IFToMM WC 2019: Advances in Mechanism and Machine Science pp 4205-4215

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

• Kuatbay Bissembayev
• Assetkhan Smanov
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

## 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.

## Keywords

Vibroprotection seismic protection rolling bearer protection against vibration rolling-contact bearing non-linear vibrations stochastic oscillations

## References

1. 1.
Amir Fateh A, Farzad Hejazi A, Amond Salehjaafar A, Izian ABD. Karim A, Azlan Bin Adnan. Design of a variable stiffness bracing system, Mathematical modeling, fabrication, and dynamic analysis, Soil Dynamics and Earthquake Engineering 80, p. 87-101(2016).Google Scholar
2. 2.
Athanasios A. Markou, George D. Manolis, Mechanical models for shear behavior in high damping rubber bearings, Soil Dynamics and Earthquake Engineering, Volume 90, November, p. 221-226(2016).Google Scholar
3. 3.
Massa G., Pagano S., Rocca E., and Strano S. Sensitive equipments on WRS-BTU isolators Meccanica 48, p. 1777-1790 (2013)Google Scholar
4. 4.
Cherepinskiy D. The seismic isolation of residential buildings, Research of seismic stability of buildings and structures, Alma-Ata, p. 438-462(2015)Google Scholar
5. 5.
Ying Zhou, Peng Chen, Shaking table tests and numerical studies on the effect of viscous dampers on an isolated RC building by friction pendulum bearings, Soil Dynamics and Earthquake Engineering, Volume 100, September, p. 330-344(2017).Google Scholar
6. 6.
Bissembayev K., Iskakov Zh. Oscillations of the orthogonal mechanism with a non-ideal source of energy in the presence of a load on the operating link, Mechanism and Machine Theory 92, p. 153-170 (2015).Google Scholar
7. 7.
Bissembayev K., Omyrzhanova Zh, Friction arising from rolling of a bearing with straightened surfaces on a relaxing ground, Proceedings of 22nd International Conference “MECHANIKA 2017”, Kaunas University of Technology, Lithuania, 19 May, p. 52-57(2017).Google Scholar
8. 8.
Bissembayev K., Omyrzhanova Z., Sultanova K. Oscillations specific for the homogeneous rod like elastic structure on the kinematic absorber basis with rolling bearers having straightened surfaces, Advances in Italian Mechanism Science Proceedings of the Second International Conference of IFToMM Italy, Mechanisms and Machine Science, vol. 68- Italy.-P. 187 - 195, Springer, Cham. DOI: (2018)
9. 9.
Bakirov Zh.B., Bakirov M.Zh. Application of the Markov process theory to the analysis of nonlinear random oscillations,Science Bulletin of the NSTU, Vol.59, No.2, p. 73–88 (2015). (In Russian)Google Scholar