Torsional vibrations of a three-layer circular cylindrical elastic shell
Abstract
The equations of unsteady torsional vibrations are developed in the work on the basis of exact solutions in transformations of the three-dimensional problem of elasticity theory for a three-layer circular cylindrical elastic shell. It is believed that the vibrations of the shell are excited by external forces acting on the inner and outer surfaces. The thicknesses of the layers are generally different and 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. The initial conditions are assumed to be zero. To derive the vibration equations, the method of transformed exact solutions of a three-dimensional problem of linear elasticity theory is used. From the obtained vibration equations, in particular cases, it is possible to obtain refined and approximate vibration equations, which in the case of a homogeneous shell pass into the well-known vibration equations developed by other authors. Along with the vibration equations, an algorithm has been developed that allows determining the stress-strain state of an arbitrary cross-section of layers and the shell as a whole by spatial coordinates and time from the field of the desired functions. In addition, the results obtained allow for special cases of transition into two-layer and homogeneous shells, as well as into a round three-layer rod.