Exploration of the Nonlinear Effect of Pendulum Tuned Mass Dampers on Vibration Control
Publication: Journal of Engineering Mechanics
Volume 147, Issue 8
Abstract
Understanding the nonlinearity of pendulum tuned mass dampers (PTMDs) under large-amplitude vibration is important to enhance control performance. Here, the nonlinear effects of PTMDs on vibration control of a single-degree-of-freedom (SDOF) system under harmonic excitation are explored. The nonlinear governing equations of the linear SDOF structure coupled with the PTMD are formulated. The results obtained via the method of harmonic balance under various excitation amplitudes are compared with those obtained employing the linearized system. It is shown that the effects of PTMD nonlinearity can be ignored when the PTMD rotation angle is below about 9°. Upon increasing the excitation amplitude, remarkable differences are observed between the nonlinear and linear frequency response functions (FRFs). Large mass ratios of PTMD are found to lead to reduced PTMD motion and attenuated nonlinear effects. A parametric study is performed to find the optimal parameters of the nonlinear PTMD under various excitation amplitudes. The results indicate that the optimal tuning frequency ratio increases significantly with excitation amplitudes, whereas the optimal damping is less sensitive to excitation amplitudes. Finally, a 61-m-high steel chimney structure subjected to harmonic and random wind loadings is investigated to verify the proposed PTMD design method.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The work described in this paper is supported by the National Science Fund for Distinguished Young Scholars (No. 52025082), National Natural Science Foundation of China (No. 51808210), and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2018B218).
References
Areemit, N., and P. Warnitchai. 2001. “Vibration suppression of a 90-m-tall steel stack by using a high-damping tuned mass damper.” In Proc., 8th East Asia-Pacific Conf. on Structural Engineering and Construction. Singapore: Nanyang Technological Univ.
Battista, R. C., R. S. Rodrigues, and M. S. Pfeil. 2003. “Dynamic behavior and stability of transmission line towers under wind forces.” J. Wind Eng. Ind. Aerodyn. 91 (8): 1051–1067. https://doi.org/10.1016/S0167-6105(03)00052-7.
Bevilacqua L., R. B. Battista, and N. F. F. Ebecken. 2000. “Dynamical analysis of an offshore platform with vibration absorbers.” In Proc., IUTAM Symp. on Recent Developments in Non-linear Oscillations of Mechanical Systems, edited by N. Van Dao and E. J. Kreuzer. Berlin: Springer.
Brzeski, P., E. Pavlovskaia, T. Kapitaniak, and P. Perlikowski. 2015. “The application of inerter in tuned mass absorber.” Int. J. Non Linear Mech. 70 (10): 20–29. https://doi.org/10.1016/j.ijnonlinmec.2014.10.013.
Brzeski, P., P. Perlikowski, and T. Kapitaniak. 2014. “Numerical optimization of tuned mass absorbers attached to strongly nonlinear Duffing oscillator.” Commun. Nonlinear Sci. Numer. Simul. 19 (1): 298–310. https://doi.org/10.1016/j.cnsns.2013.06.001.
Cao, L. Y., C. X. Li, and X. Chen. 2020. “Performance of multiple tuned mass dampers-inerters for structures under harmonic ground acceleration.” Smart Struct. Syst. 26 (1): 49–61. https://doi.org/10.12989/sss.2020.26.1.049.
Christie, M. D., S. Sun, L. Deng, D. H. Ning, H. Du, S. W. Zhang, and W. H. Li. 2019. “A variable resonance magnetorheological-fluid-based pendulum tuned mass damper for seismic vibration suppression.” Mech. Syst. Sig. Process. 116 (7): 530–544. https://doi.org/10.1016/j.ymssp.2018.07.007.
Den Hartog, J. P. 1985. Mechanical vibrations. New York: Dover.
Eason, R. P., C. Sun, A. J. Dick, and S. Nagarajaiah. 2015. “Steady-state response attenuation of a linear oscillator–nonlinear absorber system by using an adjustable-length pendulum in series: Numerical and experimental results.” J. Sound Vib. 344 (1): 332–344. https://doi.org/10.1016/j.jsv.2015.01.030.
