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Computerdynamik der Tragwerke pp 74–178Cite as

Eigenschwingungen ungedämpfter Systeme

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Zusammenfassung

Auf den ersten Blick mag es nicht ganz verständlich sein, weshalb den Eigenschwingungen ungedämpfter Systeme (deutlicher müßte man sagen:… linearer Systeme) ein so breiter Raum gewährt wird. In der Praxis wird sich dem Ingenieur in der Regel die Aufgabe stellen, die Systemantwort (Verschiebungen, Beanspruchungen etc.) auf vorgegebene, konkrete Belastungen (diese mögen deterministischer oder stochastischer Natur sein) zu bestimmen, während Eigenschwingungen gerade durch das Fehlen äußerer Belastungen charakterisiert sind.

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Literatur zu Kapitel 17

  1. K. A. Braun, et. al.; Linear dynamic analysis — Lecture notes and example problems, ASKA UM 212, Stuttgart (1982); auch: ISD-Bericht Nr. 155, Stuttgart (1974).

    Google Scholar 

  2. J. Argyris, S. Kelsey; Modern fuselage analysis and the elastic aircraft, Butterworths, London (1963) 93–100.

    Google Scholar 

  3. J. Argyris; Some results on the free-free oscillations of aircraft type structures, Revue Française de Mécanique, 15 (1965); 3e trimèstre 59–73. auch: ISD-Bericht Nr. 1, Stuttgart (1964).

    Google Scholar 

  4. O. E. Brønlund, Th. L. Johnsen; QR-faktorization of partitioned matrices, Comp. Meths. Appl. Mech. Eng., 3 (1974) 153–172.

    Article  Google Scholar 

  5. H. Rutishauser; Computational aspects of F. L. Bauer’s simultaneous iteration method; Numerische Mathematik, 13 (1969) 4–13.

    Article  MATH  Google Scholar 

  6. G. Dietrich; Improved simultaneous vector iteration; in: ASKA extensions ‘78, ISD-Bericht Nr. 239, Stuttgart (1978).

    Google Scholar 

  7. J. H. Wilkinson; Rundungsfehler, Heidelberger Taschenbücher Band 44 (Springer, Berlin, 1969).

    Google Scholar 

  8. H. R. Schwarz, H. Rutishauser, E. Stiefel; Numerik symmetrischer Matrizen (Teubner, Stuttgart, 1968).

    MATH  Google Scholar 

  9. P. Henrici; On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices, J. Soc. Industr. Appl. Math., 6 (1958) 144–162.

    Article  MathSciNet  MATH  Google Scholar 

  10. K. A. Braun, et. al.; Some hypermatrix algorithms in linear algebra; in: Lecture notes in economics and mathematical systems, Vol. 134, Springer, Berlin-Heidelberg-New York (1976).

    Google Scholar 

  11. A. S. Householder; Principles of numerical analysis (McGraw-Hill, New York, 1953).

    MATH  Google Scholar 

  12. J. H. Wilkinson; The algebraic eigenvalue problem (Clarendon Press, Oxford, 1965).

    MATH  Google Scholar 

  13. G. Dietrich; A new formulation of the hypermatrix Householder — QR decomposition, Comp. Meths. Appl. Mech. Eng., 9 (1976) 273–280.

    Article  MATH  Google Scholar 

  14. R. J. Guyan; Reduction of stiffness and mass, AIAA Journal, Vol. 3 (1965).

    Google Scholar 

  15. C. M. Harris, Ch. E. Crede; Shock and vibration handbook, Vol. 1 (basic theory and measurements) (McGraw-Hill, New York, 1961).

    Google Scholar 

  16. K. Klotter; Technische Schwingungslehre, Band 2 (Schwinger von mehreren Freiheitsgraden) (Springer, Berlin, 1960).

    Book  Google Scholar 

  17. J. P. den Hartog; Mechanical vibrations (McGraw-Hill, New York, 1956).

    MATH  Google Scholar 

  18. S. Iguchi; Die Eigenschwingungen und Klangfiguren der vierseitig freien rechteckigen Platte, Ing. Archiv, 21 (1953) 303–322.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Argyris, et. al.; Aspects of the finite element method as applied to aero-space structures, XXIIIrd Intern. Astronautical Congress, Wien (1972), ISD-Bericht Nr. 138, Stuttgart (1973).

