BİTİŞİK NİZAM YAPILARIN ÇARPIŞMASINI ÖNLEMEK İÇİN BİR HEDEF SÖNÜM ORANI VE RÖLATİF DEPLASMAN DÜŞÜNÜLEREK OPTİMUM SÖNÜMLEYİCİ YERLEŞİMİ

Öz

   Bu çalışmada, bitişik nizam iki yapı arasına, sönümleyiciler çarpışmayı önlemek için optimum olarak yerleştirilir. Optimizasyon problemi için yönetici denklemler zaman tanım alanında türetilir. Hedef sönüm oranı girişimli sistem için bulunur ve sayısal optimizasyon aşamasında aktif kısıtlamalar kullanılır. Sönümleyicilerin sönüm katsayıları tasarım değişkeni olarak seçilir ve sönüm katsayılarının toplamı kısıtlamalar altında minimize edilir. Deprem yükleri altında aday optimum tasarımı test etmek için zaman tanım alanında analizleri ve sayısal optimizasyonu içeren bir algoritma gösterilir. Bütün katlarda rölatif deplasmanların hedef değerlerin altına düşüp düşmediği kontrol edilir. Amaçlanan metodun geçerliliğini göstermek için 4 katlı bitişik nizam kayma çerçeveleri sayısal örnek olarak kullanılır. Bitişik yapıların arasına lineer viskoz sönümleyicilerin uygun yerleri ve sayıları hesaplanır ve onların yapısal davranış üzerindeki etkileri araştırılır.   

Anahtar Kelimeler

• Çekiçleme,hedef sönüm oranı,ek sönümleyiciler,optimum pasif kontrol,çekiçlemenin önlenmesi

OPTIMAL DAMPER PLACEMENT TO PREVENT POUNDING OF ADJACENT STRUCTURES CONSIDERING A TARGET DAMPING RATIO AND RELATIVE DISPLACEMENT

Abstract

   In this study, viscous dampers are optimally placed between two adjacent structures with the aim of preventing pounding. Governing equations are derived in time domain for the optimization problem. Target damping ratios are obtained for the coupled system and used as active constraints in the numerical optimization stage. The damping coefficients of the dampers are chosen as design variables, and the sum of the damping coefficients is minimized under the constraints. An algorithm featuring numerical optimization and time history analysis is put forward to test the candidate optimal design under the earthquake loads of interest. The relative displacements are checked at all storey levels to ensure that they remain below the target values. Two 4-storey adjacent shear-building models are used in numerical examples to validate the proposed method. The appropriate number and locations of linear viscous dampers between adjacent structures are determined, and their effects on structural behaviour are evaluated.

Keywords

• Pounding,target damping ratio,added dampers,optimal passive control

Kaynakça

1. [1] ANAGNOSTOPOULOS, S.A., “Earthquake Induced Pounding: State of the Art. Procc 10th European Conference on Earthquake Engineering”, Rotterdam, Nederland, 897-905, 1995.
2. [2] KASAI, K., JAGIASI, A.R., JENG, V., “Inelastic Vibration Phase Theory for Seismic Pounding Mitigation”, Journal of Structural Engineering, 122(10), 1136-1146, 1996.
3. [3] PENZIEN, J., “Evaluation of Building Separation Distance Required to Prevent Pounding During Strong Earthquakes”, Earthquake Engineering and Structural Dynamics, 26(8), 849-858, 1997.
4. [4] ROSENBLUETH, E., MELI, R., “The 1985 Earthquake: Cause and Effects in Mexico City”, Concrete Int., ACI, 8(5), 23-24, 1986.
5. [5] ANAGNASTOPOULOS, S.A., “Pounding of Buildings in Series during Earthquakes”, Earthquake Engineering and Structural Dynamics, 16(3), 443-456, 1988.
6. [6] STAVROULAKIS, G.E., ABDALLA, K.A., “Contact between Adjacent Structures”, Journal of Structural Engineering, 117(10), 2838-2850, 1991.
7. [7] JENG, V., KASAI, K., MAISON, B.F., “A Spectral Difference Method to Estimate Building Separations to Avoid Pounding”, Earthquake Spectra, 8(2), 201-223, 1992.
8. [8] LIN, J.H., “Separation Distance to Avoid Seismic Pounding of Adjacent Buildings”, Earthquake Engineering and Structural Dynamics, 26, 395-403, 1997.

