Coupled Vibrating Systems

  • Thomas D. Rossing
  • Neville H. Fletcher


In Chapter 1, we considered the free vibrations of a two-mass system with three springs of equal stiffness; we found that there were two normal modes of vibration. Such a system could have been viewed as consisting of two separate mass/spring vibrators coupled together by the center spring (see Fig. 1.20). If the coupling spring were made successively weaker, the two modes would become closer and closer in frequency.


Normal Mode Modal Analysis Frequency Response Function Equivalent Electrical Circuit Normal Mode Frequency 
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. Allemang, R.J., and Brown, D.L. (1987). Experimental modal analysis. In “Handbook of Experimental Mechanics” ( A.S. Kabayashi ed.). Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  2. Clough, R.W. (1960). The finite method in plane stress analysis. Proc. 2nd ASCE Conf. on Electronic Computation, Pittsburgh, Pennsylvania.Google Scholar
  3. Courant, R. (1943). Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc. 49, 1.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ewins, D.J. (1984). “Modal Testing: Theory and Practice.” Research Studies Press, Letchworth, England.Google Scholar
  5. French, A.P. (1971) “Vibrations and Waves,” W.W. Norton, New York.Google Scholar
  6. Gough, C E. (1981). The theory of string resonances on musical instruments. Acustica 49, 124–141.Google Scholar
  7. Halvorsen, W.G., and Brown, D.L. (1977). Impulse techniques for structural frequency response testing. Sound and Vibration 11 (11), 8–21.Google Scholar
  8. Hansen, U.J., and Rossing, T.D. (1986). Modal analysis of a handbell (abstract). J. Acoust. Soc. Am. 79, S92.ADSCrossRefGoogle Scholar
  9. Hansen, U.J., and Rossing, T.D. (1987). Modal analysis of a Caribbean steel drum (abstract). J. Acoust. Soc. Am. 82, S68.ADSCrossRefGoogle Scholar
  10. Jacobson, L.S., and Ayre, R.S. (1958). “Engineering Vibrations.” McGraw-Hill, New York.Google Scholar
  11. Jansson, E., Bork, I., and Meyer, J. (1986). Investigation into the acoustical properties of the violin. Acustica 62, 1–15.Google Scholar
  12. Kindel, J. and Wang, I. (1987), Modal analysis and finite element analysis of a piano soundboard, Proc. 5th Intl Conf. on Modal Analysis (IMAC), 1545–1549.Google Scholar
  13. Marshall, K.D. (1986). Modal analysis of a violin. J. Acoust. Soc. Am. 77, 695–709.ADSCrossRefGoogle Scholar
  14. Marshall, K.D. (1987). Modal analysis: A primer on theory and practice. J. Catgut Acoust. Soc. 46, 7–17.Google Scholar
  15. Popp, J., Hansen, U., Rossing. T.D., and Strong, W.Y. (1985). Modal analysis of classical and folk guitars (abstract). J. Acoust. Soc. Am. 77, S45.Google Scholar
  16. Ramsey, K.A. (1975/1976). Effective measurements for structural dynamics testing. Sound and Vibration 9 (11), 24–34; 10 (4), 18–31.Google Scholar
  17. Rieger, N.F. (1986). The relationship between finite element analysis and modal analysis. Sound and Vibration 20 (1), 20–31.Google Scholar
  18. Suzuki, H. (1986). Vibration and sound radiation of a piano soundboard. J. Acoust. Soc. Am. 80, 1573–1582.ADSCrossRefGoogle Scholar
  19. Weinreich, G. (1977). Coupled piano strings. J. Acoust. Soc. Am. 62, 1474–1484.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Thomas D. Rossing
    • 1
  • Neville H. Fletcher
    • 2
  1. 1.Physics DepartmentNorthern Illinois UniversityDeKalbUSA
  2. 2.Department of Physical Sciences Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

Personalised recommendations