Kinematically excited parametric vibration of a tall building model with a TMD - Part 1: Numerical analyses

• Autorzy: Majcher K. , Wójcicki Z.

Identyfikatory

DOI

10.1016/j.acme.2013.09.004

• Języki publikacji: EN

Abstrakty

EN

This paper undertakes to analyze the research problem of vibration of a tall building with a Pendulum Tuned Mass Damper (PTMD). The vibration of the building-damper system is due to kinematic excitation representing seismic load. It was assumed that during an earthquake the ground can move horizontally and vertically. An analysis of various earthquakes reveals that, sometimes, the vibration has comparable amplitudes in both these directions. It is usually the horizontal vibration that is catastrophic to structures. Vertical vibration is therefore often omitted. As this paper will show, in cases where the TMD model is a pendulum, the vertical ground motion can be transmitted through the building structure to the pendulum suspension point. In such cases, parametric resonance may occur in the system, which is especially dangerous as it amplifies vibration despite the presence of damping. Taking this phenomenon into consideration will make it possible to better secure the structure against earthquakes. As the teams carrying out theoretical and experimental analyses differed, the paper was purposely divided into two parts. In the first part, the idea was formulated and the MES model of the building-TMD system was created. The second part contains an experimental verification of the theoretical analyses.

Słowa kluczowe

EN

parametric vibration; tall building; kinematical excitation; pendulum tuned mass damper; finite element method

PL

drgania parametryczne; metoda elementów skończonych; trzęsienie ziemi; wysoki budynek

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2014
• Tom: Vol. 14, no. 1
• Strony: 204--217
• Opis fizyczny: Bibliogr. 51 poz., rys., wykr.

Twórcy

autor

Majcher K.

• Wrocław University of Technology, 27 Wybrzeże Wyspiańskiego St, 50-370 Wrocław, Poland

autor

Wójcicki Z.

• Wrocław University of Technology, 27 Wybrzeże Wyspiańskiego St, 50-370 Wrocław, Poland

