Stationary stress-strain state of a three-layer viscoelastic cylindrical shell under normal loading

Multilayer viscoelastic cylindrical shells have found their wide application in construction, mechanical engineering, aircraft and rocket engineering. The aim of the work is to investigation the reaction of an infinitely long three-layer cylindrical shell to the action of a normal load moving along an axis with a constant to resonant velocity. The paper presents a mathematical formulation of the problem, developed solution methods and obtained numerical results for the problems of stationary deformation of an infinitely long three-layered cylindrical shell under normal loading. The equations of motion of the bearing layers satisfy the Kirchhoff-Love hypotheses. The solution methods are based on the joint application of the integral Fourier transform in the axial coordinate and the decomposition of all given and desired quantities into Fourier series in the angular coordinate. The outer and inner shells satisfy the Kirchhoff-Love hypotheses. The Lame viscoelasticity equation is used as a linear equation of the filler motion. An effective algorithm for solving the problem of osculations of a three-layer viscoelastic cylindrical shell under normal loading has been developed on a computer. Critical velocities of wave propagation in a three-layer shell under the influence of moving loads are found.