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
typ es of rolling-contact b earings. The rolling-contact b earing is used for creation of moving base
of b o dy 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 b o dy on kinematic foundations, the main elements
of which are rolling b earers b ounded 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 mo des of the oscillatory pro cess of the system
have b een investigated. It is determined that several stationary regimes of the oscillatory pro cess
exist. Equations of motion have b een investigated also by quantitative metho ds.
In this pap er the cumulative curves in the phase plane are plotted, a qualitative analysis for singular p oints and study of them for stability is p erformed. In the Hayashi plane a cumulative curve
of b o dy protected against vibration forms a closed path which do es not tend to the stability of
singular p oint. This means that the vibration amplitude of b o dy protected against vibration is not
remain constant in steady-state, but changes p erio dically.