Axially symmetric periodical wave processes in a rotating elastic hollow circular cylinder surrounded by an acoustic medium

In this paper the spectral characteristics of a
strain-stress state of an infinitely long elastic hollow circular cylinder with
arbitrary thickness rotating about its axis of symmetry with time-dependent
angular velocity is investigated. It is assumed that a cylinder is empty inside
and surrounded by ideal (non-viscous) compressible fluid or gas. The exact
solution of this problem is obtained using the Fourier transform with respect to
time. Calculations are carried out for a case of the Armco iron tube immersed in
water. The detailed analysis of temporal and spatial spectral characteristics of
the elastic displacements and stresses, the material density and the power flow
density averaged in the period of vibrations in elastic cylinder, are presented.