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Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics

Published online by Cambridge University Press:  02 July 2018

A. V. Ilyashenko
Affiliation:
Moscow State University of Civil EngineeringMoscow, Russia
S. V. Kuznetsov
Affiliation:
Institute for Problems in MechanicsMoscow, Russia
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Abstract

The exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

Type
Research Article
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

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