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Journal of the Acoustical Society of America / Volume 131 / Issue 2 / GENERAL LINEAR ACOUSTICS [20]

Wave motion and dispersion phenomena: Veering, locking and strong coupling effects

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1015-1028 (2012); (14 pages)

Brian R. Mace1 and Elisabetta Manconi2

1Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
2University of Parma, Department of Industrial Engineering, Parco Area delle Scienze 181/A, 43100 Parma, Italy

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The dispersion curves describe wave propagation in a structure, each branch representing a wave mode. As frequency varies the wavenumbers change and a number of dispersion phenomena may occur. This paper characterizes, analyzes, and quantifies these phenomena in general terms and illustrates them with examples. Two classes of phenomena occur. Weak coupling phenomena—veering and locking—arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which, for undamped waveguides, the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. These phenomena also occur in damped systems unless the levels of damping of the uncoupled waveguides are sufficiently different. Other phenomena can be attributed to strong coupling effects, where arbitrarily light stiffness or gyroscopic coupling changes the qualitative nature of the dispersion curves.

© 2012 Acoustical Society of America

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support provided by the Royal Society through the International Joint Project 2009/R4.

Article Outline

  1. INTRODUCTION
  2. DISPERSION PHENOMENA IN SIMPLE WAVEGUIDES
  3. DISPERSION PHENOMENA IN COUPLED WAVEGUIDES
    1. The equations of motion, dispersion equations and strength of coupling
      1. Waves in the uncoupled system
      2. Strength of coupling
    2. Weak coupling: veering and locking
      1. Veering: co-directional coupling
      2. Locking: contra-directional coupling
      3. Damping
    3. Strong coupling
      1. Stiffness coupling effects
      2. Gyroscopic coupling effects
      3. Summary
  4. ILLUSTRATIVE EXAMPLES
    1. A. Stiffness coupling: a string on an elastic foundation and a beam
    2. Damped beam-string system
    3. Gyroscopic coupling of an acoustic duct and a panel
  5. CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

acoustic dispersion, acoustic wave propagation, acoustic waveguides, damping, structural acoustics

PACS

  • 43.20.Bi

    Mathematical theory of wave propagation

  • 43.20.Jr

    Velocity and attenuation of elastic and poroelastic waves

  • 43.20.Hq

    Velocity and attenuation of acoustic waves

  • 43.20.Mv

    Waveguides, wave propagation in tubes and ducts

ARTICLE DATA

History
Received 09 Jun 2011
Accepted 16 Nov 2011
Revised 03 Nov 2011
Digital Object Identifier
http://dx.doi.org/10.1121/1.3672647

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

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