Optimum tuning of mass dampers for seismic structures using flower pollination algorithm

Transcription

1 Sinan Melih Nigeli et al International Journal of Theoretical an Applie Mechanics Optimum tuning of mass ampers for seismic structures using flower pollination algorithm SİNAN MELİH NİGDELİ Department of Civil Engineering Istanbul University Avcılar, Faculty of Engineering, Istanbul, Turkey TURKEY GEBRAİL BEKDAŞ Department of Civil Engineering Istanbul University Avcılar, Faculty of Engineering, Istanbul, Turkey TURKEY XIN-SHE YANG Design engineering an mathematics Milesex University The Burroughs Lonon, UK UNITED KINGDOM Abstract: - For the esign of amping of vibrations of seismic structures, tune mass ampers can be use For efficiency, the implemente mass amper (TMD must be optimally tune The optimum values cannot be foun by mathematical methos ue to the consieration of multiple structural moes, inherent amping an earthquake excitations with ranom frequency In that case, metaheuristic methos an swarm intelligence base algorithms are suitable in searching for the optimum values of tune mass ampers In this stuy, the flower pollination algorithm (FPA is employe in orer to fin the optimum mass, perio an amping ratio of tune mass amper positione on the top of the structure In the numerical example, the best solution is search uner a set of earthquake excitations for a ten story structure an the stroke capacity limit of TMD is consiere The comparisons with the existing approaches show the feasibility of the FPA base metho Key-Wors: Tune mass amper, Optimization, Earthquake, Swarm Intelligence, Flower Pollination Algorithm, Structures 1 Introuction Tune mass ampers (TMD are a combination of stiffness an amping members attache to a mass an TMDs are use as vibration absorber evices in mechanical systems Since structures are also esigne accoring to principles of mechanics of materials, the stability of the structures uner natural an human mae excitations can be reuce by aing TMDs an the properties of TMDs must be tune accoring to the frequency behavior of the structure for an effective gain in the reuction of structural vibrations For multi-story civil structures with amping, the optimum values of a tune mass amper for ranom vibrations cannot be mathematically erive For that reason, the iealization of structure to a single egree of freeom system is neee In that case, the first natural frequency of the structure can be only consiere Aitionally, the inherent amping of the structure cannot be mathematically consiere Also, the ranom frequency characteristic of earthquake excitations cannot be formulize in the mathematical methos In ocumente methos, several mathematical ISSN: Volume 1, 2016

2 Sinan Melih Nigeli et al International Journal of Theoretical an Applie Mechanics expressions are propose but only approximate optimum results are obtaine by using these methos The first optimum esign solutions of TMDs were given by Den Hartog an the formulations of Den Hartog are only for unampe single egree of freeom (SDOF systems [1] Then, Warburton propose simple expressions for frequency an amping ratio of TMDs for harmonic an ranom excitations [2] Since the optimum formulations of TMD cannot be erive if the inherent amping is inclue for the main system, Saek et al use numerical trials results an curve fitting technique in obtaining several expressions An approximate moification for multiple egree of freeom (MDOF structures were also propose by Saek et al [3] Then, numerical optimization techniques are consiere in several stuies [4-7] Metaheuristic methos an swarm intelligence base methos are suitable for TMD optimization for structure uner ranom vibrations Several metaheuristic methos such as genetic algorithms [8-12], particle swarm optimization [13-14], bionic optimization [15], harmony search (HS algorithm [16-19], ant colony optimization [20], artificial bee optimization [21], shuffle complex evolution [22] an teaching learning base optimization (TLBO [23] In this paper, the flower pollination algorithm (FPA evelope by Yang [24] is employe in the evelopment of the optimization approach for TMD tuning In methoology, the stroke capacity limit is also consiere for a TMD positione on the top of the structure The propose metho is applie for a 10-story structure an the optimum results were compare with the other metho employing HS [19] For a global solution, 44 ifferent earthquake recors were use an these earthquakes are groupe as a far-fault groun motion set in FEMA P-695 [25] 2 Methoology In Fig 1, a shear builing moel containing a TMD is shown N is the number of stories an moes of uncontrolle structure In TMD controlle structure, the number of the moes is N+1 The equations of motion of the shear builing can be written as M x ( t + Cx ( t + Kx( t = M{ 1} x g ( t (1 if the structure is unergroun acceleration excitation The M, C an K matrices are iagonal lumpe mass, amping an stiffness matrices, respectively These matrices are shown as Eqs (2- (4 In these equations, x(t, x g (t an {1} are the vector containing structural isplacements of all stories an TMD (shown as Eq (5, groun acceleration in horizontal irection an a vector of ones with a imension of (N+1,1, respectively Figure 1 Moel of N-story shear builing incluing a TMD on the top M=iag[m 1 m 2 m N m ] (2 ( c1 + c2 c2 C = ( k1 + k2 k2 K = c2 ( c2 + c3 k2 ( k2 + k3 c3 k3 cn kn ( cn + c c ( kn + k k c c k k (3 (4 x(t=iag[x 1 x 2 x N x ] T (5 In the matrices an vectors, m i, c i, k i an x i are mass, amping coefficient, stiffness coefficient an isplacement of i th story of structure The properties of the TMD are mass (m, amping coefficient (c an stiffness coefficient (k, respectively The isplacement of the TMD is shown as x The ISSN: Volume 1, 2016