9. [9] VALLES, R.E., REINHORN, A.M., “Evaluation, Prevention and Mitigation of Pounding Effects in Building Structures”, Report No NCEER-97-0001, National Center for Earthquake Engineering Res., State University of New York, Buffalo, N.Y., 1997.
10. [10] LUCO, J.E., DE BARROS, F.C.P., “Optimal Damping between Two Adjacent Elastic Structures”, Earthquake Engineering and Structural Dynamics, 27, 649-659, 1998.
11. [11] ZHANG , W.S., XU, Y.L., “Dynamic Characteristics and Seismic Response of Adjacent Buildings Linked by Discrete Dampers”, Earthquake Engineering and Structural Dynamics, 28, 1163-1185, 1999.
12. [12] ABDULLAH, M.M., HANIF, J.H., RICHARSON, A., SOBANJO, J., “Use of a Shared Tuned Mass Damper (STMD) to Reduce Vibration and Pounding in Adjacent Structures”, Earthquake Engineering and Structural Dynamics, 30, 633-651, 2001.
13. [13] LIN, H., WENG, C.C., “Probability Analysis of Seismic Pounding Adjacent Buildings”, Earthquake Engineering and Structural Dynamics, 30, 1539-1557, 2001.
14. [14] ZU, H.P., XU, Y.L., “Optimum Parameters of Maxwell Model Defined Damper Used to Link Adjacent Structures”, Journal of Sound and Vibration, 279, 253-274, 2005.
15. [15] ZHU, H.P., WEN, Y., IEMURA, H., “A Study on Interaction Control for Seismic Response of Parallel Structures”, Computers and Structures, 79, 231-242, 2001.
16. [16] ALDEMIR, U., AYDIN, A., “An Active Control Algorithm to Prevent the Pounding of Adjacent Structures”, Vibration Problems ICOVP, 33-38, 2005.
17. [17] CONSTANTINOU, M.C., SYMANS, M.D., “Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental Fluid Viscous Dampers”, Technical Report NCEER-92-0032 National Center for Earthquake Engineering Research, Buffalo, New York, 1992.
18. [18] AGRAWAL, A.K., YANG, J.N., “Design Passive Energy Dissipation Systems Based on LQR Methods”, Journal of Intelligent Material Systems and Structures, 10(20), 933-944, 2000.
19. [19] AGRAWAL, A.K., YANG, J.N., “Optimal Placement of Passive Dampers on Buildings Using Combinatorial Optimization”, Journal of Intelligent Material Systems and Structures, 10(12), 997-1014, 2000.
20. [20] CIMELLARO, G.P., LAVAN, O., REINHORN, A.M., “Design of Passive Systems for Controlled Inelastic Structures”, Earthquake Engineering and Structural Dynamics, 38(6), 783-804, 2009.
21. [21] GLUCK, N., REINHORN, A.M., GLUCK, J., LEVY, R., “Design of Supplemental Dampers for Control of Structure”, Journal of Structural Engineering ASCE, 122(12), 1394-1399, 1996.
22. [22] GÜRGÖZE, M., MÜLLER, P.C., “Optimum Position of Dampers in Multi Body Systems”, Journal of Sound and Vibration, 158(3), 517-530, 1992.
23. [23] HWANG, J.S., MIN, K.W., HONG, S.M., “Optimal Design of Passive Viscoelastic Dampers Having Active Control Effect for Building Structures”, Transactions of the Korean Society for Noise and Vibration Engineering, 5(2), 225-234, 1995.
24. [24] LAVAN, O., CIMELLARO, G.P., REINHORN, A.M., “Noniterative Optimization Procedure for Seismic Weakening and Damping of Inelastic Structures”, Journal of Structural Engineering ASCE, 134(10), 1638-1648, 2008.
25. [25] LOH, C.H., LIN, P.Y., CHUNG, N.H., “Design of Dampers for Structures Based on Optimal Control Theory”, Earthquake Engineering & Structural Dynamics, 29, 1307-1323, 2000.
26. [26] YANG, J.N., LIN, S., KIM, J.H., AGRAWAL, A.K., “Optimal Design of Passive Energy Dissipation Systems Based on H and H2 Performances”, Earthquake Engineering & Structural Dynamics, 31, 921-936, 2002.
