Advertisement

Abstract

Part V deals with sensitivity analysis and structural optimization in stability and vibration problems. Chapter 1 is an introduction. Chapter 2 is devoted to qualitative and quantitative sensitivity analysis of vibrational frequencies of mechanical systems with respect to problem parameters. As an example linear gyroscopic system is considered. In chapters 3 and 4 sensitivity analysis for nonconservative problems of elastic stability is given and discussed. Discrete as well as distributed structures are considered. Chapter 5 is devoted to optimization of critical loads of columns subjected to follower forces. Chapter 6 is devoted to optimization of aeroelastic stability of panels in supersonic gas flow. Both static and dynamic forms of the loss of stability are considered. In chapters 7 and 8 bending-torsional flutter problem of a wing in incompressible flow is considered. Influence of mass and stiffness distributions on aeroelastic stability characteristics is studied. Optimization problem how to maximize the critical speed at which aeroelastic stability is lost is stated and solved numerically.

Keywords

Critical Load Critical Speed Gradient Function Adjoint Problem Follower Force 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Seyranian, A.P.: Sensitivity analysis and optimization of aeroelastic stability characteristics, Institute of Problems in Mechanics, USSR Academy of Sciences, N 162, Moscow 1980 (in Russian).Google Scholar
  2. 2.
    Seyranian, A.P.: Sensitivity analysis and optimization of aeroelastic stability, Int. J. Solids Struct., 18, (1982), 791–807.CrossRefMATHGoogle Scholar
  3. 3.
    Seyranian, A.P.: Optimization of structures subjected to aeroelastic instability phenomena, Arch. Mech., 34 (1982), 133–146.MATHGoogle Scholar
  4. 4.
    Seyranian, A.P.: Optimization of stability of a plate in supersonic gas flow, Mechanics of Solids, 15 (1980), 5, 141–147.Google Scholar
  5. 5.
    Seyranian, A.P.: Homogeneous functionals and structural optimization problems. Int. J. Solids Struct., 15 (1979), 749–759.CrossRefMATHGoogle Scholar
  6. 6.
    Seyranian, A.P. and Sharanyuk, A.V.: Sensitivity and optimization of critical parameters in dynamic stability problems, Mechanics of Solids, 18 (1983), 5, 174–183.MathSciNetGoogle Scholar
  7. 7.
    Seyranian, A.P. and Sharanyuk, A.V.: Optimization of flutter characteristics, Izv. AN Armenian SSR, Mekhanica, 37 (1984), 5, 38–51 (in Russian).MATHGoogle Scholar
  8. 8.
    Seyranian, A.P. and Sharanyuk, A.V.: Sensitivity analysis of vibrational frequencies of mechanical systems, Mechanics of Solids, 22 (1987), 2, 34–38.Google Scholar
  9. 9.
    Pedersen, P. and Seyranian, A.P.: Sensitivity analysis for problems of dynamic stability. Int. J. Solids Struct., 19 (1983) 315–335.CrossRefMATHGoogle Scholar
  10. 10.
    Bolotin, V.V.: Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, Oxford 1963.MATHGoogle Scholar
  11. 11.
    Ziegler, H.: Principles of Structural Stability, Blaisdell, Waltham, Mass. 1968.Google Scholar
  12. 12.
    Leipholz, H.: Stability of Elastic Systems, Sijthoff and Noordhoff, Amsterdam 1980.MATHGoogle Scholar
  13. 13.
    Hanaoka, H. and Washizu, K.: Optimum design of Beck’s column, Coraput. Struct., 11 (1980), 473–480.CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Claudon, J.-L. and Sunakawa, M.: Optimizing distributed structures for maximum flutter load, AIAA J., 19 (1981), 957–959.CrossRefMATHGoogle Scholar
  15. 15.
    Pierson, B.L. and Hajela, O.: Optimal aeroelastic design of an unsymmetrically supported panel, J. Struct. Mech., 8 (1980), 331–346.CrossRefGoogle Scholar
  16. 16.
    Sheu, C.Y. and Prager, W.: Recent developments in optimal structural design, Appl. Mech. Rev., 21 (1968), 985–992.Google Scholar
  17. 17.
    Poston, T. and Stewart, I.: Catastrophe Theory and its Applications, Pitman 1978.MATHGoogle Scholar
  18. 18.
    Thompson, J.M.T.: Instabilities and Catastrophes in Science and Engineering, John Wiley and Sons, New York 1982MATHGoogle Scholar
  19. 19.
    Bratus, A.S. and Seyranian, A.P.: Bimodal solutions in optimization problems of eigenvalues, PMM, 47 (1983) 451–457.MathSciNetGoogle Scholar
  20. 20.
    Bratus, A.S., Seyranian, A.P.: Sufficient optimality conditions in optimization problems of eigenvalues, PMM, 48 (1984), 466–474.MathSciNetGoogle Scholar
  21. 21.
    Seyranian, A.P.: Multiple eigenvalues in optimization problems, PMM, 51 (1987), 349–352.Google Scholar
  22. 22.
    Olhoff, N.: Optimal Design with Respect to Structural Eigenvalues, in: Proc. 15th Inter. Congress of Theor. Appl. Mech., Toronto, 1980, North-Holland, Toronto 1981, 133–149.Google Scholar
  23. 23.
    Haug, E.J. and Cea, I., eds.: Optimization of Distributed Parameter Structural Systems, Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands, 1981, 2 vols.MATHGoogle Scholar
  24. 24.
    Eschenauer, H., Olhoff, N., eds.: Optimization Methods in Structural Design, B.-I. Wissenschaftsverlag, Wien 1983.MATHGoogle Scholar
  25. 25.
    Gajewski, A. and Życzkowski, M.: Optimal Structural Design under Stability Constraints, Njhoff, Dordrecht 1987.Google Scholar
  26. 26.
    Medvedev, N.G.: Some spectral singularities in optimal problem of shell of nonuniform thickness, Dokl. Ukr. Academy of Sciences, A, 9 (1980), 59–63 (in Russian).Google Scholar
  27. 27.
    Seyranian, A.P.: A solution of a problem of Lagrange, Sov. Phys. Dokl., 28 (1983), 7, 550–551.MATHGoogle Scholar
  28. 28.
    Seyranian, A.P.: On Lagrange’s problem, Mechanics of Solids, 19 (1984), 2, 101–111.MathSciNetGoogle Scholar
  29. 29.
    Masur, E.F.: Optimal structural design under multiple eigenvalue constraints, Inter. J. Solids Struct., 20 (1984), 211–231.CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Grossman, E.P. Flutter, Transactions of CAHI, 284, Moscow (1937) (in Russian).Google Scholar
  31. 31.
    Fung, Y.C. An Introduction to the Theory of Aeroelesticity, Wiley, New York, 1955.Google Scholar

Copyright information

© Springer-Verlag Wien 1989

Authors and Affiliations

  • A. P. Seyranian
    • 1
  1. 1.USSR Academy of SciencesMoscowUSSR

Personalised recommendations