Multiple Response Optimization of Tuned Mass Dampers

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1 Multiple Response Optimization of Tuned Mass Dampers SİNAN MELİH NİGDELİ Department of Civil Engineering Istanbul University 33 Avcılar, Faculty of Engineering, Istanbul, Turkey TURKEY GEBRAİL BEKDAŞ Department of Civil Engineering Istanbul University 33 Avcılar, Faculty of Engineering, Istanbul, Turkey TURKEY Abstract: The optimum parameters of Tuned Mass Damper (TMDs) in seismic control of structure may be different according to the desired objective function in optimization. While a response of the structure under an excitation is optimally reduced, another responses or the same response under a different excitation may not be sufficiently reduced. For that reason, a multiple response optimization is proposed for the problem. The proposed method employs a music-inspired metaheuristic algorithm called Harmony Search. The method is feasible in order to reduce the objective function which is the average of maximum displacement, velocity and acceleration of all stories under different excitations. Key-Words: Tuned mass damper, Optimization, Multiple response, Harmony search, Metaheuristic. Introduction Tuned mass dampers (TMDs) are vibration absorber devices which are also used in civil structures subjected to wind and earthquake effects. The main aim in the design of TMDs is to tune the parameters of TMD according to the characteristics of the main structure. In order to find optimum TMD parameters such as mass (or mass ratio), period (or stiffness) and damping ratio (or damping coefficient), several numerical algorithms have been employed [ 9]. Most of these algorithms are metaheuristic algorithms which are inspired from several processes or behavior of organisms. By using these algorithms, TMDs are optimized according to responses of the main structure in time or frequency domain. This paper proposes a multiple response optimization for TMDs. In this approach, an objective function which is the ratio of sum of the responses of the structure with and without TMD, is used. This objective function considers all story responses and excitations of six different ground motions. Also, displacements, velocities and accelerations are also considered. Methodology Harmony search (HS) algorithm is employed in the optimization process. HS is a metaheuristic algorithm inspired from musical processes []. It uses randomly assigned numbers in order to reach the optimum solution. HS has special rules in generation of randomization. A solution set can be constructed from the initial range of parameters or existing sets can be used in the construction of new set. Thus, local optima problem is prevented. The methodology involves dynamic analyses of shear building for each iterations of optimization process. First, properties of structures, HS parameters, earthquake records and a possible solution range are defined. Then, the structure without TMD is analyzed for comparisons of objective function. The initial harmony memory matrix (HM) containing harmony vectors (HVs) are generated. HVs contain design variables such as ISBN:

2 mass, period and damping ratio of TMD and the numbers of HVs are defined with Harmony Memory Size (HMS). The design variables are randomly chosen from the selected range. After the generation of initial harmony memory matrix, a new HV is generated by using the same procedure or an existing vector in HM with a possibility defined as Harmony Memory Considering Rate (HMCR). The solution range is limited with a parameter called Pitch Adjacent Rate (PAR) if generation is done around an existing vector. The worst vector is replaced with the newly generated HV. The worst one is chosen according to the objective function and iterative generation of new HVs continue until the objective function is higher than the user defined value. The objective function is average of the maximum value of displacement, velocity and acceleration of all stories of structure under six different earthquake records. 3 Numerical Examples As a numerical example, a -storey building was investigated []. The mass of the each story is 98 tons. The stiffness coefficients (k) of the stories are linearly decreased from 3 MN/s to 998 MN/s by the increase of the story numbers. The damping coefficients (c) are. times of the stiffness coefficients. The six different earthquake records used in the study are KJM, PET9, ERZ-NS, LGP, RRS8 and SYL3 records of, Cape Mondecino,, Loma Prieata and Northridge (last records) earthquakes. An optimum TMD was searched for the following ranges. This ranges are %-% for mass ratio, %- 3% for damping ratio and.8 s-. s for period of TMD. The optimum mass, period and damping ratio of TMD were found as 38 t, 3.3 s and.9, respectively. Top storey displacement (x ), velocity and acceleration including ground acceleration (a g ) plots are given in Fig. -3, respectively... x x x x x x Fig.. Top story displacements 3 ISBN:

