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.
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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.
Clough, R.W. (1960). The finite method in plane stress analysis. Proc. 2nd ASCE Conf. on Electronic Computation, Pittsburgh, Pennsylvania.
Courant, R. (1943). Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc. 49, 1.
Ewins, D.J. (1984). “Modal Testing: Theory and Practice.” Research Studies Press, Letchworth, England.
French, A.P. (1971) “Vibrations and Waves,” W.W. Norton, New York.
Gough, C E. (1981). The theory of string resonances on musical instruments. Acustica 49, 124–141.
Halvorsen, W.G., and Brown, D.L. (1977). Impulse techniques for structural frequency response testing. Sound and Vibration 11 (11), 8–21.
Hansen, U.J., and Rossing, T.D. (1986). Modal analysis of a handbell (abstract). J. Acoust. Soc. Am. 79, S92.
Hansen, U.J., and Rossing, T.D. (1987). Modal analysis of a Caribbean steel drum (abstract). J. Acoust. Soc. Am. 82, S68.
Jacobson, L.S., and Ayre, R.S. (1958). “Engineering Vibrations.” McGraw-Hill, New York.
Jansson, E., Bork, I., and Meyer, J. (1986). Investigation into the acoustical properties of the violin. Acustica 62, 1–15.
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.
Marshall, K.D. (1986). Modal analysis of a violin. J. Acoust. Soc. Am. 77, 695–709.
Marshall, K.D. (1987). Modal analysis: A primer on theory and practice. J. Catgut Acoust. Soc. 46, 7–17.
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.
Ramsey, K.A. (1975/1976). Effective measurements for structural dynamics testing. Sound and Vibration 9 (11), 24–34; 10 (4), 18–31.
Rieger, N.F. (1986). The relationship between finite element analysis and modal analysis. Sound and Vibration 20 (1), 20–31.
Suzuki, H. (1986). Vibration and sound radiation of a piano soundboard. J. Acoust. Soc. Am. 80, 1573–1582.
Weinreich, G. (1977). Coupled piano strings. J. Acoust. Soc. Am. 62, 1474–1484.
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Rossing, T.D., Fletcher, N.H. (2004). Coupled Vibrating Systems. In: Principles of Vibration and Sound. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3822-3_4
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DOI: https://doi.org/10.1007/978-1-4757-3822-3_4
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