This paper investigates the dispersion of the torsional wave propagation in the finitely pre-strained bi-material compounded cylinder. This investigation is made within the framework of the piecewise homogenous body model with the use of the three dimensional linear theory of the elastic waves in initially stressed bodies. The mechanical relations of the materials of the components of the cylinder are described by the harmonic potential. The numerical results on the influence of the initial strains on the wave propagation velocity are presented and discussed. It is established in particularly that the initial stretching of the cylinders causes to increase the torsional wave propagation velocity.

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