طراحی بهینه ی چندهدفه ی میراگر جرمی تنظیم‌شده تحت تحریک بحرانی

نویسندگان
رضا کامگار 1
محسن خطیبی نیا 2
1 شهرکرد، بلوار رهبر، کیلومتر 2 جاده ی سامان، دانشگاه دولتی شهرکرد، دانشکده ی فنی و مهندسی، گروه مهندسی عمران، اتاق 57
2 بیرجند،دانشگاه دولتی بیرجند، دانشکده ی فنی و مهندسی، گروه مهندسی عمران
چکیده
بهینه‌سازی سازه‌ها تحت بار زلزله به‌گونه‌ای که ضمن حفظ امنیت جانی، صرفه‌ی اقتصادی نیز داشته باشد امری ضروری است. عدم تکرارپذیری زلزله‌های با خصوصیات کاملاً مشابه، روند طراحی و بهینه‌سازی سازه‌ها تحت زلزله‌های رخ‌داده درگذشته را امری ناصحیح جلوه می‌دهد و این امر سبب ظهور نوعی طراحی بر اساس زلزله‌ی بحرانی می‌شود. در این مقاله، روشی مؤثر جهت تعیین پارامترهای بهینهی میراگر جرمی تنظیم‌شده با استفاده از الگوریتم بهینه‌سازی چندهدفه‌ی ازدحام ذرات تحت زلزلهی بحرانی پیشنهاد می‌شود. برای این منظور، ابتدا با توجه به اطلاعات زلزله‌های رخ‌داده درگذشته، زلزلههای بحرانی برای قاب برشی‌ ده طبقه تحت قیود انرژی، بیشینه شتاب و طیف دامنه‌ی فوریه‌ی حرکت زمین محاسبه می‌شوند به-گونه‌ای که تابع هدف را بیشینه نمایند. سپس از بین زمین‌لرزه‌های تولیدشده، زمین‌لرزه‌ای که بیشینه مقدار را برای تابع هدف ایجاد می‌نماید به‌عنوان تحریک بحرانی درنظر گرفته می‌شود. درنهایت با استفاده از فرآیند بهینهسازی چندهدفه، پارامترهای بهینه‌ی میراگر جرمی تنظیم‌شده به‌گونه‌ای محاسبه می-شوند، که بیشینه جابجایی و بیشینه شتاب بام سازه کمینه گردد. نتایج مثال عددی ارائه‌شده حاکی از نیاز به جرم بیشتر میراگر جرمی تنظیم‌شده‌ تحت تحریک بحرانی پالس گونه نسبت به تحریک بحرانی غیرپالس گونه است. همچنین نتایج نشان می‌دهند که الگوریتم بهینه‌سازی چندهدفه‌ی ازدحام ذرات توانایی محاسبه‌ی مقادیر بهینه برای پارامترهای میراگر جرمی تنظیم‌شده جهت دستیابی به کمینه‌نمودن بیشینه شتاب و بیشینه جابجایی در بام سازه را دارا است.

کلیدواژه‌ها

عنوان مقاله English

Multi-objective Optimization Design of Tuned Mass Damper System Subjected to Critical Excitation

نویسندگان English

Reza Kamgar 1
Mohsen Khatibinia 2
1 Room 57, Department of Civil Engineering, Shahrekord University, Shahrekord, Iran
2 Department of Civil Engineering, University of Birjand, Birjand, Iran
چکیده English

