Аңдатпа
The paper considers forced vibrations of two absolutely rigid bodies connected by a viscoelastic circular cylindrical shell. The steady-state motion of a system consisting of two absolutely rigid bodies with masses m and M, which are connected by a circular cylindrical shell of mass m0, under the action of a force F(t) applied to the body of mass m and located on the axis of symmetry is studied. Before the force F(t) was applied, the system was in a state of equilibrium. Both bodies are attached to the shell rigidly. Axisymmetric vibrations of the shell are considered. The equations of motion of the shell satisfy the Kirchhoff-Love hypotheses. The cylindrical shell is rigidly connected to the masses. The main goal is to determine the amplitude of the shell displacements depending on the frequency of external forces. The Boltzmann-Voltaire integral is used to describe the viscous properties of the shell material. The three- parameter weakly singular Rzhanitsyn-Koltunov kernel is used as the relaxation kernel of viscoelastic materials. To solve this problem, a methodology and algorithm based on the methods of separation of variables, Gauss and Muller, have been developed. Taking into account the viscoelastic properties of the shell material makes it possible to reduce the maximum values of amplitude and displacement to 15%.