27. [27] ADACHI, F., YOSHITOMI, S., TSUJI, M., TAKEWAKI, I., “Nonlinear Optimal Oil Damper Design in Seismically Controlled Multi-Story Building Frame”, Soil Dynamics and Earthquake Engineering, 44, 1-13, 2013.
28. [28] AMINI F., GHADERI, P., “Hybridization of Harmony Search and Ant Colony Optimization for Optimal Locating of Structural Dampers”, Applied Soft Computing, 13, 2272-2280, 2013.
29. [29] AYDIN, E., BODUROGLU, M.H., GUNEY, D., “Optimal Damper Distribution for Seismic Rehabilitation of Planar Building Structures”, Engineering Structures, 29, 176-185, 2007.
30. [30] AYDIN, E., “Optimal Damper Placement Based on Base Moment in Steel Building Frames”, Journal of Constructional Steel Research, 79, 216-225, 2012.
31. [31] AYDIN, E., “A Simple Damper Optimization Algorithm for Both Target Added Damping Ratio and Interstorey Drift Ratio”, Earthquakes and Structures, 88, 083-109, 2013.
32. [32] BISHOP, J.A., STRIZ, A.G., “On Using Genetic Algorithms for Optimum Damper Placement in Space Trusses”, Structural and Multidisciplinary Optimization, 28, 136-145, 2004.
33. [33] CIMELLARO, G.P., “Simultaneous Stiffness-Damping Optimization of Structures with Respect to Acceleration Displacement and Base Shear”, Engineering Structures, 29, 2853-2870, 2007.
34. [34] CIMELLARO, G.P., SOONG, T.T., REINHORN, A.M., “Integrated Design of Controlled Linear Structural Systems” Journal of Structural Engineering, ASCE, 135(7), 853-862, 2009.
35. [35] DARGUSH, G.F., SANT, R.S., “Evolutionary Aseismic Design and Retrofit of Structures with Passive Energy Dissipation”, Earthquake Engineering & Structural Dynamics, 34(13), 1601-1626, 2005.
36. [36] FUJITA, K., MOUSTAFA, A., TAKEWAKI, I., “Optimal Placement of Visco-Elastic Dampers and Supporting Members Under Variable Critical Excitations”, Earthquakes and Structures, 1, 43-67, 2010.
37. [37] FUJITA, K., YAMAMOTO, K., TAKEWAKI, I., “An Evolutionary Algorithm for Optimal Damper Placement to Minimize Interstorey-Drift Transfer Function in Shear Building”, Earthquakes and Structures, 1(3), 289-306, 2010.
38. [38] LAVAN, O., LEVY, R., “Optimal Design of Supplemental Viscous Dampers for Irregular Shear Frames in The Presence of the Yielding”, Earthquake Engineering & Structural Dynamics, 34, 889-907, 2005.
39. [39] LAVAN, O., DARGUSH, G.F., “Multi-Objective Optimal Seismic Retrofitting of Structures”, Journal of Earthquake Engineering, 13, 758–790, 2009.
40. [40] LAVAN, O., LEVY, R., “Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Design of Passive Devices in Framed Structures”, Journal of Earthquake Engineering, 13(5), 650-666, 2009.
41. [41] LAVAN, O., LEVY, R., “Performance Based Optimal Seismic Retrofitting of Yielding Plane Frames Using Added Viscous Damping”, Earthquakes and Structures, 1(3), 307-326, 2010.
42. [42] LEVY, R., LAVAN, O., “Fully Stressed Design of Passive Controllers in Framed Structures for Seismic Loadings”, Structural and Multidisciplinary Optimization, 32(6), 485-489, 2006.
43. [43] LOPEZ GARCIA, D., SOONG, T.T., “Efficiency of A Simple Approach to Damper Allocation in MDOF Structures”, Journal of Structural Control, 9, 19-30, 2002.
44. [44] MOUSAVI, S.A., GHORBANI-TANHA, A.K., “Optimum Placement and Characteristics of Velocity-Depend Dampers under Seismic Excitation”, Earthquake Engineering and Engineering Vibration, 11(3), 403-414, 2012.
45. [45] SHUKLA, A.K., DATTA, T.K., “Optimal Use of Viscoelastic Dampers in Building Frames for Seismic Force”, Journal of Structural Engineering, 125(4), 401-409, 1999.