3 TABLE I. THE MAXIMUM RESPONSES FOR STRUCTURE WITHOUT TMD Earthquakes PET9 KJM ERZ-NS RRS8 SYL3 LGP displacement velocity (m/s) acceleration (m/s ) TABLE II. THE MAXIMUM RESPONSES FOR STRUCTURE WITH TMD Earthquakes PET9 KJM ERZ-NS RRS8 SYL3 LGP displacement velocity (m/s) acceleration (m/s ) dx - dx dx dx dx - dx -3 3 Fig.. Top story velocities - 3 ISBN:

4 d x /dt + a g (m/s ) - - d x /dt + a g (m/s ) d x /dt + a g (m/s ) d x /dt + a g (m/s ) d x /dt + a g (m/s ) d x /dt + a g (m/s ) - 3 Fig. 3. Top story accelerations - 3 The maximum responses of structures under optimization earthquakes are given in Table and for structures without and with TMD, respectively. The maximum displacement of the structure without TMD is.73 m and this displacement occurs under excitation. The optimum TMD is effective to reduce this displacement to. m (3.% reduction). As seen in Fig., the optimum TMD is effective to reduce peak displacements and to obtain a steady state response. The same behaviour is also seen for velocities and accelerations. Conclusion According to the results, optimum TMD is effective to reduce the objective function by.3%. Separately, the optimum TMD can reduce maximum displacement, velocity and acceleration for the most critical earthquake excitation by 3.%, 38.7% and.%,respectively. According to these results, the optimum TMD is not effective only for a single response of the structure. The proposed method is feasible in order to find a general optimum result which is acceptable for different responses of all stories under multiple ground motions. References: [] F. Sadek, B. Mohraz, A.W. Taylor, R.M. Chung, A method of estimating the parametersdof tuned mass dampers for seismic applications, Earthq. Eng. Struct. D.,vol., pp. 7-3, 997. [] R. Rana, T. T. Soong, Parametric study and simplified design of tuned mass dampers, Engineering Structures, Vol., 998, pp. 93. ISBN:

5 [3] C. C. Chang, Mass dampers and their optimal designs for building vibration control, Engineering Structures, Vol., 999, pp [] M. N. S. Hadi, Y. Arfiadi, Optimum design of absorber for MDOF structures, Journal of Structural Engineering-ASCE, Vol., 998, pp [] G. C. Marano, R. Greco, B. Chiaia, A comparison between different optimization criteria for tuned mass dampers design, Journal of Sound and Vibration, Vol. 39,, pp [] A. Y. T. Leung, H. Zhang, C. C. Cheng, Y. Y. Lee, Particle swarm optimization of TMD by non-stationary base excitation during earthquake, Earthquake Engineering and Structural Dynamics, Vol. 37, 8, pp. 3-. [7] A. Y. T. Leung, H. Zhang, H., Particle swarm optimization of tuned mass dampers, Engineering Structures, Vol. 3, 9, pp [8] G. Bekdaş, S.M. Nigdeli, Estimating Optimum Parameters of Tuned Mass DampersUsing Harmony Search, Eng. Struct., vol. 33, pp. 773,. [9] R. Steinbuch, Bionic optimisation of the earthquake resistance of high buildings by tunedmass dampers, J. Bionic Eng., vol. 8, pp. 33-3,. [] Z.W. Geem, J.H. Kim, G.V. Loganathan, A new heuristic optimization algorithm: harmony search, Simul.,vol.7, pp. -8,. [] M.-Y. Liua, W.-L. Chiangb, J.-H. Hwangb, C.-R. Chub, Wind-induced vibration of highrise building with tuned mass damper including soilstructure interaction, Journal of Wind Engineering and Industrial Aerodynamics,vol. 9, pp. 9, 8. ISBN:

Seismic Analysis of Structure by Introducing Weak Story on Top as Tuned Mass Damper

Seismic Analysis of Structure by Introducing Weak Story on Top as Tuned Mass Damper Dr. S.A. Halkude 1, Mr. C.G.Konapure 2, Vanishri. S. Kulkarni 3 1,2,3 Department of Civil Engineering, Walchand Institute