    Google Scholar 

  20. K. A. Braun, Th. L. Johnsen; Eigencomputation of symmetric hypermatrices using a generalization of the Householder method, 2nd Int. Conf. SMIRT, Berlin (1973).

    Google Scholar 

  21. Forschungsgruppe Reaktordruckbehälter des ISD; Rotationssymmetrische Berechnung des 1:5 THTR Spannbetonbehälter-Modells, ISD-Bericht Nr. 102, Stuttgart (1971).

    Google Scholar 

  22. J. Argyris, et. at.; Finite Elemente zur Berechnung von Spannbeton-Reaktordruckbehältern, ISD-Bericht Nr. 137, Stuttgart (1973).

    Google Scholar 

  23. C. Lanczos; An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45 (1950) 255–282.

    Article  MathSciNet  Google Scholar 

  24. C. C. Paige; The computation of eigenvalues and eigenvectors of very large sparse matrices, Ph. D. Thesis, University of London (1971).

    Google Scholar 

  25. C. C. Paige; Computational variants of the Lanczos method for the eigenproblem, J. Inst. Math. Appl., 10 (1972) 373–381.

    Article  MathSciNet  MATH  Google Scholar 

  26. C. C. Paige; Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix, J. Inst. Math. Appl., 18 (1976) 341–349.

    Article  MathSciNet  MATH  Google Scholar 

  27. B. N. Parlett, D. S. Scott; The Lanczos algorithm with selective orthogonalization, Math. Comp., 33 (1979) 217–238.

    Article  MathSciNet  MATH  Google Scholar 

  28. B. N. Parlett; The symmetric eigenvalue problem (Prentice-Hall, Englewood Cliffs, N.J., 1980).

    MATH  Google Scholar 

  29. D. K. Faddejew, W. N. Faddejewa; Numerische Methoden der linearen Algebra. 3. Aufl. (Oldenbourg Verlag, München-Wien, 1973).

    MATH  Google Scholar 

  30. G. H. Golub, C. F. van Loan; Matrix computations (North Oxford Academic, Oxford, 1983).

    MATH  Google Scholar 

  31. Y. Saad; On the rate of convergence of the Lanczos and the block-Lanczos methods, SIAM J. Num. Anal., 17 (1980) 687–706.

    Article  MathSciNet  MATH  Google Scholar 

  32. A. Ruhe; Computation of eigenvalues and eigenvectors, in: Sparse Matrix Techniques (ed. V. A. Baker), Lecture Notes in Mathematics 572, Springer-Verlag, Berlin (1977) 130–184.

    Chapter  Google Scholar 

  33. T. Ericsson, A. Ruhe; The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems, Math. Comp., 35 (1980) 1251–1268.

    MathSciNet  MATH  Google Scholar 

  34. B. Nour-Omid, B. N. Parlett, R. L. Taylor; Lanczos versus subspace iteration for solution of eigenvalue problems, Int. J. Num. Meth. Eng., 19 (1983) 859–871.

    Article  MATH  Google Scholar 

  35. H. G. Matthies; A subspace Lanczos method for the generalized symmetric eigenproblem, Comp. & Struct., 21 (1985) 319–325.

    Article  MathSciNet  MATH  Google Scholar 

  36. K.-J. Bathe, S. Ramaswamy; An accelerated subspace iteration method, Comp. Meth. Appl. Mech. Eng., 23 (1980) 313–331.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut für Computer-Anwendungen, Universität Stuttgart, Deutschland

    Prof. em. Dr. Dr. h. c. mult. John Argyris F. Eng., F.R.S. & Dr. Ing. Hans-Peter Mlejnek (Gruppenleiter)

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  1. Prof. em. Dr. Dr. h. c. mult. John Argyris F. Eng., F.R.S.
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  2. Dr. Ing. Hans-Peter Mlejnek
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© 1997 Springer Fachmedien Wiesbaden

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Argyris, J., Mlejnek, HP. (1997). Eigenschwingungen ungedämpfter Systeme. In: Computerdynamik der Tragwerke. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-89564-6_4

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  • DOI: https://doi.org/10.1007/978-3-322-89564-6_4

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-06916-2

  • Online ISBN: 978-3-322-89564-6

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