Introduction and Fundamental Concepts

  • George J. Simitses


Dynamic stability or instability of elastic structures has drawn considerable attention in the past 30 years. The beginning of the subject can be traced to the investigation of Koning and Taub [1], who considered the response of an imperfect (half-sine wave), simply supported column subjected to a sudden axial load of specified duration. Since then, many studies have been conducted by various investigators on structural systems that are either suddenly loaded or subjected to time-dependent loads (periodic or nonperiodic), and several attempts have been made to find common response features and to define critical conditions for these systems. As a result of this, the term dynamic stability encompasses many classes of problems and many different physical phenomena; in some instances the term is used for two distincly different responses for the same configuration subjected to the same dynamic loads. Therefore, it is not surprising that there exist several uses and interpretations of the term.


Dynamic Stability Parametric Resonance Parametric Excitation Total Potential Initial Kinetic Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Koning, C., Taub, J. Impact buckling of thin bars in the elastic range hinged at both ends.Luftfahrtforschung, 10, 2, 1933, 55–64 (translated as NACA TM 748 in 1934).Google Scholar
  2. 2.
    Stoker, J.J. On the stability of mechanical systems.Commun. Pure Appl. Math., VIII, 1955, 133–142.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Thompson, W., Tait, P.G. Treatise on Natural Philosophy, part I. Cambridge University Press, Cambridge, England, 1923. (It was first published in 1867.).Google Scholar
  4. 4.
    Routh , E.J. Stability of Motion (edited by A.T. Fuller).Taylor & Francis,Halsted Press, New York,1975. (Originally it appeared in 1877.)Google Scholar
  5. 5.
    Lefschetz, S. Stability of Nonlinear Control Systems. Academic Press, New York, 1965.MATHGoogle Scholar
  6. 6.
    Seckel, E.Stability and Control of Airplanes and Helicopters. Academic Press, New York, 1964.Google Scholar
  7. 7.
    Crocco, L., Cheng, S.I. Theory of Combustion Instability in Liquid Propellant Rocket Motors, AGARD Monograph No. 8. Butterworths, London, 1956.Google Scholar
  8. 8.
    Bolotin, V.V. The Dynamic Stability of Elastic Systems (translated by V.I. Weingarten et al). Holden-Day, San Francisco, 1964. MATHGoogle Scholar
  9. 9.
    Stoker, J.J. Non-Linear Vibrations in Mechanical and Electrical Systems, vol. II. Interscience, London, 1950.Google Scholar
  10. 10.
    Simitses, GJ. Elastic Stability of Structures. Prentice-Hall, Englewood Cliffs, N.J., 1976 (second printing, R.E. Krieger, Melbourne, Fla., 1985).Google Scholar
  11. 11.
    Ziegler, H. Principles of Structural Stability. Blaisdell, Waltham, Mass1968. Google Scholar
  12. 12.
    Herrmann, G. Stability of equilibrium of elastic systems subjected to nonconservative forces. Appl. Mech. Rev., 20, 2, Feb. 1967, 103–108.Google Scholar
  13. 13.
    Ziegler, H. On the concept of elastic stability. Advances in Applied Mechanics, vol. 4, pp. 351–403. Academic Press, New York, 1956. Google Scholar
  14. 14.
    Herrmann, G., Bungay, R.W. On the stability of elastic systems subjected to nonconservative forces.J. Appl. Mech 31, 3, 1964, 435–440. MathSciNetGoogle Scholar
  15. 15.
    Benjamin, T.B. Dynamics of a system of articulated pipes conveying fluid. Proc. R. Soc. London Ser. A, 261, 1961, 452–486.Google Scholar
  16. 16.
    Gregory , R.W., Paidoussis, M.P. Unstable oscillation of tubular cantilevers conveying fluid. Prod. R. Soc. London Ser. A, 293, 1966, 512–527. ADSCrossRefGoogle Scholar
  17. 17.
