Comparison of Single- and Bi-Tuned Mass Dampers under Equal Total Auxiliary Mass and Different Dynamic Loads in a Wind Turbine Tower–Nacelle System

Abstract

This study compares a single tuned mass damper and a bi-tuned mass damper in a single-degree-of-freedom wind turbine tower–nacelle model. Four configurations are evaluated under the same total auxiliary mass: the classical Den Hartog design, a single damper retuned with the common objective, a bi-tuned damper with equal branch masses, and a bi-tuned damper with a free mass split. The objective combines normalized displacement and acceleration responses over a frequency band around the main natural frequency, and the designs are optimized for total auxiliary mass ratios of 0.02, 0.05, and 0.20. A coarse sweep is followed by a toolbox-free particle swarm optimization; independent differential evolution, extended-bound searches, equal-split coverage, and internal consistency checks are used for verification. The equal-branch bi-tuned damper gave a lower band objective than the retuned single damper at all three mass ratios. The free-split search did not improve on the equal split at the two lower mass ratios and provided only a small additional gain at 0.20. The retuned single damper performed best under single-frequency harmonic loading, whereas both bi-tuned configurations yielded marginally lower objective values under the chirp load. For ten zero-mean Kaimal realizations normalized to 100 N root mean square, paired analysis at a mass ratio of 0.20 identified small but statistically significant differences; the equal-branch bi-tuned damper had the lowest mean objective. Frequency-response and ±10% natural-frequency-deviation analyses showed that two tuning branches redistribute the response across the band, but do not provide unconditional detuning robustness. The practical choice therefore depends not only on the objective value but also on stroke demand, transmitted force, component count, and maintenance requirements.

Keywords

• Bi-tuned mass damper
• Mass split
• Multi-frequency optimization
• Tuned mass damper
• Vibration control
• Wind turbine

Ethical Statement

Ethics committee approval was not required because the study did not involve human participants or animals.

References

1. Abé, M., & Fujino, Y. (1994). Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthquake Engineering & Structural Dynamics, 23(8), 813–835. https://doi.org/10.1002/eqe.4290230802
2. Bertollucci Colherinhas, G., Petrini, F., de Morais, M. V. G., & Bontempi, F. (2021). Optimal design of passive-adaptive pendulum tuned mass damper for the global vibration control of offshore wind turbines. Wind Energy, 24(6), 573–595. https://doi.org/10.1002/we.2590
3. Cao, H. Q., & Tran, N.-A. (2023). Multi-objective optimal design of double tuned mass dampers for structural vibration control. Archive of Applied Mechanics, 93(5), 2129–2144. https://doi.org/10.1007/s00419-023-02376-6
4. Den Hartog, J. P. (1985). Mechanical vibrations (4th ed.). Dover Publications.
5. Han, D., Wang, W., Li, X., & Su, X. (2022). Optimization design of multiple tuned mass dampers for semi-submersible floating wind turbine. Ocean Engineering, 264, Article 112536. https://doi.org/10.1016/j.oceaneng.2022.112536
6. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.
7. IEC. (2005). Wind turbines – Part 1: Design requirements (IEC 61400-1:2005, 3rd ed.). International Electrotechnical Commission.
8. Igusa, T., & Xu, K. (1994). Vibration control using multiple tuned mass dampers. Journal of Sound and Vibration, 175(4), 491–503. https://doi.org/10.1006/jsvi.1994.1341

