On the modeling of hysteretic oscillations of mechanical systems

The paper considers nonstationary vibrations of mechanical systems with hysteretic dampers. To describe the hysteresis, a phenomenological approach is suggested, which is demonstrated on the problem of forced vibrations produced by the antigalloping device used for protection of power transmission lines. In accordance with this approach, the force and kinematic parameters of the mechanical system are correlated via the first-order ordinary differential equation. The right-hand part of the equation is chosen from the class of functions that ensure the asymptotic approximation of the solution to the curves of the enveloping (boundary) hysteretic cycle of steady-state vibrations. Identification of the equation coefficients is carried out based on experimental data for the enveloping cycle. The proposed approach allows us to describe the trajectory of hysteresis under the conditions of nonstationary vibrations, as well as to evaluate the effectiveness of damping devices and to select the frequency ranges of their application.