Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress-strain state of the half-space is examined Introduction. The mathematical simulation of the dynamic behavior of tunnels and pipelines subject to transport loads leads to boundary-value problems for an elastic medium with cylindrical cavities reinforced with elastic single-and many-layer shells. The effect of the daylight surface is usually neglected for deep underground structures (their depth of burial is more than five typical transverse dimensions). The bibliography of such models can be found in [5]. Pozhuev [7] was the first to find the solution for an axisymmetric normal load moving with a constant subsonic velocity over a thin-walled cylindrical shell in an elastic medium. Similar studies for a two-layer shell were conducted in [1,3]. It was shown that there are critical velocities exceeding which causes free undamped vibrations in tunnels [3,5].For shallow underground structures (depth of burial is less than five typical transverse dimensions), the effect of the daylight surface should be taken into account. The motion of a subsonic periodic load along a nonreinforced cylindrical cavity in an elastic half-space was studied in [2,5], where incomplete separation of variables and reexpansion of cylindrical and plane waves were used to obtain the exact analytic solutions of the relevant boundary-value problems. However, finding such solutions for models of shallow lined tunnels is still a challenge. Note that a few publications address dynamic problems for a prestressed elastic layered half-space under a moving load [9, 10] and for shells under a nonstationary load [11, 12, etc.].We will find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the shell axis. In finding the analytic solution, we will plot and analyze dispersion curves for the cases of sliding and tight contacts between the shell and the half-space. The influence of shell parameters on the stress-strain state (SSS) of the half-space will be examined.1. Formulation and the Solution of a Periodic Problem. Consider a thin infinitely long cylindrical shell with mid-surface radius R and thickness h 0 in an elastic, homogeneous, isotropic half-space with Lamé parameters l, m and density r. We choose a Cartesian coordinate system with the Z-axis aligned with the axis of the cavity parallel to the load-free flat boundary of the half-space and the X-axis perpendicular to this boundary: x £ h, where h is the...

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Based on the solution of the problem of the action of a transport loads moving at a constant speed on a three-layer or two-layer shells in an elastic half-space, a comparative analysis was performed for the rock mass in the vicinity of a shallows circular tunnel with various designs of their lining (three-layer and two-layer), along the inner surface of which an axisymmetric normal load moves at a constant speed. The inner layer of the three-layer lining is a thick-walled concrete shell, and the outer layers are thin-walled steel shells of equal thickness. The two-layer lining is structurally different from the considered three-layer lining by the absence of the inner layer of the lining. Dynamic equations of elasticity theory in Lame potentials are used to describe the motion of the half-space and the inner layer of the shell. The vibrations of the outer layers of the shell are described by the classical equations of the theory of thin shells. The equations are represented in a movable coordinate system. The contact between the shell and the array is assumed to be either rigid or sliding. The contact between the layers of the shell is supposed to be rigid. To solve the problem, the method of incomplete separation of variables is used. The solution for potentials is presented in the form of a superposition of Fourier-Bessel series and contour integrals of the Fourier type. Next, the method of decomposition of potentials into plane waves and re-decomposition of plane waves into series according to cylindrical functions is used. The solution is obtained for the case when the velocity of the load is less than its critical velocities. The calculation results are presented in the form of graphs and are analyzed in detail. From the analysis of the calculation results, it follows that the use of a three-layer lining as a building envelope is more efficient than a two-layer lining, since in this case the dynamic effect of the moving loads on the rock mass is significantly less.