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Archive of Applied Mechanics

, Volume 88, Issue 8, pp 1385–1394 | Cite as

Pochhammer–Chree waves: polarization of the axially symmetric modes

  • Alla V. Ilyashenko
  • Sergey V. Kuznetsov
Original
  • 100 Downloads

Abstract

The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed (\(c_2\)) all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree wave can propagate at \(c_2\) phase speed.

Keywords

Pochhammer–Chree waves Polarization Dispersion Spectral analysis 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Moscow State University of Civil EngineeringMoscowRussia
  2. 2.Institute for Problems in MechanicsMoscowRussia

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