Controlling the maximum acceleration and displacement of the roof within the acceptable range is important and essential. In order to control structures, a number of control systems have been introduced that are categorized into four system including active, passive, semi active and hybrid system. One of the most used passive systems is the tuned mass damper system which is placed on the roof of structure for controlling the behavior of building. In addition, the optimization of structures subjected to the earthquake load is an essential task for the safe and economic design of structures. It must be noted that earthquakes are random phenomena and the precise prediction of forthcoming events is a hard task. However, in seismic design codes, the static and modal seismic methods for the seismic design of structures are adopted by the design spectrum produced based on previous earthquakes. Hence, in order to overcome this problem, the concept of critical excitation as a robust method has been presented and developed to generate worst–case critical excitations. The critical excitation method have been presented in the framework of an optimization problem to maximize the structural responses subjected to some constraints. In this paper, an effective method is presented to determine the optimum values for the parameters of the tuned mass damper system subjected to critical earthquakes. The critical earthquakes are unique and are computed based on the dynamical properties of the structure. For this purpose, based on the obtained information from the past occurred earthquakes the critical earthquakes of a ten story shear building are established subjected to the constraints. The constraint scenarios include some computable properties of the ground motion such as energy, peak ground acceleration an upper bound Fourier amplitude spectrum. In fact, in this stage, to compute the critical earthquakes an inverse nonlinear constraint optimization problem must be solved for each time step. Then, the building equipped by a tuned mass damper system at roof of the structure (controlled building) is considered and the optimal design of tuned mass damper subjected to critical earthquakes are implemented. The maximum absolute displacement and acceleration of the roof are considered as the objective functions. Finally, among the computed earthquakes, one of them which produces the maximum objective functions is selected as the critical earthquake. In the optimization procedure, the mass, damping and stiffness of the tuned mass damper (TMD) system are adopted as the design variables. Multi-objective particle swarm optimization method is used to optimize the parameters of the tuned mass damper system. Since, the optimal design of the tuned mass damper system is presented as a multi-objective optimization problem, a set of optimal solutions are obtained. Numerical examples demonstrate the ability and efficiency of the proposed method in the optimal design of the tuned mass damper system subjected to the critical earthquakes. In addition, the numerical results show that the maximum absolute values of the displacement and acceleration of the roof efficiently decreases when the building is controlled by the optimum tuned mass damper system. Also, the results show that the severe earthquake needs a bigger mass for tuned mass damper in order to control the displacement and acceleration of the roof.

کلیدواژه‌ها English

Critical excitation
Tuned mass damper
Multi-optimization
Particle swarm optimization method
 
