Acta Mechanica Sinica

, Volume 34, Issue 3, pp 475–481 | Cite as

Zero group velocity longitudinal modes in an isotropic cylinder

  • Takasar Hussain
  • Faiz Ahmad
  • Muhammad Ozair
Research Paper


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.


Isotropic cylinder Longitudinal modes Zero group velocity point 



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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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyAttockPakistan
  2. 2.School of Natural SciencesNational University of Sciences and TechnologyIslamabadPakistan

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