Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2019-4pp.598-606

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A.V. Ilyashenko, "Pochhammer-Cree Longitudinal Waves: Anomalous Polarization," Mech. Solids. 54 (4), 598-606 (2019)
Year 2019 Volume 54 Number 4 Pages 598-606
DOI 10.3103/S0025654419040149
Title Pochhammer-Cree Longitudinal Waves: Anomalous Polarization
Author(s) A.V. Ilyashenko (Moscow State University of Civil Engineering Yaroslavskoye sh. 26, Moscow, 129337 Russia, avi_56@mail.ru)
Abstract The exact solutions of the Pochhammer-Cree wave equation, which describes the propagation of harmonic waves in an elastic cylindrical rod, are analyzed. For longitudinal axially symmetric modes, a spectral analysis of the matrix of the dispersion equation is carried out for the first time. Analytical expressions for wave polarization are obtained. On the surface of the rod for the fundamental longitudinal axially symmetric mode, the polarization coefficients of the corresponding waves are determined and the variation of these coefficients depending on the frequency is analyzed. It was found that at the phase velocity of the fundamental axially symmetric longitudinal mode, which coincides with the shear wave velocity, all components of displacements on the side surface of the rod simultaneously vanish, which seems to be extremely important for the design of acoustic waveguides.
Keywords Pochhammer-Cree waves, polarization, dispersion, spectral analysis
Received 25 December 2017
Link to Fulltext https://link.springer.com/article/10.3103/S0025654419040149
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