OPTIMUM DESIGN FOR FORCE-RESTRICTED TUNED VISCOUS MASS DAMPER BASED ON ENERGY RESPONSE

Abstract

　The tuned viscous mass damper (TVMD) and its optimum designing method based on the fixed-point theorem have been proposed by Ikago et al. The validity of the damper system as a supplemental energy dissipation device has also been proved analytically and experimentally alike. However, analyses revealed that an installation of inertial mass in the viscous mass damper, and an increase in input ground motions might result in excessive stresses on the supporting member, the damper body, and the primary structure connected to the damper system. Kida et al. then developed the rotation-slipping mechanism to limit the maximum damper force up to a given criterion, such as yield strength, and calling it the “force restriction mechanism.” The TVMD connected with the force restriction mechanism is called force-restricted tuned viscous mass damper (FRTVMD), and the FRTVMD is modeled with a TVMD and a coulomb slider connected in series. Although the effectivity of the FRTVMD is proven experimentally, there are no theoretical backups shown so far due to the complex non-linear response property of the coulomb slider.

　This paper firstly presents a way to equivalently-linearize the coulomb slider stochastically without repetitive numerical computations. In the process of linearization, an RMS of the damper force under a white noise excitation is utilized. Numerical examples show the validity of the linearization method under non-stationary ground motions.

　This paper then presents the performance evaluation of the FRTVMD from total energy dissipation in the damper system and the optimum design variable of the force restriction mechanism using the area of an energy transfer function. The energy transfer function is an expression of input energy to an energy-dissipation element in the frequency domain, and the area of it indicates the total input energy under a white noise excitation. Considering that the FRTVMD dissipates energy in two-part, the dashpot and the coulomb slider, maximization of the total damper dissipation energy may minimize the energy input to the primary structure, if the total earthquake input energy depends little on the damper specifications. Response analyses under a couple of recorded ground motions lastly show the effectiveness of the proposed optimum design variables.