeroelasticity.” J. Am. Helicopter Soc., 25, 36–44.
Garrick, E. I., and Reed, W. H., III (1981). “Historical development of aircraft flutter.” J. Aircr., 18(1), 897–912.
Grandall, S. H., and Mark, W. D. (1963). Random vibration in mechanical systems, Academic, New York.
Grandhi, R. V., and Moradmand, J. K.(1989). “Optimum synthesis of thin-walled vibrating beams with coupled bending and torsion.” ASME J. Mech., Transm., Autom. Des., 111, 555–560.
Guo, L., and Chen, Y.-J. D.(2001). “Disk flutter and it’s impact on hard disk drive servo-performance.” IEEE Trans. Magn., 37(2), 866–870.
Hallauer, W. L., and Liu, R. Y. L.(1982). “Beam bending-torsion dynamic stiffness method for calculation of exact vibration modes.” J. Sound Vib., 85, 105–113.
Hanagud, S., Chattopadhyay, A., and Smith, C. V.(1987). “Optimal design of a vibrating beam with coupled bending and torsion.” AIAA J., 25, 1231–1240.
Hansen, M. H., Raman, A., and Mote, C. D., Jr. (1999). “Estimation of non-conservative aerodynamic pressure leading to flutter of spinning disks.” Tech Rep. No. 605, Danish Center for Applied Mathematics and Mechanics, Technical Univ. of Denmark.
Hansen, M. H., Roman, A., and Mote, C. D., Jr. (2001). “Estimation of nonconservative aerodynamic pressure leading to flutter in spinning disks.” J. Fluids Struct., 15, 39–57.
Heo, B., Shen, I. Y., and Riley, J. J.(2001). “Reducing disk flutter by improving aerodynamic design of case castings.” IEEE Trans. Magn., 36(5), 2222–2224.
Hosaka, H., and Crandall, S.(1992). “Self-excited vibrations of a flexible disk rotating on an air film above a flat surface.” Acta Mech., 3, 115–127.
Houbolt, J. C., Steiner, R., and Pratt, K. G. (1964). “Dynamic response of airplanes to atmospheric turbulence including flight data on input response.” NASA TR-R, 199.
Huang, L.(1998). “Reversal of the Bernoulli effect and channel flutter.” J. Fluids Struct., 12, 131–151.
Huang, F., and Mote, C. D., Jr., (1995). “On the instability mechanism of a disk rotating close to a rigid surface.” J. Appl. Mech., 62, 764–771.
Huang, F., and Mote, C. D., Jr., (1996). “Mathematical analysis of stability of a spinning disk under rotating, arbitrarily large damping forces.” J. Vibr. Acoust., 118, 657–662.
Imai, S., Tokuyama, M., and Yamaguchi, Y.(1999). “Reduction of disk flutter by decreasing disk-to-shroud spacing.” IEEE Trans. Magn., 35, 2301–2303.
Kim, B. C., Raman, A., and Mote, C. D., Jr., (2000). “Reduction of aeroelastic flutter in a hard disk drive.” J. Sound Vib., 238(2), 309–325.
Kwon, S.-D., Jung, M. S. S., and Chang, S. P.(2000). “A new passive aerodynamic control method for bridge flutter.” J. Wind Eng. Ind. Aerodyn., 86(2-3), 187–202.
Lee, C. W., and Kim, M. E.(1995). “Separation of travelling wave modes in rotating disk via directional spectral analysis.” J. Sound Vib., 187, 851–864.
Lennemann, E.(1974). “Aerodynamic aspects of disk files.” J. Res. Dev.,18(6), 480–488.
Lilico, M., Butler, R., Banerjee, J. R., and Guo, S. (1994). “Aeroelastic optimization of high aspect ratio wings using an exact dynamic stiffness matrix nethod.” Proc., 5th AIAA/NASA/USAF/ISSMO Symp. on Multidisciplinary Analysis and Optimization, AIAA Paper 94-4401, American Institute of Aeronautics Astronautics, Reston, Va., 1301–1309.
Nakamura, Y.(1980). “Galloping of bundled power line conductors.” J. Sound Vib., 73, 363–377.
Nakamura, Y.(1996). “Flutter of coupled bending-torsion systems with a frequency ratio close to one.” J. Fluids Struct., 10, 47–56.
Newland, D. E. (1984). An introduction to random vibration and spectral analysis, Longman, London.
Perry, B., Pototzky, A. S., and Woods, J. S.(1990). “NASA Investigation of a claimed ‘overlap’ between two gust response analysis methods.” J. Aircr., 27, 605–611.
Renshaw, A. A.(1998). “Critical speeds for floppy disks.” J. Appl. Mech., 65, 116–120.
Renshaw, A. A., D’Angelo, C., and Mote, C. D., Jr., (1994). “Aerodynamically excited vibration of a rotating disk.” J. Sound Vib., 177, 577–590.
Shubov, M. A. (2004a). “Flutter phenomenon and its mathematical analysis.” J. Aerospace. Eng., in press.
Shubov, M. A.(2004b). “Mathematical modeling and analysis of flutter in long-span suspension bridges and in blood vessel walls.” J. Aerospace Eng.,17(2), 70–82.
Weaver, W., Timoshenko, S., and Young, D. H. (1990). Vibration Problems in Engineering, 5th Ed., Wiley, New York.
Wilde, K., Omenzettler, P., and Fujino, Y.(2001). “Suppression of bridge flutter by active deck-flaps control system.” J. Eng. Mech., 127(1), 80–89.
Yasuda, K., Toru, T., and Shimizu, T.(1992). “Self-excited oscillation of a circular disk rotating in air.” Int’l Journal,35, 347–352.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 17 • Issue 2 • April 2004
Pages: 56 - 69
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Dec 13, 2002
Accepted: May 20, 2003
Published online: Mar 15, 2004
Published in print: Apr 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.