Calculation of the natural frequencies of the transverse of cable oscillations at the area of application of insulation

Researches the transverse vibrations of the cable in the area where the insulation is applied to it. The considered mathematical model takes into account a wide range of factors affecting the oscillations: longitudinal motion, variable bending stiffness, environmental resistance, cable tension. The object belongs to a wide range of one-dimensional objects with moving boundaries. Moving boundaries complicate the description of such objects. The article introduces new variables that stop the boundaries. In this paper, using the Galerkin method, a fourth-order algebraic equation is obtained, which makes it possible to obtain two first natural frequencies of cable oscillations. The considered methods of statement and solution of the problem allow to solve the problems arising in the study of oscillations of objects with moving boundaries. Results can be used to ensure reliable operation of the technological installation for the manufacture of cables.