Analysis of a nonlinear tuned mass damper by using the multi-scale method

• Autorzy: Liu Junfeng , Yao Ji , Huang Kun , Zhang Qing , Ze Li

Identyfikatory

DOI

10.15632/jtam-pl/151012

• Języki publikacji: EN

Abstrakty

EN

A tuned mass damper is a kind of vibration damping device which has been widely used in tall buildings, machinery, bridges, aerospace engineering and other fields. In practical engineering applications, due to large deformation caused by large displacement, errors in engineering constructions and the existence of limit devices, the structure and tuned mass dampers inevitably produce some nonlinear characteristics, but these nonlinearities are often ignored. The results of this study confirm that the nonlinearity of the structure and the mass damper should be considered in the process of optimal frequency design, otherwise there will be a large deviation between the design optimal frequency of the mass damper and the actual optimal frequency. In this paper, nonlinear characteristics of the tuned mass damper and the main structure are considered. The first-order differential equations are obtained by using the complex average method, and the nonlinear equations of the tuned mass damper system are derived by using the multi-scale method. On this basis, the parameters are determined. The numerical results show that the error of the approximate solution method is small in the given example. The nonlinear tuned mass damper with nonlinear design exhibits a better control performance.

Słowa kluczowe

EN

nonlinear characteristics; complex average method; multi-scale method; nonlinear design; control performance

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2022
• Tom: Vol. 60 nr 3
• Strony: 463--477
• Opis fizyczny: Bibliogr. 31 poz., rys., tab.

