Stochastic oscillations of a solid body with a kinematic system of vibration isolation

Abstract

In this paper, we study the oscillatory motion of a solid body on vibration support bounded by high-order rotation surfaces taking into account rolling friction on relaxing soils with a horizontal displacement of the base according to a random law. The nonlinear oscillations of vibration-protective systems in the transitional mode (oscillations in the process of their transition to the steady state) are investigated and the effects of rolling friction of the relaxing soil on the effectiveness of vibration protection by rolling bearings representing geometric bodies bounded by two high-order surfaces are identified. To analyze the equation of motion of a vibration-proof body on rolling bearings with straightened surfaces, methods of the theory of diffusion Markov processes are applied. Fokker-Plank-Kolmogorov (FPK) equations are constructed by the averaging method according to the scheme of V.M. Volosov and B.I.Morgunov and solving it, the density functions of the probability distribution of the vibration-protected body on rolling bearings with straightened surfaces are determined. Numerical characteristics of random dynamic variables are obtained and the dependence of the most probable amplitude value on the disturbance intensity is constructed for different values of the rolling friction coefficient. It is established that the most probable value of the amplitude weakly depends on the intensity of the disturbance. This property of rolling bearings, bounded by high-order surfaces, makes them promising for creating structural vibration protection means under conditions of strong kinematic perturbations.