Keywords: tuned viscous mass damper, dynamic vibration absorber, optimum vibration 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]. The TVMD consists of a viscous mass damper and a soft spring which connects the damper to the primary system. The fundamental frequency of the TVMD is designed to be close to that of the primary system, and large energy dissipation is achieved by the deformation and viscous resistant force amplified by the additional vibration system. The basic idea of the present device is the same as the tuned mass dampers (TMD). While a large additional mass is required for vibration control of a building structure, the apparent mass amplifier using a ball-screw mechanism allowed us to make the device smaller compared with the conventional TMDs.

While the fixed point theory [2] is applicable to an undamped single degree of freedom (SDOF) structure incorporated with a TVMD, the design method to obtain an optimum set of TVMD parameters for a damped multiple degree of freedom (MDOF) structure has not yet been presented.

In this paper, we present an optimum design method of the seismic control system for a damped MDOF structure incorporating the TVMDs.

Repetitive seismic response evaluation is required in the optimization process, and the seismic control system using TVMDs is non-classically damped. A less time-consuming evaluation method such as spectrum modal analysis is desirable. The square-root-of-the-sum-of-squares (SRSS) or the complete quadratic combination (CQC), however, are not accurate enough. We employ a complex complete quadratic combination (CCQC) [3] method to approximate the seismic response.

We formulated an optimum design problem to minimize the dynamic compliance of the primary structure subject to the damper force limit. Sequential quadratic programming is employed to obtain an optimum set of TVMD parameters for a 10 storey example model. The time-history analysis based on Newmark's beta method showed that the optimum design signficantly reduced the seismic response of the primary structure and mostly satisfied the designated damper force limit.

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

J.P. Den Hartog, "Mechanical Vibrations", fourth edition, Dover, New York, 1985.

3

J.N. Yang, S. Sarkani, "A response spectrum approach for seismic analysis of non-classically damped structures", Engineering Structures, 12, 173-184, 1990. doi:10.1016/0141-0296(90)90004-C

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