Optimum design of multiple positioned tuned mass dampers for structures constrained with axial force capacity

Abstract

The stories of structure may have different and limited axial force capacity. In order to passively control the translational movement of structures, a tuned mass damper (TMD) positioned on a story may cause to exceed axial force capacity of a story.The optimum performance is achieved when all additional masses are positioned on the top story. Whereas, the top stories of structure may be constructed with lower axial force capacity than the lower stories. In that case, the maximum allowed TMD mass for upper stories may be low. In that situation, several TMDs may be positioned on several stories. In the current study, the optimum tuning of TMDs positioned on multiple stories of structure is investigated. By using small masses, it is also possible to obtain effective passive control with dampers that have small damping coefficients comparing with a single TMD on the top of the structure. The design variables of the optimization problem such as the period and damping ratio of TMD are tuned according to a metaheuristic algorithm called flower pollination algorithm. The TMD is optimized for near-fault excitations by using impulsive motions during the optimization process. The proposal was applied to four case studies. According to the results, the multiple positioned TMDs may be a practical and effective option comparing with the use of a single heavy TMDs on the top of a structure. KEYWORDS axial force, flower pollination algorithm, impulsive motions, optimization, optimum tuning, tuned mass dampers | INTRODUCTIONIn order to reduce structural vibrations originating from seismic sources, tuned mass dampers (TMDs) can be used, but the mass of the TMD must be too big to provide an effective performance on the lateral responses of the structure. Although the responses are positively affected, the fracture or ductility limit (especially for reinforced concrete structures) of vertical structural members (columns) can be exceeded. In that situation, the structural capacity must be considered as the mass limit or the structure must be retrofitted for increasing the axial force capacity. In a civil structure, the forces of upper stories are directed to a lower story. In that case, the axial force is the maximum at the lowest story. For that reason, upper stories of civil structures may be constructed by smaller cross-sections and less reinforcements than the lower stories. In that case, the axial force capacity of upper stories may be less than the capacity of the lower stories. Generally, the optimum position of a TMD is the top of the building where the first mode shape value is the maximum for the critical mode of the structure. In that case, the number of TMDs can be increased and small TMDs can be placed on multiple stories.The most important performance index of TMDs is the optimum tuning. By using multiple TMDs on different stories, it will be a more challenging optimization problem. For this problem, to use a well-known optimum frequency and damping ratio formulation will not be effective because these formulations wer...

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