Study of forced vibrations transition processes of vibration protection devices with rolling-contact bearings

Abstract

Many seismic isolation and vibration protection devices use asan essential element the various types of rolling-contact bearings. The rolling-contact bearing is used for creation of moving base of body protected against vibration. The most dynamic disturbances acting in the constructions and structures have highly complex and irregular nature. This article considers the oscillation of a solid body on kinematic foundations, the main elements of which are rolling bearers bounded by the high order surfaces of rotation at horizontal displacement of the foundation. It is ascertained that the equations of motion are highly nonlinear differential equations. Stationary and transitional modes of the oscillatory process of the system have been investigated. It is determined that several stationary regimes of the oscillatory process exist. Equations of motion have been investigated also by quantitative methods. In this paper the cumulative curves in the phase plane are plotted, a qualitative analysis for singular points and study of them for stability is performed. In the Hayashi plane a cumulative curve of body protected against vibration forms a closed path which does not tend to the stability of singular point. This means that the vibration amplitude of body protected against vibration is not remain constant in steady-state, but changes periodically.