Linear and nonlinear oscillation dampers in the vibration protection system of buildings

The article presents an algorithm for the analysis of buildings and structures modeled as systems with a finite number of degrees of freedom, whose structural model includes a dynamic vibration damper intended to limit vibration levels. The algorithm is constructed using a method based on the numerical solution of systems of nonlinear integral equations, to which the systems of nonlinear differential equations of motion for finite-degree-of-freedom systems are reduced. The numerical procedure is implemented using a time-stepping method with iterative refinement of the nonlinear terms.

As a result, computational relationships were obtained that make it possible to analyze buildings equipped with linear and nonlinear vibration dampers, including dampers with additional links that are activated when specified displacements are reached. Calculations were performed for a building with both linear and nonlinear vibration dampers, demonstrating the effectiveness of various types of dampers within the building vibration protection system, and an analysis of the results was carried out.

1. Recommendations for the design of vibration dampers to protect buildings and structures subjected to horizontal dynamic impacts from process equipment and wind. TsNIISK im. Kucherenko. Moscow: Stroyizdat; 1978. 69 p.

2. Korenev B.G., Reznikov L.M. Dynamic vibration absorbers: Theory and technical applications. Moscow: Nauka; 1988. 304 p.

3. Dukart A.V., Oleynik A.I. Dynamic vibration dampers of structures. Moscow: Publishing House ASV; 2015. 248 p.

4. Korenev B.G., Pikulev N.A., Sheynin I.S. On measures to reduce vibrations when passing through resonance during equipment start-up and shutdown. In: Vibrations of buildings and structures. Moscow: Gosstroyizdat; 1963. p. 74-97.

5. Nizomov D.N., Kalandarbekov I. Numerical solution of problems for calculating buildings considering a dynamic vibration absorber. Doklady Natsional'noy Akademii Nauk Tadzhikistana [Proceedings of the National Academy of Sciences of Tajikistan]. 2010;53(6):460-467.

6. Nesterova O.P. Features of calculation of structures with dynamic vibration absorbers based on design earthquake accelerograms. Vestnik grazhdanskikh inzhenerov [Bulletin of Civil Engineers]. 2019;(2(73)):48-53.

7. Mirsaidov M.M., Ishmatsov A.N., Yuldoshev B.Sh., Salimov Sh.M., Khazratkulov I.O. Nonlinear oscillations of a high-rise structure with a dynamic vibration absorber. Izvestiya vuzov. PND [Proceedings of Universities. Nonlinear Dynamics]. 2025. DOI: 10.18500/0869-6632-003186.

8. Bogdanova G.A., Ivanova Zh.V. Application of dynamic vibration dampers to increase the stability of tower communication structures to wind effects. Izvestiya Peterburgskogo universiteta putey soobshcheniya [Proceedings of Petersburg Transport University]. Saint Petersburg: PGUPS; 2023;20(3):660-672. DOI: 10.20295/1815-588X-2023-3-660-672.

9. Hashim A., Taiki S. Dynamic vibration control of non-linear buildings using multiple tuned mass dampers. Building Engineering. 2023;1(1):488. DOI: 10.59400/be.v1i1.488.

10. Vilceanu V., Kavrakov I., Morgenthal G. Coupled numerical simulation of liquid sloshing dampers and wind–structure simulation model. Journal of Wind Engineering and Industrial Aerodynamics. 2023;240:105505. Germany. DOI: 10.1016/j.jweia.2023.105505.

11. Mirsaidov M., Abdikarimov R., Khudainazarov Sh., Sabirjanov T. Damping of high-rise structure vibrations with viscoelastic dynamic dampers. E3S Web of Conferences. 2020;224:02020. DOI: 10.1051/e3sconf/202022402020.

12. Bogdanova G., Benin A. Methodology for Assessing the Response Parameters of Multi-storey Buildings with Non-linear Dynamic Vibration Dampers in Case of Seismic Impacts. In: Technological Advancements in Construction 2022. p. 553-564. DOI:10.1007/978-3-030-83917-8_50.

13. Kuras P., Ortyl L., Owerko T., Kocierz R., Kedzierski M., Podstolak P. Analysis of effectiveness of steel chimneys vibration dampers using surveying methods. In: Proceedings of the 16th International Multidisciplinary Scientific GeoConference (SGEM 2016). Book 2. Vol. 3. Bulgaria; 2016. p. 255-262.

14. Chernov Yu.T. Vibrations of building structures. Analytical calculation methods. Fundamentals of design and standardization of vibrations of building structures subjected to operational dynamic impacts. 2nd ed. Moscow: Publishing House ASV; 2011. 384 p.

15. Petrov I.A. Assessment of the effectiveness of vibration protection systems with nonlinear characteristics [dissertation]. Moscow; 2013. 119 p. (In Russian)

16. Chernov Yu.T., Petrov I.A. Determination of equivalent static forces in the calculation of systems with disconnecting connections. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012;(4):98-101.

17. Zebilila M.D.Kh. Calculation of vibration protection systems with nonlinear elements. In: Construction – formation of living environment [Electronic resource]: Proceedings of the XIX International Interuniversity Scientific-Practical Conference of Students, Undergraduates, Postgraduates and Young Scientists. Moscow; 2016. p. 281-285. URL: https://mgsu.ru/resources/izdatelskaya-deyatelnost/izdaniya/izdaniya-otkr-dostupa/2016/stroy_form_2016.pdf (accessed: 12/15/2025).

18. Kbeili D., Chernov Yu.T. Calculation of a vibration-isolated building system with nonlinear characteristics under kinematic excitation (base displacement). Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Structures and Buildings]. 2024;20(4):374-387.

19. Chernov Yu.T. Integral equations of the second kind in problems of calculating nonlinear systems with a finite number of degrees of freedom under arbitrary dynamic impacts and the nature of physical dependencies. Vestnik NITs "Stroitel'stvo" [Bulletin of the Research Center "Construction"]. 2023;38(3):155-167.

20. Barkan D.D. Dynamics of bases and foundations. Moscow: Stroyvoenmorizdat; 1948. 411 p.

21. Recommendations for vibration protection of load-bearing structures of industrial buildings. TsNIISK im. V.A. Kucherenko. Moscow: Stroyizdat; 1988. 217 p.

22. Clough R.W., Penzien J. Dynamics of structures. New York: McGraw-Hill; 1975. (Russian translation: Moscow: Stroyizdat; 1979. 320 p.)