Bibliografia

• [1] J. Ormondroyd, J.P. Den Hartog, The theory of the dynamic vibration absorber, Transactions of the ASME49–50 (1928) 9–22.
• [2] R.E.D. Bishop, D.B. Welbourn, The problem of the dynamic vibration absorber, Engineering, London (1952) 174–769.
• [3] K.C. Falcon, B.J. Stone, W.D Simcock, C Andrew, Optimization of vibration absorbers: a graphical method for use on idealized systems with restricted damping, Journal of Mechanical Engineering Science 9 (1967) 374–381.
• [4] C.M. Harris, Ch. E. Crede, Shock and Vibration Handbook, The McGraw-Hill Companies Inc., USA, 1961.
• [5] S. Kaliski, et al., Vibration and Waves in a Solid Body (in Polish), PWN, Warsaw, 1966.
• [6] B.S. Taranath, Wind and Earth quake Resistant Buildings Structural Analysis and Design, 1sted., Marcel Dekker, New York, 2005.
• [7] J.D. Holmes, Auxiliary damping systems for mitigation of wind-induced vibration, Engineering Structures 17 (9) (1995) 608.
• [8] T.T. Soong, G.F. Dargush, Passive Energy Dissipation Systems in Structural Engineering, 1sted., John Wiley & Sons, Inc, New York, 1997.
• [9] R. Lewandowski, Dynamic of a Civil Engineering Structures (in Polish), 1sted., Wydawnictwo Politechniki Poznańskiej, Poznań, 2006.
• [10] M.D. Symans, M.C. Constantinou, Semi-active control systems for seismic protection of structures: a state-of-the- art review, Engineering Structures 21 (1999) 469–487.
• [11] S. Narasimhan, S. Nagarajaiah, ASTFT semi active controller for base isolated building swith variable stiffness isolation systems, Engineering Structures 27 (2005) 514–523.
• [12] H. Cao, A.M. Reinhorn, T.T. Soong, Design of an active mass damper for at all TV tower in Nanjing, China, Engineering Structures 20 (3) (1998) 134–143.
• [13] J.C.H. Chang, T.T. Soong, Structural control using active tuned mass damper, Journal of Engineering Mechanics – ASCE, 106, 1091–1098.
• [14] T.T. Soong, Active Structural Control: Theory and Practice, 1st ed., Longman, New York, 1990.
• [15] S.T. Wu, Active pendulum vibration absorbers with a spinning support, Journal of Sound and Vibration 323 (2009) 1–16.
• [16] Y.L. Xu, Parametric study of active mass dampers for wind-excited tall buildings, Engineering Structures 2 (1) (1996) 64–76.
• [17] M. Abdel-Rohman, H.H.E. Leipholz, Active control of tall buildings, Journal of Structural Engineering – ASCE, 109, 628–645.
• [18] L.L. Chung, A. M. Reinhorn, T.T. Soong, Experiments on active control of seismic structures, Journal of Engineering Mechanics – ASCE, 114, 241–256.
• [19] T.T. Soong, State-of-the-art review: active structure control in civil engineering, Engineering Structures 10 (2) (1988) 73–84.
• [20] R.J. Facioni, K.C.S. Kwok, B. Samali, Wind tunnel investigation of active vibration control of tall buildings, Journal of Wind Engineering and Industrial Aerodynamics 54/55 (1995) 397–412.
• [21] Y.L. Xu, K.C.S. Kwok, B. Samali, Control of wind-induced all building vibration by tuned mass dampers, Journal of Wind Engineering and Industrial Aerodynamics 40 (1992) 1–32.
• [22] Z. Osiński, et al., Damping of Vibrations (in Polish), 1sted., PWN, Warsaw,1997.
• [23] H. Gao, K.C.S. Kwok, B. Samali, Optimization of tuned liquid column dampers, Engineering Structure 19 (6) (1997) 476–486.
• [24] N. Yan, C.M. Wang, T. Balendra, Composite mass dampers for vibration control of wind-excited towers, Journal of Sound and Vibration 213 (2) (1998) 301–316.
• [25] R. Rana, T.T. Soong, Parametric study and simplified design of tuned mass dampers, Engineering Structure 12 (3) (1998) 193–204.
• [26] Y. Tamura, Application of damping devices to suppress wind-induced responses of buildings, Journal of Wind Engineering and Industrial Aerodynamics 74–76 (1998) 49–72.
• [27] C.C. Chang, Mass dampers and their optimal designs for building vibration control, Engineering Structure 21 (1999) 454–463.
• [28] A. Kareem, T. Kijewski, Y. Tamura, Mitigation of motions of tall buildings with specific examples of recent applications, Wind and Structures: An International Journal 2 (3) (1999) 201–251.
• [29] A. Tondl, T. Ruijgrok, F. Verhulst, R. Nabergoj, Auto parametric Resonance in Mechanical Systems, 1sted., Cambridge University Press, Cambridge, 2000.
• [30] A. Tondl, R. Nabergoj, Dynamic absorbers for an externally excited pendulum, Journal of Sound and Vibration 234 (4) (2000) 611–624.
• [31] R.R. Gerges, B.J. Vickery, Parametric experimental study of wire rope spring tuned mass dampers, Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 1363–1385.
• [32] J. Warmiński, K. Kecik, Auto parametric vibrations of a nonlinear system with pendulum, Mathematical Problem sin Engineering (2005) 1–19, http://dx.doi.org/10.1155/80705.
• [33] J. Warmiński, K. Kecik, Instabilities in the main parametric resonance area of a mechanical system with a pendulum, Journal of Sound and Vibration 322 (2009) 612–628.
• [34] G. Litak, M. Borowiec, M. Wiercigroch, Phase lock and rotational motion of aparametric pendulum in noisy and chaotic conditions, Dynamical Systems: An International Journal (2006) 1–8.
• [35] L. Hatvani, Stability problems for the mathematical pendulum, Periodica Mathematica Hungarica 56 (1) (2008) 71–82.
• [36] Y. Liang, B.F. Feeny, Parametric identification of a base- excited single pendulum, Nonlinear Dynamics 46 (2006) 17–29.
• [37] Y. Liang, B.F. Feeny, Parametric identification of a chaotic base-excited double pendulum experiment, Nonlinear Dynamics 52 (2008) 181–197.
• [38] V. Graizer, E. Kalkan, Response of pendulums to complex input ground motion, Soil Dynamics and Earth quake Engineering 28 (2008) 621–631.
• [39] N.D. Anh, H. Matsuhisa, L.D. Viet, M. Yasuda, Vibration control of an inverted pendulum type structure by passive mass-spring-pendulum dynamic vibration absorber, Journal of Sound and Vibration 307 (2007) 187–201.
• [40] S.T. Wu, Active pendulum vibration absorbers with a spinning support, Journal of Sound and Vibration 323 (2009) 1–16.
• [41] F.Y. Cheng, H. Jiang, K. Lou, Smart Structures: Innovative Systems for Seismic Response Control, 1sted.,Taylor & Francis Group, LLC, USA, 2008.
• [42] L.A. Pipes, Matrix solution of quations of Mathieu–Hill type, Journal of Applied Physics 24 (1953) 902–910.
• [43] W.W. Bolotin, in: The Dynamic Stability of Elastic Systems (in Polish), 1sted., GITTL, Moscow, 1956.
• [44] R. Gutowski, et al., The Stability and Sensitivity of Mechanical Systems (in Polish), 1sted., Ossolineum, Wroclaw, 1978.
• [45] J. Osiński, Parametric vibration of nonlinear systems, Nonlinear Vibration Problems 25 (1993) 336–349.
• [46] K. Szabelski, J. Warmiński, Parametric self-excited non-linear system vibrations analysis with inertial excitation, International Journal of Non-Linear Mechanics 30 (2) (1995) 179–189.
• [47] Z. Wójcicki, Sensitivity analysis as a method of absorber tuning for reduction of steady state response of linear parametric systems, Journal of Sound and Vibration 253 (4) (2002) 755–772.
• [48] Z. Wójcicki, Dynamic Elimination of a Parametric Resonance Vibration (In Polish), 1sted., Oficyna Wydawnicza Politechniki Wrocławskiej, Wroclaw, 2003.
• [49] W. Glabisz, MATHEMATICA in Structural Mechanics Problems (In Polish), 1sted.,Oficyna Wydawnicza Politechniki Wrocławskiej, Wroclaw, 2003.
• [50] W. Szcześniak, in: Analytical Dynamice and MATHEMATICA in Computational Examples (In Polish), 2sted., Oficyna Wydawnicza Politechniki Warszawskiej, Warsaw, 2005.
• [51] K. Majcher, Z. Wójcicki, J. Grosel, W. Pakos, W. Sawicki, Kinematically excited parametric vibration of at all building model with a TMD. Part2: experimental analyses, Archives of Civil and Mechanical Engineering (2013) (in press).