On the number and location of zero-group-velocity modes
Name
ZGV_Paper.pdf
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366.23 KB
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Adobe PDF
Checksum (MD5)
446283c3e557a267dbd506abfe979948
Author(s)
Kausel, Eduardo A.
Alternative Title
Number and location of zero-group-velocity modes
Date Issued
June 2012
Journal
The Journal of the Acoustical Society of America
Publisher
Acoustical Society of America (ASA)
Citation
Kausel, Eduardo. “Number and Location of Zero-group-velocity Modes.” The Journal of the Acoustical Society of America 131.5 (2012): 3601.
Version
Author's final manuscript
Abstract
The frequency-wavenumber spectra of laminated media often exhibit anomalous modes with descending branches whose group velocity is negative, and these terminate at a minimum point at which the group velocity transitions from negative to positive. These minima are associated with resonant conditions in the medium, which have been clearly observed in experiments and in the nondestructive testing of laminated plates. Starting from first principles, this paper provides a theoretical analysis on the number and location of such zero-group-velocity (ZGV) modes for horizontally layered media bounded by any arbitrary combination of external boundaries. It is found that these ZGV points are few in number and show up mostly in low-order modes which are characterized by a negative second derivative at the cutoff frequencies, a condition that can readily be tested. It is also shown that the effective number of ZGVs is small even when the ratio of the dilatational and shear wave velocity is a rational number and there exist coincidences in cutoff frequencies, a condition that at first would suggest that the number of ZGVs is infinite. Finally, it is shown that the number of ZGVs decreases with the Poisson’s ratio.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1121/1.3695398
