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

Abstract

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.