ИСТИНА

The exact solutions of the linear Pochhammer – Chree equation for propagating harmonic waves in cylindrical piles, are analysed and reviewed emphasizing the role of both propagating and non-propagating wave modes. The notion of limiting wave velocities for the Pochhammer – Chree waves is discussed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes of the Pochhammer – Chree waves is performed, revealing existence of the non-propagating mode at the phase velocity coinciding with the c2 shear wave velocity. Analytical expressions for displacement fields are derived for both interior and exterior domains.