3 Sinan Melih Nigeli et al International Journal of Theoretical an Applie Mechanics properties can be also written as the perio (T an amping ratio (ξ of TMD as shown in Eqs (6 an (7 T m = 2 π (6 k k ξ = 2c m (7 m Flowers use pollination for reprouction an such pollination can be in two ways Pollens can be transferre by pollinators such as insects, birs, bats or other animals (cross-pollination or some flower types have ability for self-pollination By using the flowing rules of the nature of the pollination, FPA is evelope [24] 1The pollinators obey the rules of a Lévy istribution by jumping or flying istance steps Cross-pollination is the global pollination process 2Self-pollination is local pollination process which occurs from pollen of the same flower of other flowers of the same plant 3Flower constancy is use as a reprouction strategy which consiers the similarity of two flowers involve in pollination 4A probability calle the switch probability is controlle for selecting local pollination an global pollination In the methoology, structural properties, external excitations an ranges of esign variables are efine as constants Then, the structure without TMD is analyze in orer to compare the effectiveness of the TMD After that, the initial solutions are generate for TMD parameters such as mass, perio an amping ratio For all set of variables, the ynamic analyses are one for the structure Then, the essential optimization process starts In the global pollination, the first an thir rules of nature are employe an the solution (or a esign variable of the next step (x i t+1 is foun by using the values of the previous step (step t efine as x i t (Eq (8 x i t+1 = x i t +L(x i t -g * (8 Here, Eq (8, the subscript; i represents the i-th pollen (or flower, g * is the current best solution an L is the strength of the pollination which is foun by rawing a ranom number from a Lévy istribution Local pollination is formulize accoring to secon an thir rule by using ranom walks as seen in Eq (9 x i t+1 = x i t + (x j t - x k t (9 t t where x j an x k are solution of ifferent plants while is ranomize between 0 an 1 By using the fourth rule, a switch probability (p is use to choose the type of pollination The objective functions are given in Eqs (10 an (11 The first one is the reuction of maximum top story isplacement of the structure to a user efine value (x max The other objective is relate with the stroke capacity of the TMD The objective given as Eq (11 is consiere comparison of set of esign variables If this objective function is lower than st_max, the objective function given in Eq (10 is consiere This iterative optimization is one until the criteria given by two objectives are provie x N x max (10 max [ xn +1 xn ] [ x ] max N withtmd withouttmd st _ max (11 3 Numerical Example A ten story structure with equal properties was optimize [10] The mass, stiffness coefficient an amping coefficient of a story is 360 t, 62 MNs/m an 650 MN/m, respectively The ranges for the esign variables an optimum TMD parameters are given in Table 1 for two ifferent stroke capacity cases The st_max limitation is taken as 1 an 2 for Case 1 an 2, respectively The user efine value, x max was taken as zero an it is iteratively increase in orer to fin a solution with maximum efficiency The etaile maximum responses of Case 2 are shown in Table 2 The table contains the maximum isplacement, total acceleration values an the scale maximum TMD isplacement (x all excitations The most critical excitation is the secon component of Duzce recor (plot shown in Fig 2 for Case 2 since the stroke objective is applie only for the critical excitation Top Story Displacement (m with TMD without TMD Time (s Figure 2 The time history isplacement plot for the critical excitation ISSN: Volume 1, 2016

4 Sinan Melih Nigeli et al International Journal of Theoretical an Applie Mechanics 4 Conclusions The maximum isplacement uner the critical excitation is 041 m for the uncontrolle structure This value is reuce to m an m for Case 1 an 2, respectively The same values are foun as m an m for HS approach For such reason, FPA is foun to be effective on upating the existing optimum solution by fining precise optimum values TABLE I THE RANGES OF DESIGN VARIABLES AND OPTIMUM VALUES (FPA APPROACH Design variable Range efinition Optimum values (Case 1 Optimum values (Case 2 Mass (t between 1% an 5% total mass of structure Perio (s between 05 an 15 times of the critical perio of structure Damping ratio (% between 01% an 30% TABLE II MAXIMUM RESPONSES WITH FEMA P-695 FAR-FIELD GROUND MOTION RECORDS max (x (m max ( g x Earthquake Number Component without with without TMD TMD TMD with TMD Northrige NORTHR/MUL NORTHR/MUL Northrige NORTHR/LOS NORTHR/LOS Duzce, Turkey DUZCE/BOL DUZCE/BOL Hector Mine HECTOR/HEC HECTOR/HEC Imperial Valley IMPVALL/H-DLT IMPVALL/H-DLT Imperial Valley IMPVALL/H-E IMPVALL/H-E Kobe, Japan KOBE/NIS KOBE/NIS Kobe, Japan KOBE/SHI KOBE/SHI Kocaeli, Turkey KOCAELI/DZC KOCAELI/DZC Kocaeli, Turkey KOCAELI/ARC KOCAELI/ARC Laners LANDERS/YER LANDERS/YER Laners LANDERS/CLW-LN LANDERS/CLW-TR Loma Prieta LOMAP/CAP LOMAP/CAP Loma Prieta LOMAP/G LOMAP/G Manjil, Iran MANJIL/ABBAR--L MANJIL/ABBAR--T Superstition Hills SUPERST/B-ICC SUPERST/B-ICC Superstition Hills SUPERST/B-POE SUPERST/B-POE Cape Menocino CAPEMEND/RIO CAPEMEND/RIO Chi-Chi, Taiwan CHICHI/CHY101-E CHICHI/CHY101-N Chi-Chi, Taiwan CHICHI/TCU045-E CHICHI/TCU045-N San Fernano SFERN/PEL SFERN/PEL Friuli, Italy FRIULI/A-TMZ FRIULI/A-TMZ ISSN: Volume 1, 2016