9. Jahangiri, V., & Sun, C. (2020). Three-dimensional vibration control of offshore floating wind turbines using multiple tuned mass dampers. Ocean Engineering, 206, Article 107196. https://doi.org/10.1016/j.oceaneng.2020.107196
10. Jahani, K., Langlois, R. G., & Afagh, F. F. (2022). Structural dynamics of offshore wind turbines: A review. Ocean Engineering, 251, Article 111136. https://doi.org/10.1016/j.oceaneng.2022.111136
11. Jangid, R. S. (1999). Optimum multiple tuned mass dampers for base-excited undamped system. Earthquake Engineering & Structural Dynamics, 28(9), 1041–1049. https://doi.org/10.1002/(SICI)1096-9845(199909)28:9<1041::AID-EQE853>3.0.CO;2-E
12. Kaimal, J. C., Wyngaard, J. C., Izumi, Y., & Coté, O. R. (1972). Spectral characteristics of surface-layer turbulence. Quarterly Journal of the Royal Meteorological Society, 98(417), 563–589. https://doi.org/10.1002/qj.49709841707
13. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN'95 – International Conference on Neural Networks (pp. 1942–1948). IEEE. https://doi.org/10.1109/ICNN.1995.488968
14. Kim, S.-Y., & Lee, C.-H. (2018). Optimum design of linear multiple tuned mass dampers subjected to white-noise base acceleration considering practical configurations. Engineering Structures, 171, 516–528. https://doi.org/10.1016/j.engstruct.2018.06.002
15. Li, C. (2000). Performance of multiple tuned mass dampers for attenuating undesirable oscillations of structures under the ground acceleration. Earthquake Engineering & Structural Dynamics, 29(9), 1405–1421. https://doi.org/10.1002/1096-9845(200009)29:9<1405::AID-EQE976>3.0.CO;2-4
16. Luan, Z., Dou, P., Chen, Y., Zhang, H., & Ku, Y. (2024). Optimization study of a tuned mass damper for a large monopile wind turbine. Energies, 17(17), Article 4460. https://doi.org/10.3390/en17174460
17. Martynowicz, P. (2019). Nonlinear optimal-based vibration control for systems with MR tuned vibration absorbers. Journal of Low Frequency Noise, Vibration and Active Control, 38(3–4), 1607–1628. https://doi.org/10.1177/1461348418819410
18. Martynowicz, P. (2022). Experimental study on the optimal-based vibration control of a wind turbine tower using a small-scale electric drive with MR damper support. Energies, 15(24), Article 9530. https://doi.org/10.3390/en15249530
19. McNamara, D., Pandit, A., & Malekjafarian, A. (2024). Optimized design of multiple tuned mass dampers for vibration control of offshore wind turbines. Ocean Engineering, 305, Article 117912. https://doi.org/10.1016/j.oceaneng.2024.117912
20. Ok, S. Y., Song, J., & Park, K. S. (2009). Development of optimal design formula for bi-tuned mass dampers using multi-objective optimization. Journal of Sound and Vibration, 322(1–2), 60–77. https://doi.org/10.1016/j.jsv.2008.11.023
21. Shampine, L. F., & Reichelt, M. W. (1997). The MATLAB ODE suite. SIAM Journal on Scientific Computing, 18(1), 1–22. https://doi.org/10.1137/S1064827594276424
22. Snamina, J., Martynowicz, P., & Łatas, W. (2014). Dynamic similarity of wind turbine's tower-nacelle system and its scaled model. Solid State Phenomena, 208, 29–39. https://doi.org/10.4028/www.scientific.net/SSP.208.29
23. Storn, R., & Price, K. (1997). Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359. https://doi.org/10.1023/A:1008202821328
24. Verma, M., Nartu, M. K., & Subbulakshmi, A. (2022). Optimal TMD design for floating offshore wind turbines considering model uncertainties and physical constraints. Ocean Engineering, 243, Article 110236. https://doi.org/10.1016/j.oceaneng.2021.110236
25. Wang, B., Han, D., Wang, W., Li, X., Shen, K., & Li, Y. (2022). Modeling and optimization of multiple tuned mass dampers for a barge-type floating offshore wind turbine. Frontiers in Marine Science, 9, Article 994848. https://doi.org/10.3389/fmars.2022.994848
26. Warburton, G. B. (1982). Optimum absorber parameters for various combinations of response and excitation parameters. Earthquake Engineering & Structural Dynamics, 10(3), 381–401. https://doi.org/10.1002/eqe.4290100304
27. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–83. https://doi.org/10.2307/3001968
28. Yadukrishnan, A. S., Subbulakshmi, A., & Verma, M. (2024). Experimental validation of optimal TMD for wind turbines using real-time hybrid simulation. Journal of Vibration and Control, 30(21–22), 5060–5077. https://doi.org/10.1177/10775463231217618
29. Yamaguchi, H., & Harnpornchai, N. (1993). Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations. Earthquake Engineering & Structural Dynamics, 22(1), 51–62. https://doi.org/10.1002/eqe.4290220105
30. Yaylagul, Z., & Aggumus, H. (2026). Değişken kütle paylaşımının çift-ayarlı kütle sönümleyicilerin titreşim sönümleme performansına etkisi: Bir ön parametrik çalışma. In ASES VII. International Van Scientific Research Congress (pp. 195–202). Ases Yayınevi.
31. Zhang, J. W., Liang, X., Wang, L. Z., Wang, B. X., & Wang, L. L. (2023). The influence of tuned mass dampers on vibration control of monopile offshore wind turbines under wind-wave loadings. Ocean Engineering, 278, Article 114394. https://doi.org/10.1016/j.oceaneng.2023.114394
32. Zuo, H., Bi, K., & Hao, H. (2017). Using multiple tuned mass dampers to control offshore wind turbine vibrations under multiple hazards. Engineering Structures, 141, 303–315. https://doi.org/10.1016/j.engstruct.2017.03.006
33. Zuo, H., Bi, K., & Hao, H. (2020). A state-of-the-art review on the vibration mitigation of wind turbines. Renewable and Sustainable Energy Reviews, 121, Article 109710. https://doi.org/10.1016/j.rser.2020.109710