Twórcy

autor

Liu Junfeng

• Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China

autor

Yao Ji

• Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China

autor

Huang Kun

• Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China

autor

Zhang Qing

• Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China

autor

Ze Li

• Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China

Bibliografia

• 1. Alexander N.A., Schilder F., 2009, Exploring the performance of a nonlinear tuned mass damper, Journal of Sound and Vibration, 319, 1-2, 445-462.
• 2. Almazán J.L., De la Llera J., Inaudi J.A., López-Garcia D., Izquierdo L.E., 2007, A bidirectional and homogeneous tuned mass damper: A new device for passive control of vibrations, Engineering Structures, 29, 7, 1548-1560.
• 3. Badamchi K., Khalili M.K., Badamchi K., 2021, Investigation of new proposed model for mass damper with geometrically nonlinear stiffness, Journal of Structural and Construction Engineering, 8, 5, 163-178.
• 4. Banerjee S., Ghosh A., Matsagar V.A., 2022, Optimum design of nonlinear tuned mass damper for dynamic response control under earthquake and wind excitations, Structural Control and Health Monitoring, 29, 7.
• 5. Bhowmik K., Debnath N., 2022, Stochastic design of multiple tuned mass damper system under seismic excitation, Archive of Applied Mechanics, 92, 1, 383-404.
• 6. Den Hartog J.P., 1956, Mechanical Vibrations, 4th Ed., Graw-Hill, New York.
• 7. Elias S., , Matsagar V., 2017, Research developments in vibration control of structures using passive tuned mass dampers, Annual Reviews in Control, 44, 129-156.
• 8. Farshi B., Assadi A., 2011, Development of a chaotic nonlinear tuned mass damper for optimal vibration response, Communications in Nonlinear Science and Numerical Simulation, 16, 11, 4514-4523.
• 9. Frahm H., 1911, Device for Damping Vibrations of Bodies, U.S. Patent No. 989958.
• 10. Housner G.W., Bergman L.A., Caughey T.K., Chassiakos A. G., Claus R.O., Masri S.F., Skelton R.E., Soong T.T., Spencer B.F., Yao J.T.P., 1997, Structural control: past, present, and future, Journal of Engineering Mechanics, 123, 9, 897-971.
• 11. Jiang X.A., McFarland D.M., Bergman L.A, Vakakis A.F., 2003, Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results, Nonlinear Dynamics, 33, 1, 87-102.
• 12. Kecik K., Mitura A., 2020, Energy recovery from a pendulum tuned mass damper with two independent harvesting sources, International Journal of Mechanical Sciences, 174, 105568.
• 13. Kim S.Y., Lee C.H., 2020, Analysis and optimization of multiple tuned mass dampers with Coulomb dry friction, Engineering Structures, 209, 110011.
• 14. Li B.W., Dai K.S., Meng J.Y., Liu K., Wang J.Z., Tesfamariam S., 2020, Simplified design procedure for nonconventional multiple tuned mass damper and experimental validation, The Structural Design of Tall and Special Buildings, 30, 2, e1818.
• 15. Li L.Y., Zhang T., 2020, Analytical analysis for the design of nonlinear tuned mass damper, Journal of Vibration and Control, 26, 9-10, 646-658.
• 16. Lian J.J., Zhao Y., Lian C., Wang H., Dong X., Jiang Q., Zhou H., Jiang J., 2018, Application of an eddy current-tuned mass damper to vibration mitigation of offshore wind turbines, Energies, 11, 12, 3319.
• 17. Lin G.L., Lin C.C., Chen B.C., Soong T.T., 2015, Vibration control performance of tuned mass dampers with resettable variable stiffness, Engineering Structures, 83, 187-197.
• 18. Lu Z., Wang Z.X., Zhou Y., Lu X.L., 2018, Nonlinear dissipative devices in structural vibration control: A review, Journal of Sound and Vibration, 423, 18-49.
• 19. Manevitch L.I., Gourdon E., Lamarque C.H., 2007, Parameters optimization for energy pumping in strongly nonhomogeneous 2 dof system, Chaos Solitons and Fractals, 31, 4, 900-911.
• 20. Matin A., Elias S., Matsagar V., 2020, Distributed multiple tuned mass dampers for seismic response control in bridges, Proceedings of the Institution of Civil Engineers – Structures and Buildings, 173, 3, 217-234.
• 21. Natsiavas S., 1992, Steady state oscillations and stability of non-linear dynamic vibration absorbers, Journal of Sound and Vibration, 156, 2, 227-245.
• 22. Nayfeh A.H., Mook A.D., 1981, Nonlinear Oscillations, Clarendon, Texas.
• 23. Ormondroyd J., Hartog J., 1928, The theory of the dynamic vibration absorber, Transactions of the American Society of Mechanical Engineers, 50, A9-A22.
• 24. Qiu D., Seguy S., Paredes M., 2018, Design criteria for optimally tuned vibro-impact nonlinear energy sink, Journal of Sound and Vibration, 442, 497-513.
• 25. Ramlan R., Brennan M.J., Mace B.R., Kovacic I., 2010, Potential benefits of a non-linear stiffness in an energy harvesting device, Nonlinear Dynamics, 59, 4, 545-558.
• 26. Roberson R.E., 1952, Synthesis of a nonlinear dynamic vibration absorber, Journal of the Franklin Institute, 254, 3, 205-220.
• 27. Tai W.C., 2020, Optimum design of a new tuned inerter-torsional-mass-damper passive vibration control for stochastically motion-excited structures, Journal of Vibration and Acoustics, 142, 1, 011015.
• 28. Tsai H.-C., Lin G.-C., 1993, Optimum tuned-mass dampers for minimizing steady-state response of support-excited and damped systems, Earthquake Engineering and Structural Dynamics, 22, 11, 957-973.
• 29. Warburton G., Ayorinde E., 1980, Optimum absorber parameters for simple systems, Earthquake Engineering and Structural Dynamics, 8, 197-217.
• 30. Zhang X., Han Q., Bi K.M., Du X.L., 2022, An improved multi-mode seismic vibration control method using multiple tuned mass dampers, Advances in Structural Engineering, 25, 4, 804-819.
• 31. Zhao D., Du M., Ni T., Gong M., Ma L., 2020, Dual adaptive robust control for uncertain nonlinear active suspension systems actuated by asymmetric electrohydraulic actuators, Journal of Low Frequency Noise Vibration and Active Control, 40, 3, 1607-1632.