ASYMPTOTIC ANALYSIS OF THE DYNAMIC PROBLEM OF THE THEORY OF ELASTICITY FOR A TRANSVERSE ISOTROPIC HOLLOW CYLINDER

The forced vibrations of a transverse isotropic hollow cylinder, loaded by an axisymmetric harmonic force at the butt ends, are studied using the homogeneous solutions method. A dispersion equation for the corresponding three-dimensional elastic problem is derived that relates the wave number to the frequency of oscillations. This equation is solved by an asymptotic method in the case of a thin wall and the possible waveforms of the tube are found.