5 Sinan Melih Nigeli et al International Journal of Theoretical an Applie Mechanics References: [1] J P Den Hartog, Mechanical Vibrations, thir e, Mc Graw-Hill, New York, 1947 [2] GB Warburton, Optimum absorber parameters for various combinations of response an excitation parameters, Earthq Eng Struct D 10 ( [3] F Saek, B Mohraz, AW Taylor, RM Chung, A metho of estimating the parameters of tune mass ampers for seismic applications, Earthq Eng Struct D 26 ( [4] R Rana, TT Soong, Parametric stuy an simplifie esign of tune mass ampers, Eng Struct 20 ( [5] CC Chang, Mass ampers an their optimal esigns for builing vibration control, Eng Struct 21 ( [6] CL Lee, YT Chen, LL Chung, YP Wang, Optimal esign theories an applications of tune mass ampers, Eng Struct 28 ( [7] SV Bakre, RS Jangi, Optimal parameters of tune mass amper for ampe main system, Struct Control Hlth 14 ( [8] MNS Hai, Y Arfiai, Optimum esign of absorber for MDOF structures, JStruct Eng- ASCE 124 ( [9] G C Marano, R Greco, B Chiaia, A comparison between ifferent optimization criteria for tune mass ampers esign, J Soun Vib 329 ( [10] MP Singh, S Singh, LM Moreschi, Tune mass ampers for response control of torsional builings, Earthq Eng Struct D 31 ( [11] NB Desu, SK Deb, A Dutta, Couple tune mass ampers for control of couple vibrations in asymmetric builings, Struct Control Hlth 13 ( [12] S Pourzeynali, HH Lavasani, AH Moarayi, Active control of high rise builing structures using fuzzy logic an genetic algorithms, Eng Struct 29 ( [13] AYT Leung, H Zhang, Particle swarm optimization of tune mass ampers, Eng Struct 31 ( [14] AYT Leung, H Zhang, CC Cheng, YY Lee, Particle swarm optimization of TMD by non-stationary base excitation uring earthquake, Earthq Eng Struct D 37 ( [15] R Steinbuch, Bionic optimisation of the earthquake resistance of high builings by tune mass ampers, J Bionic Eng 8 ( [16] G Bekaş, SM Nigeli, Estimating Optimum Parameters of Tune Mass Dampers Using Harmony Search, Eng Struct 33 ( [17] G Bekaş, SM Nigeli, Mass Ratio Factor for Optimum Tune Mass Damper Strategies, Int J Mech Sci 71 ( [18] SM Nigeli, G Bekaş, Optimum Tune Mass Damper Design for Preventing Brittle Fracture of RC Builings, Smart Struc Syst 12(2 ( [19] X-S Yang, G Bekaş, SM Nigeli, Review an Applications of Metaheuristic Algorithms in Civil Engineering In Metaheuristics an Optimization in Civil Engineering Eite by X-S Yang, G Bekaş, SM Nigeli, Springer, Chapter 1, 2016 [20] A Farshiianfar, S Soheili, Ant colony optimization of tune mass ampers for earthquake oscillations of high-rise structures incluing soil structure interaction, Soil Dyn Earthquake Eng 51 ( [21] A Farshiianfar, S Soheili, ABC optimization of TMD parameters for tall builings with soil structure interaction, Interact Multiscale Mech 6 ( [22] A Farshiianfar, S Soheili, Optimization of TMD parameters for Earthquake Vibrations of Tall Builings Incluing Soil Structure Interaction, Int J Optim Civ Eng 3 ( [23] SM Nigeli, G Bekaş, Teaching-Learning- Base Optimization for Estimating Tune Mass Damper Parameters, 3r International Conference on Optimization Techniques in Engineering (OTENG '15, 7-9 November 2015, Rome, Italy [24] X-S Yang, Flower pollination algorithm for global optimization, in: Unconventional Computation an Natural Computation 2012, Lecture Notes in Computer Science, Vol 7445, pp (2012 [25] FEMA P-695, Quantification of Builing Seismic Performance Factors, Feeral Emergency Management Agency, Washington DC, 2009 ISSN: Volume 1, 2016