46. [46] SILVESTRI, S., TROMBETTI, T., “Physical and Numerical Approaches for the Optimal Insertion of Seismic Viscous Dampers in Shear-Type Structures”, Journal of Earthquake Engineering, 11(5), 787-828, 2007.
47. [47] SILVESTRI, S., GASPARINI, G., TROMBETTI, T., “Seismic Design of a Precast R.C. Structure Equipped with Viscous Dampers”, Earthquakes and Structures, 2(3), 297-321, 2011.
48. [48] SINGH, M.P., MORESCHI, L.M., “Optimum Seismic Response Control with Dampers”, Earthquake Engineering & Structural Dynamics, 30, 553-572, 2001.
49. [49] SINGH, M.P., MORESCHI, L.M., “Optimal Placement of Dampers for Passive Response Control”, Earthquake Engineering & Structural Dynamics, 31, 955-976, 2002.
50. [50] SONMEZ, M., AYDIN, E., KARABORK, T., “Using an Artificial Bee Colony Algorithm for the Optimal Placement of Viscous Dampers in Planar Building Frames”, Structural and Multidisciplinary Optimization, 48, 395-409, 2013.
51. [51] TAKEWAKI, I., “Efficient Redesign of Damped Structural Systems for Target Transfer Functions”, Computer Methods in Applied Mechanics and Engineering, 147, 275-286, 1997.
52. [52] TAKEWAKI, I., “Optimal Damper Placement for Minimum Transfer Functions”, Earthquake Engineering & Structural Dynamics, 26, 1113-1124, 1997.
53. [53] TAKEWAKI, I., “Optimal Damper Positioning in Beams for Minimum Dynamic Compliance”, Computer Methods in Applied Mechanics and Engineering, 156, 363-373, 1998.
54. [54] TAKEWAKI, I., YOSHITOMI, S., “Effects of Support Stiffnesses on Optimal Damper Placement for a Planar Building Frame”, The Structural Design of Tall Buildings, 7, 323-336, 1998.
55. [55] TAKEWAKI, I., “Non-Monotonic Optimal Damper Placement via Steepest Direction Search”, Earthquake Engineering & Structural Dynamics, 28, 655-670, 1999.
56. [56] TAKEWAKI, I., “Displacement-Acceleration Control via Stiffness-Damping Collaboration”, Earthquake Engineering & Structural Dynamics, 28, 1567-1585, 1999.
57. [57] TAKEWAKI, I., “Optimal Damper Placement for Critical Excitation”, Probabilistic Engineering Mechanics, 15, 317-325. 1999.
58. [58] TAKEWAKI, I., “Optimum Damper Placement for Planar Building Frames Using Transfer Functions”, Structural and Multidisciplinary Optimization, 20, 280-287, 2000.
59. [59] TAKEWAKI, I., “An Approach to Stiffness-Damping Simultaneous Optimization”, Computer Methods in Applied Mechanics and Engineering, 189, 641-650, 2000.
60. [60] TROMBETTI, T., SILVESTRE, S., “Novel Schemes for Inserting Seismic Dampers in Shear-Type Systems Based Upon the Mass Proportional Component of the Rayleigh Damping Matrix”, Journal of Sound and Vibration, 302(3), 486-526, 2007.
61. [61] UETANI, K., TSUJI, M., TAKEWAKI, I., “Application of an Optimum Design Method to Practical Building Frames with Viscous Dampers and Hysteretic Dampers”, Engineering Structures, 25, 579-592, 2003.
62. [62] WANG, H., LI, A.Q., JIAO, C.K., SPENCER, B.F., “Damper Placement for Seismic Control of Super-Long-Span Suspension Bridges Based on the First-Order Optimization Method”, Science China Technological Sciences, 53(7), 2010.
63. [63] WHITTLE, J.K., WILLIAMS, M.S., KARAVASILIS, T.L., BLAKEBOROUGH, A., “A Comparison of Viscous Damper Placement Methods for Improving Seismic Building Design”, Journal of Earthquake Engineering, 16, 540-560, 2012.
64. [64] WONGPRASERT, N., SYMANS, M.D., “Application of a Genetic Algorithm for Optimal Damper Distribution within the Nonlinear Seismic Benchmark Building”, Journal of Engineering Mechanics, 130(4), 401-406, 2004.
65. [65] Turkish Earthquake Code, 2016.
66. [66] WOLFRAM RESEARCH, Mathematica Edition, Version 5.0, Wolfram Research, Champaign, Illinois, 2003.