Matrix Methods

  • J. S. Rao
Part of the History of Mechanism and Machine Science book series (HMMS, volume 20)


The kinetic and potential energies in a free vibration problem are expressible as homogeneous quadratic forms in the velocities q̇ i and coordinates q i respectively, leads to important conclusions to be drawn concerning normal coordinates.


Transfer Matrix Matrix Method Torsional Vibration Transfer Matrix Method Vibration Problem 
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.
    Biezeno, C.B., Grammel, R.: Technische Dynamik. Springer, Heidelberg (1939)Google Scholar
  2. 2.
    Den Hartog, J.P.: Mechanical Vibration. McGraw-Hill Book Co., New York (1940)Google Scholar
  3. 3.
    Duncan, W.J., Collar, A.R.: Solution of Oscillation Problems by Matrices. Philos. Mag. 17, 866 (1934)Google Scholar
  4. 4.
    Goldstine, H.H., Goldstine, A.: The Electronic Numerical Integrator and Computer, ENIAC (1946); reprinted in The Origins of Digital Computers: Selected Papers, p. 359. Springer, HeidelbergGoogle Scholar
  5. 5.
    Hahn: Note sur la vitesse critique et la formule du Dunkerley, Schweiz. Bauztg., vol. 72, p. 191 (1918)Google Scholar
  6. 6.
    Householder, A.S.: Dandelin, Lobachevskii, or Gräffe? Amer. Math. Monthly 66, 464 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Jacobsen, L.S., Ayre, R.S.: Engineering Vibrations. McGraw-Hill Book Co., New York (1958)Google Scholar
  8. 8.
    Nestorides, E.J.: A Handbook of Torsional Vibrations. Cambridge University Press, Cambridge (1958)Google Scholar
  9. 9.
    Pipes, L.A.: Applied Mathematics for Engineers and Physicists. McGraw-Hill Book Co., New York (1946)Google Scholar
  10. 10.
    Priebs, R.: Ein einfaches Rechenschema zur Aufstellung der Frequenzgleichung eines an den Enden freien Drehschwingers. Ing. Archiv. 80(2), 14 (1962)Google Scholar
  11. 11.
    Rao, D.K., Rao, J.S.: Computer Programs for Predicting the Torsional Vibration Characteristics of Diesel Engine – Driven Sets. Garden Reach Workshops Ltd., 43/46 Garden Reach, Calcutta (1974)Google Scholar
  12. 12.
    Rao, J.S.: Vibration of Cantilever Beams in Torsion. Journal of Science and Engineering Research 8 part 2, 351 (1964)Google Scholar
  13. 13.
    Rao, J.S., Sarma, K.V.B., Gupta, K.: Transient Analysis of Rotors by Transfer Matrix Method. Rotating Machinery Dynamics, ASME DE 2, 545 (1987)Google Scholar
  14. 14.
    Rao, J.S., Gupta, K.: Introductory Course on Theory and Practice of Mechanical Vibrations. New Age International (1999)Google Scholar
  15. 15.
    Sagan, C.: The Dragons of Eden. Random House (1988)Google Scholar
  16. 16.
    Scanlan, R.H., Rosenbaum, R.: Introduction to the Study of Aircraft Vibration and Flutter. Macmillan, Basingstoke (1951)zbMATHGoogle Scholar
  17. 17.
    Sylvester, J.J.: Philos. Mag., vol. 4, p. 138 (1852)Google Scholar
  18. 18.
    Thomson, W.T.: Matrix Solution of Vibration of Non-Uniform Beams, ASME Paper 49 A-11 (1949)Google Scholar
  19. 19.
    Thomson, W.T.: A Note on Tabular Methods for Flexural Vibrations. J. Aero. Sci. 20, 62 (1953)Google Scholar
  20. 20.
    Timoshenko, S.P.: Vibration Problems in Engineering. D. Van Nostrand Co. Inc. (1955)Google Scholar
  21. 21.
    Wilson, W.K.: Practical Solution of Torsional Vibration Problems, vol. 1. John Wiley & Sons, Chichester (1949)Google Scholar
  22. 22.
    Wilson, W.K.: Practical Solution of Torsional Vibration Problems, vol. 2. John Wiley & Sons, Chichester (1949)Google Scholar
  23. 23.
    Wilson, W.K.: Practical Solution of Torsional Vibration Problems, vol. 3. Chapman and Hall, Boca Raton (1965)Google Scholar

Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • J. S. Rao

    There are no affiliations available

    Personalised recommendations