UNSTEADY DYNAMICS OF A CYLINDRICAL SHELL WITH A VISCOELASTIC FILLER UNDER THE ACTION OF A MOVING LOAD

Abstract

In the course of the study, the problems of the action of moving loads on cylindrical shells filled or surrounded by an elastic medium were considered, and a refined approach to solving such problems for three-layer shells, when the movement of the filler is described by the dynamic equations of the theory of elasticity, was analyzed in detail. The main emphasis was placed on the application of the principle of correspondence between elastic and viscoelastic problems. This principle consists of replacing the Lame coefficients in the equations for displacements and stresses of points of the medium in image space with complex values. The final solution is found by applying the inverse Fourier and Laplace transform. It is shown that this principle allows one to generalize previously considered problems of this class in the case of viscoelastic media. If it is used for unsteady problems, the mechanical properties of a viscoelastic material can be specified in a fairly general form. The proposed approach is applied to solving the problem of the action of a moving load on an infinitely long cylindrical shell containing a viscoelastic filler, the inner surface of which is stress-free. Numerical results were obtained for the problem of the motion of an axisymmetric normal load. As a result of the damping properties of the viscoelastic filler, the resulting unsteady solution is unique at any load speed. The inversion integrals are special and their values are found using a special algorithm containing the joint application of the Failon method and the shifted Legendre polynomials. The distribution of dimensionless deflections along the length of the shell is given for different loading speeds. It has been determined that taking into account the viscoelastic properties of the filler allows us to consider all modes of load movement equally from the point of view of calculating the inversion integrals. The results of the study can be used for the calculation and design of cylindrical shells with viscoelastic filler used in aircraft and mechanical engineering, construction and other industries.