Action of Moving Load on a Two-Layer Shell in Elastic Medium

Based on the stationary solution of the problem of the action of a uniformly moving load on a two-layer cylindrical shell in an unbounded elastic medium (mass), the influence of its outer layer on the values ​​of the critical load velocities and the reaction of an elastic medium rigidly coupled to it is studied. The speed of the load movement is assumed to be subsonic (less than the speed of propagation of shear waves in the elastic medium and the outer layer of the shell). The need for research is due to the fact that the design scheme widely used in the dynamic calculation of a deep tunnel - a homogeneous (single-layer) shell in an elastic space, in some cases is not adequate to the considered underground structure. The inner (bearing) layer of the considered shell is a thin-walled shell, rigidly coupled to its outer (enclosing) layer of arbitrary thickness. To describe the motion of the massif and the outer (enclosing) layer of the shell, the dynamic equations of the theory of elasticity in Lame potentials are used. Oscillations of the inner (bearing) layer of the shell are described by the classical equations of shell theory based on the Kirchhoff-Love hypotheses. The equations are presented in a moving cylindrical coordinate system associated with a moving load. When solving the problem, the integral Fourier transform along the axial coordinate is used, which makes it possible to consider the load distributed along the shell axis according to an arbitrary law. When carrying out numerical experiments, the load moving at a given speed was assumed to be uniformly distributed in a certain area along the lower half of the inner surface of the shell. The outer (enclosing) layer was assumed to have different rigidity in relation to the rigidity of the array. The calculation results presented in the form of tables and graphs are analyzed in detail. From the analysis of the calculation results, it follows that the enclosing layer, as well as its rigidity, to a large extent affects both the critical load speeds and the displacements and stresses in the array.