Device topology optimization for an inerter-based structural dynamic vibration absorber

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A tuned viscous mass damper (TVMD) and a tuned inerter damper (TID) have been proposed as devices that can achieve weight reduction by replacing the mass element of a structural dynamic vibration absorber (DVA) with an inerter. In the TID, the damping element is arranged in parallel with the spring, making its device topology the same as conventional dynamic vibration absorbers. In contrast, in the TVMD the damping element is arranged in parallel with the inerter. This parallel mechanism of inerter and damping element can be realized in a single device, and the member of the building that supports the device can be used as the spring element, making the TVMD highly practical. In fact, TVMDs with a mass effect equivalent to thousands of tons have been commercialized and applied to high-rise buildings in Japan. This paper aims to clarify the effects of the choice of objective functions and damping element arrangement on the seismic response control effectiveness of inerter-based structural DVAs, providing guidelines for structural engineers in selecting suitable devices to achieve desired control effects. The method of investigation considers a model that encompasses both TVMD and TID configurations and formulates a multi-objective optimization problem to simultaneously minimize the displacement amplification factor and floor response acceleration amplification factor. The results of the multi-objective optimization reveal that the TVMD is optimal when the focus is on controlling displacement response, while the TID is optimal when prioritizing the control of floor response acceleration. It was found that the floor response acceleration amplification factor of a structure containing TVMD could be significantly improved by slightly compromising the displacement response amplification factor, leading to the recommendation of adopting the TVMD configuration as an inerter-based structural DVA.