    Paidoussis, M.P., Deksnis, B.E. Articulated models of cantilevers conveying fluid: The study of a paradox. J. Mech. Eng. Sci., 42, 4, 1970, 288–300.CrossRefGoogle Scholar
  18. 18.
    Paidoussis, M.P. Dynamics of tubular cantilevers conveying fluid. J. Mech. Sci, 12, 2, 1970, 85–103.CrossRefGoogle Scholar
  19. 19.
    Hill, J.L., Swanson, CP. Effects of lumped masses on the stability of fluid conveying tubes. J. Appl. Mech., 37, 2, 1970, 494–497.Google Scholar
  20. 20.
    Junger, M, Feit, D. Sound, Structures and Their Interaction. MIT Press, Cambridge, Mass., 1972. MATHGoogle Scholar
  21. 21.
    Blevins, R.D. Flow-Induced Vibration. Van Nostrand-Reinhold, New York, 1977.MATHGoogle Scholar
  22. 22.
    Scanlan, R.H., Simin, E. Wind Effects on Structures: An Introduction to Wind Engineering. Wiley, New York, 1978.Google Scholar
  23. 23.
    King, R. A review of vortex shedding research and its applications. Ocean Eng., 4, 1977, 141–171.ADSCrossRefGoogle Scholar
  24. 24.
    Chen, S.S. Vibration of nuclear fuel bundles. Nucl. Eng. Des., 35,3,1975,399–422.CrossRefGoogle Scholar
  25. 25.
    Chen, S.S. Vibration of a row of circular cylinders in a liquid. J. Eng. Ind., Trans. ASME, 91, 4, 1975, 1212–1218. CrossRefGoogle Scholar
  26. 26.
    Chen, S.S. Crossflow-induced vibrations of heat exchanger tube banks. Nucl. Eng. Des., 47, 1, 1978, 67–86.CrossRefGoogle Scholar
  27. 27.
    Reusselet, J., Herrmann, G. Flutter of articulated pipes at finite amplitude. Trans. ASME, 99, 1, 1977, 154–158.Google Scholar
  28. 28.
    Au-Yang, M.K., Brown, S.J., Jr. (editors). Fluid Structure Interaction Phenomena in Pressure Vessel and Piping Systems, PVP-PB-026. ASME, New York, 1977.Google Scholar
  29. 29.
    Chen, S.S. Fluid damping for circular cylindrical structures. Nucl. Eng. Des., 63, 1, 1981, 81–100.CrossRefGoogle Scholar
  30. 30.
    Ginsberg, J.H. The dynamic stability of a pipe conveying a pulsatile flow. Int. J. Eng. Sci., 11, 1973, 1013–1024. MATHCrossRefGoogle Scholar
  31. 31.
    Bohn, M.P., Herrmann, G. The dynamic behavior of articulated pipes conveying fluid with periodic flow rate. J. Appl. Mech., 41, 1, 1974, 55–62.ADSMATHCrossRefGoogle Scholar
  32. 32.
    Paidoussis, M.P.,, Issid, N.T. Experiments on parametric resonance of pipes containing pulsatile flow. J. Appl. Mech., Trans. ASME, 98, 1976, 198–202. CrossRefGoogle Scholar
  33. 33.
    Paidoussis, M.P., Sundararajan, C. Parametric and combination resonances of a pipe conveying pulsating fluid. J. Appl. Mech., 42, 4, 1975, 780–784.ADSMATHCrossRefGoogle Scholar
  34. 34.
    Dowell, E. Nonlinear flutter of curved plates, AIAA J., 7,3, March 1969,424–431.ADSMATHCrossRefGoogle Scholar
  35. 35.
    Morino, L. Perturbation method for treating nonlinear panel flutter problems. AIAA J., 7, 3, March 1969, 405–411.ADSMATHCrossRefGoogle Scholar
  36. 36.
