Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

On complex flutter and buckling analysis of a beam structure subjected to static follower force

  • Wang, Q. (Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida)
  • Received : 2002.11.08
  • Accepted : 2003.07.28
  • Published : 2003.11.25
⟨ Previous Next ⟩

Abstract

The flutter and buckling analysis of a beam structure subjected to a static follower force is completely studied in the paper. The beam is fixed in the transverse direction and constrained by a rotational spring at one end, and by a translational spring and a rotational spring at the other end. The co-existence of flutter and buckling in this beam due to the presence of the follower force is an interesting and important phenomenon. The results from this theoretical analysis will be useful for the stability design of structures in engineering applications, such as the potential of flutter control of aircrafts by smart materials. The transition-curve surface for differentiating the two distinct instability regions of the beam is first obtained with respect to the variations of the stiffness of the springs at the two ends. Second, the capacity of the follower force is derived for flutter and buckling of the beam as a function of the stiffness of the springs by observing the variation of the first two frequencies obtained from dynamic analysis of the beam. The research in the paper may be used as a benchmark for the flutter and buckling analysis of beams.

Keywords

References

  1. Alfutov, N.A. (1999), Stability of Elastic Structures. Springer-Verlag, Berlin.
  2. Anderson, S.B. and Thompsen, J.J. (2002), "Post-critical behaviour of Beck's column with a tip mass", Int. J. Non-linear Mech., 37, 131-151.
  3. Atanackvic, T.M. and Cveticanin, L. (1994), "Dynamics of in-plane motion of a robot arm. in Mechatronics", 147-152. Acar, M.J. Makra and E. Penny editors. Computational Mech. Publ. Boston.
  4. Bailey, C. and Haines, J.L. (1981), "Vibration and stability of non-conservative follower force systems", Comput. Meth. Appl. Mech. Eng., 26, 1-31. https://doi.org/10.1016/0045-7825(81)90128-6
  5. Beck, M. (1952), "Die Knicklast des einseitig eingespannten tangential gedruckten Stabes", Z. Angew. Math. Phys., 3.
  6. Bolotin, V.V. (1963), Non-conservative Problems of the Theory of Elastic Stability. Macmillan, New York.
  7. Bolotin, V.V., Grishko, A.A., Kounadis, A.N. and Gants, C.J. (1998), "Non-linear panel flutter in remote postcritical domains", Int. J. Non-linear Mech., 33, 753-764. https://doi.org/10.1016/S0020-7462(97)00048-6
  8. Carr, J. and Malhardeen, M.Z.M. (1979), " Beck's problem", SIAM Journal of Applied Mathematics, 37, 261-262. https://doi.org/10.1137/0137017
  9. Deineko, K.S. and Leonov, M.IA. (1955), The Dynamic Method of Investigating the Stability of a Bar in Compression. PMM. 19.
  10. Feodos'ev, V.I. (1953), Selected Problems and Questions in Strength of Materials. Gostekhizdat.
  11. Hauger, W. and Vetter, K. (1976), "Influence of an elastic foundation on the stability of a tangentially loaded column", J. Sound Vib., 47, 296-299. https://doi.org/10.1016/0022-460X(76)90726-4
  12. Hanaoka, M. and Washizu, K. (1979), "Optimum design of Beck's column", Comput. Struct., 11, 473-480. https://doi.org/10.1016/0045-7949(80)90054-1
  13. Jankovic, M.S. (1993), "Comments on 'Eigenvalue sensitivity in the stability analysis of Beck's column with a concentrated Mass at the free end", J. Sound Vib., 167, 557-559. https://doi.org/10.1006/jsvi.1993.1353
  14. Kounadis, A.N. (1981), "Divergence and flutter instability of elastically restrained structures under follower forces", Int. J. Eng. Sci., 19, 553-562. https://doi.org/10.1016/0020-7225(81)90089-6
  15. Kounadis, A.N. (1983), "The existence of regions of divergence instability for nonconservative systems under follower forces", Int. J. Solids Struct., 19, 725-733. https://doi.org/10.1016/0020-7683(83)90067-7
  16. Kounadis, A.N. (1991), "Some new instability aspects for nonconservative systems under follower loads", Int. J. Mech. Sci., 33, 297-311. https://doi.org/10.1016/0020-7403(91)90042-2
  17. Kounadis, A.N. and Katsikadelis (1980), "On the discontinuity of the flutter load for various types of cantilevers", Int. J. Solids Struct., 16, 375-383. https://doi.org/10.1016/0020-7683(80)90089-X
  18. Kounadis, A.N. (1998), "Qualitative criteria for dynamic buckling of imperfection sensitive nonconservative systems", Int. J. Mech. Sci., 40, 949-962. https://doi.org/10.1016/S0020-7403(97)00139-2
  19. Langthjem, M.A. and Sugiyama, Y. (2000), "Optimum design of cantilevered columns under the combined action of conservative and nonconservation loads: Part I: The undamped case", Comput. Struct., 74, 385-398. https://doi.org/10.1016/S0045-7949(99)00050-4
  20. Leipholz, H. (1983), "Assessing stability of elastic systems by considering their small Vibrations", Ingenieur-Archiv., 53, 345-362. https://doi.org/10.1007/BF00532523
  21. Matsuda, H., Sakiyama, T. and Morita, Ch. (1993), "Variable cross sectional Beck's column subjected to nonconservative load", Zeitschrift fur angwandte Mathematik und Mechanik (ZAMM), 73, 383-385.
  22. Pedersen, Pauli. (1977), " Influence of boundary conditions on the stability of a column under non-conservative load", Int. J. Solids Struct., 13, 445-455. https://doi.org/10.1016/0020-7683(77)90039-7
  23. Pfluger, A. (1950), Stabilitats Probleme Der Elastostatik, Springer-Verlag, Berlin.
  24. Ryu, Si-Ung and Sugiyama, Y. (2003), "Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force", Comput. Struct., 81, 265-271. https://doi.org/10.1016/S0045-7949(02)00436-4
  25. Sugiyama, Y., Katayama, K. and Kinoi, S. (1995), "Flutter of cantilevered column under rocket thrust", J. Aerospace Eng., 8, 9-15. https://doi.org/10.1061/(ASCE)0893-1321(1995)8:1(9)
  26. Sundararajan, C. (1974), "Stability of columns on elastic foundations subjected to conservative and nonconservative forces", J. Sounds Vib., 37, 79-85. https://doi.org/10.1016/S0022-460X(74)80059-3
  27. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability. McGraw-Hill International Book Company, Singapore.
  28. Wang, Q. and Quek, S.T. (2002), "Enhancing flutter and buckling capacity of column by piezoelectric layers", Int. J. Solids Struct., 39, 4167-4180. https://doi.org/10.1016/S0020-7683(02)00334-7

Cited by

  1. Computational Modeling of Spine and Trunk Muscles Subjected to Follower Force vol.21, pp.4, 2003, https://doi.org/10.1007/bf03026960
  2. On the limit cycles of aeroelastic systems with quadratic nonlinearities vol.30, pp.1, 2003, https://doi.org/10.12989/sem.2008.30.1.067