Optimum Parameters of Tuned Inerter Damper for Damped Structures

• Published in: Journal of sound and vibration 2022-10, Vol.537, p.117218, Article 117218
• Main Authors: Islam, Naqeeb Ul, Jangid, R S
• Format: Article
• Language: English
• Subjects: Closed-Form Expressions; Curve Fitting; Fixed Point Theory; Numerical Search; Transfer Functions; Tuned Inerter Damper
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2022.117218

•There are points independent of the damping ratio for the transfer function curves of an undamped sytem with a tuned inerter damper.•There exist a pair of optimum parameters of TID for which the response of the structure is minimum.•The numerical search technique forms a viable alternative for arriving at optimal parameters.•Structural damping influences more on optimum frequency ratio than optimum damping ratio.•Closed-form expressions for optimal parameters of TID will be handy for the design process.•An optimally designed TID is significantly effective in seismic response mitigation 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.