    Kornecki, A. Traveling wave-type flutter of infinite elastic plates. AIAA J., 8,7, July 1970, 1342–1344.ADSCrossRefGoogle Scholar
  37. 37.
    Dowell, E. Panel flutter, a review of the aeroelastic stability of plates and shells. AIAA J., 8, 3, March 1970, 385–399.ADSCrossRefGoogle Scholar
  38. 38.
    Kuo, G.C., Morino, L., Dugundji, J. Perturbation and harmonic balance methods of nonlinear panel flutter. AIAA J., 10, 11, Nov. 1972, 1479–1484.ADSCrossRefGoogle Scholar
  39. 39.
    Hoff, N.J., Bruce, V.C. Dynamic analysis of the buckling of laterally loaded flat arches. Q. Math. Phys., 32, 1954, 276–388.MathSciNetMATHGoogle Scholar
  40. 40.
    Budiansky, B., Roth, R.S. Axisymmetric dynamic buckling of clamped shallow spherical shells. Collected Papers on Instability of Shell Structures. NASA TN D-1510, 1962.Google Scholar
  41. 41.
    Budiansky, B., Hutchinson, J.W. Dynamic buckling of imperfection-sensitive structures. Proc. XI International Congress of Applied Mechanics, Munich, 1964.Google Scholar
  42. 42.
    Simitses, G.J. On the dynamic buckling of shallow spherical caps. J. Appl. Mech., 41, 1, 1974, 299–300.ADSCrossRefGoogle Scholar
  43. 43.
    Tamura, Y.S., Babcock, CD. Dynamic stability of cylindrical shells under step loading. J. Appl. Mech., 42, 1, 1975, 190–194.MATHGoogle Scholar
  44. 44.
    Budiansky, B. Dynamic buckling of elastic structures: Criteria and estimates. Dynamic Stability of Structures (edited by G. Herrmann). Pergamon, New York, 1967.Google Scholar
  45. 45.
    Hsu, CS. The effects of various parameters on the dynamic stability of a shallow arch. J. Appl. Mech., 34, 2, 1967, 349–356.Google Scholar
  46. 46.
    Hsu, CS. Stability of shallow arches against snap-through under timewise step loads. J. Appl. Mech., 35, 1, 1968, 31–39.Google Scholar
  47. 47.
    Hsu, CS. Equilibrium configurations of a shallow arch of arbitrary shape and their dynamic stability character. Int. J. Nonlinear Mech., 3, June 1968,113–136.ADSMATHCrossRefGoogle Scholar
  48. 48.
    Hsu, CS. On dynamic stability of elastic bodies with prescribed initial conditions. Int. J. Nonlinear Mech., 4, 1, 1968, 1–21.Google Scholar
  49. 49.
    Hsu, CS., Kuo, CT.,, Lee, S.S. On the final states of shallow arches on elastic foundations subjected to dynamic loads. J. Appl. Mech., 35, 4, 1968, 713–723MATHGoogle Scholar
  50. 50.
    Simitses, G.J. Dynamic snap-through buckling of low arches and shallow spherical caps. Ph.D. Dissertation, Department of Aeronautics and Astronautics, Stanford University, June 1965.Google Scholar
  51. 51.
    Hoff, N.J. Dynamic stability of structures. Dynamic Stability of Structures (edited by G. Herrmann). Pergamon, New York, 1967.Google Scholar
  52. 52.
    Thompson, J.M.T. Dynamic buckling under step loading. Dynamic Stability of Structures (edited by G. Herrmann). Pergamon, New York, 1967.Google Scholar
  53. 53.
    Wauer, J. Uber Kinetische Verweigungs Probleme Elasticher Strukturen unter Stosseblastung. Ingenieur-Arch., 49, 1980, 227–233.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • George J. Simitses
    • 1
    • 2
  1. 1.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiCincinnatiUSA

Personalised recommendations