Keywords: tuned viscous mass damper, dynamic vibration absorber, multi-modal control, fixed point theory, sequential quadratic programming, seismic control.

The authors have presented a new seismic control device the tuned viscous mass damper (TVMD) [1,2]. The TVMD consists of a viscous mass damper with an apparent mass amplifier and a soft spring that connects the damper to the primary building structure. This ensures that the fundamental frequency of the additional vibration system is close to that of the primary system, which provides an effective reduction in seismic response of the primary structure. Although the basic idea of the TVMD is the same as a dynamic vibration absorber or a tuned mass damper (TMD), it is different from them by using an amplified apparent mass for the additional mass, and the damping force generated by the TVMD is not relative to the displacement relative to the ground but to the inter-storey drift of the primary system. The mass amplifier using a ball screw mechanism allowed us to make the additional mass and device itself smaller compared with a conventional TMD.

Den Hartog [3] presented the design method, which is called fixed point theory, for dynamic vibration absorbers to minimize the peak of a resonance curve using fixed points, which exist if the primary system is an undamped single-degree-of-freedom (SDOF) system. The fixed point theory can be applied to the design of a vibration control system with the TVMD as long as the primary structure is an undamped SDOF system. For a damped multiple-degree-of-freedom (MDOF) structure, the authors have presented design methods to obtain an optimum set of damper parameters using sequential quadratic programming (SQP) [4]. The mode controlled by these methods, however, is confined to the first mode only.

Meanwhile, to control higher modes is found to be very effective to suppress the seismic response of the structure. This paper presents an optimum multi-modal seismic control design method for high-rise buildings incorporated with the TVMDs.

1

K. Saito, Y. Sugimura, S. Nakaminami, H. Kida, N. Inoue, "Vibration Tests of 1-Story Response Control System Using Inertial Mass and Optimized Soft Spring and Viscous Element", the 14th World Conference on Earthquake Engineering, Beijing, China, Oct. 2008.

2

K. Ikago, K. Saito, N. Inoue, "Seismic Control of Buildings using Tuned Viscous Mass Dampers", Proceedings of JSSI 15th Anniversary International Symposium on Seismic Response Controlled Buildings for Sustainable Society (CD-ROM), Paper ID RC-5, September 16-17 2009 Tokyo Japan, 2009.

3

J.P. Den Hartog, "Mechanical Vibrations", (4th edn), Dover, New York, 1985.

4

K. Ikago, Y. Sugimura, K. Saito, N. Inoue, "Optimum Seismic Response Control of Multiple Degree of Freedom Structures using Tuned Viscous Mass Dampers", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 164, 2010. doi:10.4203/ccp.93.164

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