Optimum Parameters of Tuned Inerter Damper for Damped Structures

Abstract

This study evaluates optimal parameters for a damped system with a tuned inerter damper (TID). TID is a device that works similarly to a tuned mass damper, except that the actual mass is substituted with apparent mass, i.e. the inertance of the inerter. Fixed point theory is used to derive optimal parameters of TID attached to an undamped single degree of freedom (SDOF) structure considering objective responses of relative displacement, relative velocity, absolute acceleration and the force transmitted by the primary structure to the ground. Optimal TID parameters attached to the viscously damped SDOF main system are derived by minimising the four objective responses using a numerical search technique. Based on the results from the numerical search and optimal parameters obtained from the fixed point theory, a curve-fitting technique is utilised to establish explicit formulations for TID parameters for the damped primary system. The closed-form expressions thus obtained are based on the minimum mean square error between optimal parameters obtained by numerical search and corresponding explicit formulae. The expressions proposed have a negligible inaccuracy, making them useful for the design process in the damped systems. The damping of the primary system has a negligible effect on the TID's optimal damping ratio. The damping of the primary system, on the other hand, has a substantial impact on the optimum tuning frequency of TID. Finally, an optimally designed TID is applied to SDOF damped system with a fixed and flexible base as a supplemental damper. It is seen optimal TID is significantly effective in controlling the seismic responses.