Influences of ground motion parameters and structural damping on the optimum design of inerter-based tuned mass dampers

Tuned mass dampers (TMDs) are widely adopted to control the adverse vibrations of engineering structures. To further improve the effectiveness of TMD, inerter was introduced into TMD recently to form inerter-based TMD systems. Similar to TMD, inerter-based TMDs should be carefully designed (optimized) in order to get their best control performances. In the previous studies on using inerter-based devices for seismic induced vibration control, the external excitation was normally simplified as a white noise and the inherent structural damping was ignored. However, it is well known that seismic excitation cannot be simply assumed as a white noise and damping always exists in the structure. The parameters obtained by the previous optimization procedures thus do not necessarily result in the best performance of the device. In the present study, the equations of motion of a single-degree-of-freedom (SDOF) structure equipped with three types of inerter-based TMDs subjected to seismic excitation are firstly developed. Instead of using a white noise as input, the filtered Kanai-Tajimi spectrum, which is characterized by the site damping and frequency, is adopted to model seismic ground motion. Then the effects of site damping, site frequency and structural damping on the inerter-based TMDs are comprehensively investigated and formulas are proposed to estimate the optimal parameters. Lastly, the responses of a structure without control and controlled by an inerter-based TMD under simulated and recorded earthquake ground motions are analysed by using MATLAB/Simulink. Numerical results show that the optimal parameters of inerter-based TMDs are significantly dependent on the site frequency and structural damping, while the site damping has little influence. Moreover, the accuracy of the proposed formulas is validated, and the control effectiveness of the inerter-based TMD is confirmed.