Modeling the Effectiveness of Damping Systems in Building Structures under Seismic Impact Using the Generalized Ornstein-Uhlenbeck Process

Introduction. At the current stage of science and technology development, the issues of vibration protection of buildings are being intensively investigated, particularly for special structures of a high responsibility class. Various damper designs are also being developed and tested. Modeling the response of damper systems is an urgent task with both deterministic and stochastic approaches to solving it. This study demonstrates the features of the stochastic approach in a variant of the mathematical model of the generalized Ornstein-Uhlenbeck process. It is possible to the effect of using a nonlinear damper in a specific case can be evaluated by means of this model, and the conclusions can be made regarding its benefits.

Materials and Methods. The major research method is the solution of a stochastic differential equation. A numerical experiment is shown with a real example of analyzing the dynamic response of a turbo unit with a viscoelastic nonlinear damper to a random seismic impact. The application of the generalized Ornstein-Uhlenbeck process for mathematical modeling of the dynamic response of damping devices to seismic impacts on critical energy infrastructure is analyzed.

Research Results. A stochastic model is set forth that takes into account both the random nature of seismic excitations and the nonlinear rheological characteristics of dampers. The results of the numerical experiment confirm that while calculating by means of the described model, the use of a nonlinear damper is justified, the mean-square values of the displacement response are reduced by more than two times helping to reduce seismic risks for the turbine unit as well as to increase its dynamic stability and reliability of operation under the action of random impacts.

Discussion and Conclusions. The developed methodology provides a quantitative assessment of the effectiveness of a variety of classes of damper systems and allows for parametric optimization of their settings in order to maximize their protective capacity and to reduce the vibration and dynamic loads on energy equipment. The theoretical significance of the study is the suggested calculation methodology, while the practical significance is in the assessment and recommendations for making use of viscoelastic dampers for a high responsibility class of structures.

1. Khan IU, Usman M, Tanveer M Vibration Control of an Irregular Structure Using Single and Multiple Tuned Mass Dampers. Proceedings of the Institution of Civil Engineers – Structures and Buildings. 2021;176(10):778–790. https://doi.org/10.1680/jstbu.21.00011

2. Elias S, Rupakhety R, Olafsson S Tuned Mass Dampers for Response Reduction of a Reinforced Concrete Chimney Under Near-Fault Pulse-Like Ground Motions. Frontiers in Built Environment. 2020;6. https://doi.org/10.3389/fbuil.2020.00092

3. Brysin AN, Solovyev VC, Mikayeva SA, Nikiforov AN Seismic and Shock Effects Reduction by Vibration Protection Systems Equipped with Amplifiers of Inertial Characteristics. IOP Conference Series: Materials Science and Engineering, 2019;698(2):022049. https://doi.org/10.1088/1757-899X/698/2/022049

4. Wang L, Zhou Y, Shi W Dynamic Test, Monitoring and Active Control of Non-Resonant Running-Induced Vibration for Floor Structure. Structures. 2024;63:106348. https://doi.org/10.1016/j.istruc.2024.106348

5. Simbirkin VN, Panasenko YuV, Kurnavin VV Analysis of Various Damping Models in The Simulation of the Seismic Response of Structures in the STARK ES Software. Reinforced Concrete Structures. 2023;2(2):58–64. (In Russ.) https://doi.org/10.22227/2949-1622.2023.2.58-64

6. Kim YC, Lee HW, Hu JW Experimental Performance Evaluation of Elastic Friction Damper. Case Studies in Construction Materials. 2023;18:e01823. https://doi.org/10.1016/j.cscm.2023.e01823

7. Shirai K, Sano T, Suzui Y Energy Response of a Passive Variable Friction Damper and Numerical Simulation on the Control Effects for High-Rise Buildings. Structural Control Health Monitoring. 2022;29. https://doi.org/10.1002/stc.3124

8. Stanekzai M, Elias S, Chae Y Research Advances in Hybrid Vibration Control Systems. Practice Periodical on Structural Design and Construction. 2022. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000685

9. Aggumus H, Guclu R Hybrid Experimental Investigation of MR Damper Controlled Tuned Mass Damper Used for Structures under Earthquakes. Journal of Soft Computing and Artificial Intelligence. 2022;3(1):28–33. https://doi.org/10.55195/jscai.1122514

10. Pecora R A Practical Approach for the Mitigation of Seismic-Induced Vibrations in Slender Metallic Structures through Magnetorheological Fluid Dampers. Applied Sciences. 2022;12(9):4155. https://doi.org/10.3390/app12094155

11. Pushkarev IA The Analysis of Vibrations in a Floor Plate with Two Sources of Vibration. Bulletin of the South Ural State University. Ser. Construction Engineering and Architecture. 2024;24(3):24–32. (In Russ.) http://dx.doi.org/10.14529/build240303

12. Pushkarev IA Structural Diagram of Vibration Protection Means of Building Structures with Moving Loads. Vestnik IzhGTU imeni M.T. Kalashnikova. 2022;25:27–36. (In Russ.) https://doi.org/10.22213/2413-1172-2022-4-27-36

13. Etedali S, Akbari M, Seifi M Friction Tuned Mass Dampers in Seismic-Excited High-Rise Buildings with SSI Effects: A Reliability Assessment. Journal of Earthquake and Tsunami. 2023;17(2):2250022. https://doi.org/10.1142/S1793431122500221

14. Tuninetti V, Gómez Á, Bustos F, Oñate A, Hinojosa J, Gallo C et al. Computational Modeling of U-Shaped Seismic Dampers for Structural Damage Mitigation. Applied Sciences. 2024;14(22):10238. https://doi.org/10.3390/app142210238

15. Abdullazyanov EY, Sabitov LS, Garkin IN, Zakirova MA Resource-Optimization Approach during Repair Work at Tower-Type Energy Construction Facilities. Construction Production. 2025;2:105–111. (In Russ.)

16. Yevseyev AYe, Garkin IN, Abdullazyanov EYu Using Differential Equations of Body Motion in Determining Vibration Protection Parameters. Engineering and Construction Bulletin of the Caspian Region. 2024;4(50):127–131. (In Russ.) https://doi.org/10.52684/2312-3702-2024-50-4-127-131

17. Korotkov VA Analysis of Dynamic Methods for Calculating NPP Building Structures. Bulletin of Science and Research Center of Construction. 2023;2(37):7–17. (In Russ.) https://doi.org/10.37538/2224-9494-2023-2(37)-7-17

18. Simbirkin VN, Panasenko YV, Kurnavin VV Modelling of Damping Devices in the Seismic Analysis of an Airport Terminal Structures. Earthquake Engineering Constructions Safety. 2022;2:118–124 (In Russ.) https://doi.org/10.37153/2618-9283-2022-2-118-124

19. Simbirkin VN, Panasenko YV, Kurnavin VV Modelling the Operation of Liquid-Viscous Dampers when Calculating the Seismic Response of Structures. Structural Mechanics and Analysis of Constructions. 2022;2(301):2–8. (In Russ.) URL: https://stroy-mex.narod.ru/index/2022_2/0-270 (дата обращения 11.11.2025)

20. Sadenko DS, Garkin IN, Ariskin MV Scientific and Technical Support of Work on Strengthening the Building Structures of a Monolithic Multi-Storey Residential Building. Regional Architecture and Engineering. 2023;3(56):122–127. (In Russ.)