EI-Khoury, O., and H. Adeli. 2013. “Recent advances on vibration control of structures under dynamic loading.” Arch. Comput. Method Eng. 20 (4): 353–360. https://doi.org/10.1007/s11831-013-9088-2.
Elias, S., and V. Matsagar. 2017. “Research developments in vibration control of structures using passive tuned mass dampers.” Annu. Rev. Control 44 (Jan): 129–156. https://doi.org/10.1016/j.arcontrol.2017.09.015.
Ertas, A., O. Cuvalci, and S. Ekwaro-Osire. 2000. “Performance of pendulum absorber for a non-linear system of varying orientation.” J. Sound Vib. 229 (4): 913–933. https://doi.org/10.1006/jsvi.1999.2521.
Fallahpasand, S., M. Dardel, M. H. Pashaei, and H. R. Mohammadi Daniali. 2015. “Investigation and optimization of nonlinear pendulum vibration absorber for horizontal vibration suppression of damped system.” Struct. Design Tall Spec. Build. 24 (14): 873–893. https://doi.org/10.1002/tal.1216.
Farid, M., and O. V. Gendelman. 2017. “Tuned pendulum as nonlinear energy sink for broad energy range.” J. Vib. Control 23 (3): 373–388. https://doi.org/10.1177/1077546315578561.
Fujino, Y., and D. Siringoringo. 2013. “Vibration mechanisms and controls of long-span bridges: A review.” Struct. Eng. Int. 23 (3): 248–268. https://doi.org/10.2749/101686613X13439149156886.
Ghosh, A., and B. Basu. 2007. “A closed-form optimal tuning criterion for TMD in damped structures.” Struct. Control Health Monit. 14 (4): 681–692. https://doi.org/10.1002/stc.176.
Guo, A. X., Y. L. Xu, and H. Li. 2007a. “Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations—I: Theory.” Earthquake Eng. Eng. Vibr. 6 (3): 295–306. https://doi.org/10.1007/s11803-007-0747-x.
Guo, A. X., Y. L. Xu, and H. Li. 2007b. “Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations—II: Experiment.” Earthquake Eng. Eng. Vibr. 6 (4): 417–424. https://doi.org/10.1007/s11803-007-0748-9.
Hatwal, H., A. K. Mallik, and A. Ghosh. 1983. “Forced nonlinear oscillations of an autoparametric system—Part 1: Periodic responses.” J. Appl. Mech. 50 (3): 657–662. https://doi.org/10.1115/1.3167106.
Huang, Z. W., X. G. Hua, Z. Q. Chen, and H. W. Niu. 2019. “Optimal design of TVMD with linear and nonlinear viscous damping for SDOF systems subjected to harmonic excitation.” Struct. Control Health Monit. 26 (10): e2413. https://doi.org/10.1002/stc.2413.
Ikeda, T. 2011. “Nonlinear responses of dual-pendulum dynamic absorbers.” J. Comput. Nonlinear Dyn. 6 (1): 11012. https://doi.org/10.1115/1.4002385.
Kourakis I. 2007. “Structural systems and tuned mass dampers of super-tall buildings: Case study of Taipei 101.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
Kwok, K. C. S. 1983. “Full-scale measurements of wind-induced response of Sydney Tower.” J. Wind Eng. Ind. Aerodyn. 14 (1–3): 307–318. https://doi.org/10.1016/0167-6105(83)90033-8.
Kwok, K. C. S., and P. A. Macdonald. 1990. “Full-scale measurements of wind-induced acceleration response of Sydney Tower.” Eng. Struct. 12 (3): 153–162. https://doi.org/10.1016/0141-0296(90)90002-A.
Kwok, K. C. S., and B. Samali. 1995. “Performance of tuned mass dampers under wind performance of tuned mass dampers under wind loads.” Eng. Struct. 17 (9): 655–667. https://doi.org/10.1016/0141-0296(95)00035-6.
