Vibrations of mechanical systems with energy dissipation hysteresis

A phenomenological approach which we refer to as kinematic is proposed to describe hysteresis; according to this approach, the force and kinematic parameters of a mechanical system are related by a first-order ordinary differential equation. The right-hand side is chosen in the class of functions ensuring the asymptotic approach of the solution to the curves of the enveloping (limit) hysteresis cycle of steady-state vibrations. The coefficients of the equation are identified by experimental data for the enveloping cycle. The proposed approach permits describing the hysteresis trajectory under the conditions of unsteady vibrations with an arbitrary starting point inside the region of the enveloping cycle. As an example, we consider the problem on forced vibrations of a pendulum-type damper of low-frequency vibrations.