Skip to main content

Part of the book series: Springer Study Edition ((SSE))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 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 

  • Clough, R.W. (1960). The finite method in plane stress analysis. Proc. 2nd ASCE Conf. on Electronic Computation, Pittsburgh, Pennsylvania.

    Google Scholar 

  • Courant, R. (1943). Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc. 49, 1.

    Article  MathSciNet  MATH  Google Scholar 

  • Ewins, D.J. (1984). “Modal Testing: Theory and Practice.” Research Studies Press, Letchworth, England.

    Google Scholar 

  • French, A.P. (1971) “Vibrations and Waves,” W.W. Norton, New York.

    Google Scholar 

  • Gough, C.E. (1981). The theory of string resonances on musical instruments. Acustica 49, 124–141.

    Google Scholar 

  • Halvorsen, W.G., and Brown, D.L. (1977). Impulse techniques for structural frequency response testing. Sound and Vibration 11(11), 8–21.

    Google Scholar 

  • Hansen, U.J., and Rossing, T.D. (1986). Modal analysis of a handbell (abstract). J. Acoust. Soc. Am. 79, S92.

    Article  ADS  Google Scholar 

  • Hansen, U.J., and Rossing, T.D. (1987). Modal analysis of a Caribbean steel drum (abstract). J. Acoust. Soc. Am. 82, S68.

    Article  ADS  Google Scholar 

  • Jacobson, L.S., and Ayre, R.S. (1958). “Engineering Vibrations.” McGraw-Hill, New York.

    Google Scholar 

  • Jansson, E., Bork, I., and Meyer, J. (1986). Investigation into the acoustical properties of the violin. Acustica 62, 1–15.

    Google Scholar 

  • Kindel, J. and Wang, I. (1987), Modal analysis and finite element analysis of a piano soundboard, Proc. 5th Int’l Conf. on Modal Analysis (IMAC), 1545–1549.

    Google Scholar 

  • Marshall, K.D. (1986). Modal analysis of a violin. J. Acoust. Soc. Am. 77, 695–709.

    Article  ADS  Google Scholar 

  • Marshall, K.D. (1987). Modal analysis: A primer on theory and practice. J. Catgut Acoust. Soc. 46, 7–17.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ramsey, K.A. (1975/1976). Effective measurements for structural dynamics testing. Sound and Vibration 9 (11), 24–34; 10 (4), 18–31.

    Google Scholar 

  • Rieger, N.F. (1986). The relationship between finite element analysis and modal analysis. Sound and Vibration 20(1), 20–31.

    Google Scholar 

  • Suzuki, H. (1986). Vibration and sound radiation of a piano soundboard. J. Acoust. Soc. Am. 80, 1573–1582.

    Article  ADS  Google Scholar 

  • Weinreich, G. (1977). Coupled piano strings. J. Acoust. Soc. Am. 62, 1474–1784.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Fletcher, N.H., Rossing, T.D. (1991). Coupled Vibrating Systems. In: The Physics of Musical Instruments. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2980-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2980-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94151-6

  • Online ISBN: 978-1-4612-2980-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics