Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2014, Article ID 714298, 1 page http://dx.doi.org/10.1155/2014/714298
Erratum Erratum to ‘‘Anomalous Dispersion of the 𝑆1 Lamb Mode’’ Faiz Ahmad and Takasar Hussain School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan Correspondence should be addressed to Takasar Hussain;
[email protected] Received 9 December 2013; Accepted 23 December 2013; Published 4 February 2014 Copyright © 2014 F. Ahmad and T. Hussain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Recently, the present authors examined anomalous dispersion of the Lamb modes in isotropic plates as shown in their previous paper, by finding the slope of each mode first at its point of inception and secondly at a point far removed from it. If the slopes at two points differ in sign, it will indicate that a zero group velocity point occurs between them. However, Prada [1] has pointed out that analytical reasoning about the anomalous nature of modes has already been given by Mindlin in [2], where he has calculated the curvature of the modes in the 𝑘-𝜔 plane, where 𝑘 and 𝜔, respectively, denote the wave number and frequency of the wave. Shuvalov and Poncelet [3] explained this fact by looking at the sign of the first coefficient in the Taylor series for 𝜔𝑛 (𝑘) − 𝜔𝑛 (0). The statement “In all isotropic materials with 𝜅 ≠ 2 (] ≠ 1/3), only the 𝑆1 mode has this “anomalous behavior” and other modes behave normally,” which appears in Section 1 of the paper should be replaced by “In all isotropic materials with 𝜅 ≠ 2 (] ≠ 1/3), the 𝑆1 mode always has this anomalous behavior.” The paper offers an alternative and somewhat simpler, treatment of the anomalous behavior of Lamb modes.
References [1] C. Prada, Private Communication. [2] R. D. Mindlin, “Monograph,” in An Introduction to the Mathematical Theory of Vibrations of Elastic Plates, J. Yang, Ed., Sec. 2.11, U.S. Army Signal Corps Eng. Lab., Ft Monmouth, NJ, USA, 1995, World Scientific, Singapore, 2006. [3] A. L. Shuvalov and O. Poncelet, “On the backward Lamb waves near thickness resonances in anisotropic plates,” International Journal of Solids and Structures, vol. 45, no. 11-12, pp. 3430–3448, 2008.
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