[1] Takewaki I. 2002 Critical excitation method for robust design: A review. Journal of Structural Engineering, 128(5), 665–672.
[2] Stein R. S. 2003 Earthquake conversations. Journal of Scientific American, 288(1), 72–79.
[3] Takewaki I. 2013 Critical excitation methods in earthquake engineering. Elsevier, Netherlands.
[4] Takewaki I. 2001a A new method for non-stationary random critical excitation. Journal of Earthquake Engineering and Structural Dynamics, 30(4), 519-535.
[5] Takewaki I. 2001b Nonstationary random critical excitation for acceleration response. Journal of Engineering Mechanics, 127(6), 544-556.
[6] Westermo B. D. 1985 The critical excitation and response of simple dynamic systems. Journal of Sound and Vibration, 100(2), 233–242.
[7] Moustafa A. 2009 Critical earthquake load inputs for multi-degree-of-freedom inelastic structures. Journal of Sound and Vibration, 325(3), 532–544
[8] Moustafa A. 2006 Critical seismic load inputs for simple inelastic structures. Journal of Sound and Vibration, 296(4), 949–967.
[9] Moustafa A. 2011 Damage-Based Design Earthquake Loads for Single-Degree-Of-Freedom Inelastic Structures. Journal of Structural Engineering, 137(3), 456-467.
[10] Kamgar R. & Rahgozar R. 2015 Determination of critical excitation in seismic analysis of structures. International Journal of Earthquakes & Structures, 9(4), 875-891.
[11] Kamgar R., Shojaee S. & Rahgozar R. 2015 Rehabilitation of tall buildings by active control system subjected to critical seismic excitation. Asian Journal of Civil Engineering, 16(6), 819-833.
[12] Den Hartog J. P. 1956 Mechanical vibrations. McGraw-Hill.
[13] Lee C. L., Chen Y. T., Chung L. L. & Wang W. P. 2006 Optimal design theories and applications of tuned mass dampers. Engineering structures, 28(1), 43-53.
[14] Bakre S. V. & Jangid R. S. 2007 Optimum parameters of tuned mass damper for damped main system. Structural Control and Health Monitoring, 14(3), 448-470.
[15] Marano G. C., Greco R. & Chiaia B. 2010 A comparison between different optimization criteria for tuned mass dampers design. Journal of Sound and Vibration, 329(23), 4880-4890.
[16] Zilletti M., Elliott S. J. & Rustighi E. 2012 Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximize internal power dissipation. Journal of sound and Vibration, 331(18), 4093-4100.
[17] Tigli O. F. 2012 Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads. Journal of Sound and Vibration, 331(13), 3035-3049.
[18] Kaveh A., Mohammadi S., Hosseini O. K., Keyhani A. & Kalatjari V. 2015 Optimum parameters of tuned mass dampers for seismic applications using charged system search. Iranian Journal of Science and Technology. Transactions of Civil Engineering, 39(C1), 21-40.
[19] Deb K. 2001 Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, United Kingdom.
[20] Salajegheh E., Gholizadeh S. & Khatibinia M. 2008 Optimal design of structures for earthquake loads by a hybrid RBF–BPSO method. Journal of Earthquake Engineering and Engineering Vibration, 7(1), 14-24.
[21] Salajegheh E., Salajegheh J., Seyedpoor S. M. & Khatibinia M. 2009 Optimal design of geometrically nonlinear space trusses using adaptive neuro–fuzzy inference system. Scientia Iranica, 16(5), 403-414.
[22] Gharehbaghi S. & Khatibinia M. 2015 Optimal seismic design of reinforced concrete structures under time history earthquake loads using an intelligent hybrid algorithm. Journal of Earthquake Engineering and Engineering Vibration, 14(1), 97-109.
[23] Moustafa A. & Manohar C. S. 2002 Critical spatially-varying earthquake load models for extended structures. Journal of Structural Engineering, 29(1), 39-52.
[24] Arora J. S. 2012 Introduction to optimum design. Elsevier, Academic Press, USA.
[25] Kennedy J. & Eberhart R. C. 1995 Particle swarm optimization. In Proceedings of IEEE international conference on neural networks, New Jersey, IEEE Press.
 
[26] Shi Y. & Eberhart R. 1998 A modified particle swarm optimizer. IEEE International Conference on Evolutionary Computation, IEEE Press, Piscataway, NJ, 69–73.
[27] Durillo J., Garca J., Nebro A., Coello C., Luna F. & Alba E. 2009 Multi-objective particle swarm optimizers: An experimental comparison. 5th International Conference on Evolutionary Multi-Criterion Optimization, Springer Berlin Heidelberg.
[28] Sadek F., Mohraz B., Taylor A. W. & Chung R. M. 1997 A method of estimating the parameters of tuned mass dampers for seismic applications. Journal of Earthquake Engineering and Structural Dynamics, 26(6), 617-636.
[29] http://smd.bhrc.ac.ir/Portal/.
[30] BHRC. 2014 Iranian Code of Practice for Seismic Resistant Design of Buildings. Standard No. 2800, 4rd edn. BHRC, Tehran, Iran (In Persian).
[31] Arias A. 1970 A measure of earthquake intensity: seismic design for nuclear power plants. MIT Press, Cambridge, MA, pp 438-468.
[32] Li L. J., Huang Z. B., Liu F. & Wu Q. H. 2007 A heuristic particle swarm optimizer for optimization of pin connected structures. Journal of Computers and Structures, 85(7), 340–349.
مهندسی عمران مدرس
دوره 17، شماره 4
مهر و آبان 1396
صفحه 153-164