Dynamics of a Damping Device Based on Ishlinsky Material

Abstract

In present paper we consider the damping properties of the oscillating system with hysteretic nature. The mathematical model of considered system is based on the operator approach for the hysteretic nonlinearity on the example of Ishlinsky material. Such a converter is a continual analogue of the set of stops connected in parallel. In the frame of the paper we compare the various approaches to modeling of damping systems. Namely, together with the hysteretic damper we consider the so-called nonlinear viscous damper which is a generalization of a standard linear damper with dependence on the velocity. The mathematical model of the considered system is formulated in terms of second order ordinary differential equation with hysteretic nonlinearity (namely, the operator-type nonlinearity). In comparison with the phenomenological models of hysteresis (such as Bouc-Wen model) that are often used in the modeling, the Ishlinsky model allows to " feel" the hysteretic nature of the material on the physical level. The major result of the presented paper is the comparison both the hysteretic and viscous (including the linear and nonlinear cases) dampers. Such a comparison is made in terms of transmission functions that reflect the "efficiency" of suppression of the external perturbations by the force transmission from an external source to the load. The results of numerical simulations showed the high efficiency of hysteretic damper both in and outside the resonance region (at the same time it is well known that the linear viscous damper has a weak efficiency outside the resonance region). The disadvantage of the hysteretic damper lies in the fact that its ability to dump the relative motion of the system under external forces is insignificantly reduced outside the resonance region.