Boundary value problems of dynamics of three-layer cylindrical elastic shells

The paper considers the issues of setting problems about nonstationary vibrations of circular cylindrical three-layer shells made of elastic material. It is believed that the shell consists of two extreme load-bearing layers and a middle layer between them. When the space between two rigid layers is filled with a lighter, and therefore less rigid, material, the middle layer is called a filler. The basic equations of motion of torsional, longitudinal-radial and transverse vibrations are given separately for each layer of the shell, which are connected by contact conditions between the layers. When setting problems about shell vibrations, it is assumed that both the cylindrical shell as a whole and the load-bearing layers and filler strictly obey the mathematical theory of elasticity and are described in its exact formulation by its three-dimensional equations in a linear formulation. At the same time, the thicknesses of the layers are generally different and they are made of different materials. Based on the assumption that there is a hard contact between the layers, the dynamic and kinematic contact conditions of the problem are formulated. Based on this, the formulation of problems about tor-sional, longitudinal-radial and transverse vibrations of such a shell is carried out. Torsional, longitudinal-radial and trans-verse vibrations are excited by the corresponding external forces acting on the inner and outer surfaces of the shell. The main types of boundary and contact conditions of the problems under consideration are given. The initial conditions are assumed to be zero.

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