Lacarbonara, W., and S. Ballerini. 2009. “Vibration mitigation of guyed masts via tuned pendulum dampers.” Struct. Eng. Mech. 32 (4): 517–529. https://doi.org/10.12989/sem.2009.32.4.517.
Leung, A. Y. T., H. Zhang, C. C. Cheng, and Y. Y. Lee. 2008. “Particle swarm optimization of TMD by non-stationary base excitation during earthquake.” Earthquake Eng. Struct. Dyn. 37 (9): 1223–1246. https://doi.org/10.1002/eqe.811.
Lu, X. L., and J. R. Chen. 2011. “Parameter optimization and structural design of tuned mass damper for Shanghai Centre Tower.” Struct. Des. Tall Spec. Build. 20 (4): 453–471. https://doi.org/10.1002/tal.649.
Nagase, T., and T. Hisatoku. 1992. “Tuned-pendulum mass damper installed in Crystal Tower.” Struct. Des. Tall Spec. Build. 1 (1): 35–56. https://doi.org/10.1002/tal.4320010105.
Orlando, D., and P. B. Goncalves. 2013. “Hybrid nonlinear control of a tall tower with a pendulum absorber.” Struct. Eng. Mech. 46 (2): 153–177. https://doi.org/10.12989/sem.2013.46.2.153.
Ormondroyd, J., and J. P. Den Hartog. 1928. “Theory of the dynamic vibration absorber.” J. Appl. Mech. 50 (7): 11–22.
Pourzeynali, S., S. Salimi, and H. E. Kalesar. 2013. “Robust multi-objective optimization design of TMD control device to reduce tall building responses against earthquake excitations using genetic algorithms.” Sci. Iran. 20 (2): 207–221. https://doi.org/10.1016/j.scient.2012.11.015.
Pritchard, B. N. 1984. “Steel chimney oscillations: A comparative study of their reported performance versus predictions using existing design techniques.” Eng. Struct. 6 (4): 315–323. https://doi.org/10.1016/0141-0296(84)90029-4.
Rathi A. K., and A. Chakraborty. 2017. “Reliability-based performance optimization of TMD for vibration control of structures with uncertainty in parameters and excitation.” Struct. Control Health Monit. 24 (1): e1857. https://doi.org/10.1002/stc.1857.
Rob, S., R. Merello, and M. Willford. 2010. “Intrinsic and supplementary damping in tall buildings.” Proc. Inst. Civ. Eng. Struct. Build. 163 (2): 111–118. https://doi.org/10.1680/stbu.2010.163.2.111.
Roffel, A. J., and S. Narasimhan. 2016. “Results from a full-scale study on the condition assessment of pendulum tuned mass dampers.” J. Struct. Eng. 142 (1): 4015096. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001339.
Roffel, A. J., S. Narasimhan, and T. Haskett. 2013. “Performance of pendulum tuned mass dampers in reducing the responses of flexible structures.” J. Struct. Eng. 139 (12): 04013019. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000797.
Saeed, A. S., M. A. Al-Shudeifat, and A. F. Vakakis. 2019. “Rotary-oscillatory nonlinear energy sink of robust performance.” Int. J. Non Linear Mech. 117 (Dec): 103249. https://doi.org/10.1016/j.ijnonlinmec.2019.103249.
Sarkar, A., and O. T. Gudmestad. 2013. “Pendulum type liquid column damper (PLCD) for controlling vibrations of a structure—Theoretical and experimental study.” Eng. Struct. 49 (Apr): 221–233. https://doi.org/10.1016/j.engstruct.2012.10.023.
Scanlan, R. H. 1996. Wind effects on structure, fundamentals and applications to design. 3rd ed. New York: Wiley.
Sheheitli, H., and R. H. Rand. 2012. “Dynamics of a mass–spring–pendulum system with vastly different frequencies.” Nonlinear Dyn. 70 (1): 25–41. https://doi.org/10.1007/s11071-012-0428-9.
