Within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body, the problem of the axisymmetric wave propagation in an initially twisted circular compound cylinders is studied. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed, following which the numerical results are presented and discussed. In particular, it is established that as a result of the initial twisting of the circular compound cylinders, new axisymmetric wave modes arise.

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