Oscillations of a Body on Rolling Bearings with Straightened Surfaces Caused by a Random Movement of the Base

Traditional methods of protecting structures from the destructive forces of nature, appearing during earthquakes, based on the strengthening of structures, lead to a significant increase in the cost of construction in seismically hazardous areas. Rolling bearings, limited by various surfaces of rotation as the main element, are used in many seismic and vibration protection devices. In this work, random oscillations of a vibration-protected body on vibration supports with straightened surfaces are studied. Within the framework of the theory of Markov processes of non-linear mechanical systems, the Fokker-Planck-Kolmogorov (FPK) equations for the amplitude probability density describing the oscillatory movements of a vibration-protected body on vibration supports with straightened surfaces are compiled, taking into account rolling friction on relaxing soils under random kinematic influences such as “white noise”. Solutions are obtained in stationary and non-stationary formulations. The probabilistic characteristics of the amplitude of random vibrations of a vibration-protected body are determined.