Shu, Z., S. Li, X. Sun, and M. He. 2019. “Performance-based seismic design of a pendulum tuned mass damper system.” J. Earthquake Eng. 23 (2): 334–355. https://doi.org/10.1080/13632469.2017.1323042.
Shu, Z., S. Li, J. Zhang, and M. He. 2017. “Optimum seismic design of a power plant building with pendulum tuned mass damper system by its heavy suspended buckets.” Eng. Struct. 136 (Apr): 114–132. https://doi.org/10.1016/j.engstruct.2017.01.010.
Sigalov, G., O. V. Gendelman, M. A. AL-Shudeifat, L. I. Manevitch, A. F. Vakakis, and L. A. Bergman. 2012. “Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink.” Nonlinear Dyn. 69 (4): 1693–1704. https://doi.org/10.1007/s11071-012-0379-1.
Stoker, J. J. 1950. Nonlinear vibrations. New York: Wiley.
Sun, C., and V. Jahangiri. 2018. “Bi-directional vibration control of offshore wind turbines using a 3D pendulum tuned mass damper.” Mech. Syst. Sig. Process. 105 (May): 338–360. https://doi.org/10.1016/j.ymssp.2017.12.011.
Sun, H. X., L. Zuo, X. Y. Wang, J. Peng, and W. X. Wang. 2019. “Exact H2 optimal solutions to inerter-based isolation systems for building structures.” Struct. Control Health Monit. 26 (6): e2357. https://doi.org/10.1002/stc.2357.
Toshihiro, I. O. I., and I. Ken. 1978. “On the dynamic vibration damped absorber of the vibration system.” Bull. JSME 21 (151): 64–71. https://doi.org/10.1299/jsme1958.21.64.
Tuan, A. Y., and G. Q. Shang. 2014. “Vibration control in a 101-storey building using a tuned mass damper.” J. Appl. Sci. Eng. 17 (2): 141–156. https://doi.org/10.6180/jase.2014.17.2.05.
Viet, L. D., and N. B. Nghi. 2014. “On a nonlinear single-mass two-frequency pendulum tuned mass damper to reduce horizontal vibration.” Eng. Struct. 81 (Dec): 175–180. https://doi.org/10.1016/j.engstruct.2014.09.038.
Vyas, A., and A. K. Bajaj. 2001. “Dynamics of autoparametric vibration absorbers using multiple pendulums.” J. Sound Vib. 246 (1): 115–135. https://doi.org/10.1006/jsvi.2001.3616.
Wang, W. X., X. G. Hua, Z. Q. Chen, X. Y. Wang, and G. B. Song. 2019. “Modeling, simulation, and validation of a pendulum-pounding tuned mass damper for vibration control.” Struct. Control Health Monit. 26 (4): e2326. https://doi.org/10.1002/stc.2326.
Wang, W. X., X. Y. Wang, X. G. Hua, G. B. Song, and Z. Q. Chen. 2018. “Vibration control of vortex-induced vibrations of a bridge deck by a single-side pounding tuned mass damper.” Eng. Struct. 173 (Oct): 61–75. https://doi.org/10.1016/j.engstruct.2018.06.099.
Wen, Q., X. G. Hua, Z. Q. Chen, Y. Yang, and H. W. Niu. 2016. “Control of human-induced vibrations of a curved cable-stayed bridge: Design, implementation, and field validation.” J. Bridge Eng. 21 (7): 04016028. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000887.
Xiang, P., A. Nishitani, and M. Wu. 2017. “Seismic vibration and damage control of high-rise structures with the implementation of a pendulum-type nontraditional tuned mass damper.” Struct. Control Health Monit. 24 (12): e2022. https://doi.org/10.1002/stc.2022.
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Journal of Engineering Mechanics
Volume 147 • Issue 8 • August 2021
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© 2021 American Society of Civil Engineers.
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Received: Nov 10, 2020
Accepted: Mar 22, 2021
Published online: Jun 12, 2021
Published in print: Aug 1, 2021
Discussion open until: Nov 12, 2021
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