Abstract
Zero group velocity (ZGV) modes are studied in an isotropic cylinder. The L(0, 2) mode behaves anomalously for the materials with a value of the bulk velocity ratio, \(\kappa \), in the range \(\sqrt{2}<\kappa <2.64\) and normally otherwise. All higher modes, except the first few, have no ZGV point for all isotropic materials. This is explained analytically by finding the slope of phase velocity dispersion curves of modes first when the phase velocity equals \(\kappa \) and then at their initial state.
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Acknowledgements
The authors are grateful to a referee for helpful comments which led to improvement of the paper. Takasar Hussain and Muhammad Ozair acknowledge financial support from the Higher Education Commission of Pakistan under Startup Research Grant Program (Grant 21-962/SRGP/R&D/HEC/2016).
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Hussain, T., Ahmad, F. & Ozair, M. Zero group velocity longitudinal modes in an isotropic cylinder. Acta Mech. Sin. 34, 475–481 (2018). https://doi.org/10.1007/s10409-017-0730-3
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DOI: https://doi.org/10.1007/s10409-017-0730-3