A tuned rocking wall damper enhanced by an inerter to control the seismic vibration of existing mid-rise structures

This study proposes a tuned rocking wall damper (TRWD), an alternative to the conventional tuned mass damper (TMD), developed to control seismic vibrations for existing mid-rise structures. The TRWD comprises a rocking wall connected to the host structure via a linear visco-elastic device at a specific storey level. A horizontal inerter is attached to the wall to significantly enhance its supplemental inertia. The equations of motion for a singledegree-of-freedom (SDOF) system coupled with a general case of a TRWD are established, and closed-form formulas for optimal tuning parameters are derived based on fixed points theory. These parameters apply to any wall shape, any connection level, and walls with or without inerters. A parametric study in the frequency domain along with time-history analysis using 22 far-field earthquake records is conducted on the SDOF-TRWD system. Results reveal that the control effectiveness of the TRWD primarily depends on the term "mu 7," where mu represents the TRWD's mass ratio and 7 represents the inertia factor. The optimally designed TRWD with a large mu 7 can provide significant damping to the main structure, prolong the fundamental period, and minimize the detuning effect. The TRWD is shown to reduce relative displacement responses for a wide range of structural periods; however, it is only effective in reducing absolute acceleration responses for structures with periods ranging from 0.25 to 2.0 s. Finally, a numerical investigation is conducted on a 5-storey shear building using a finite element model, verifying the effectiveness of the TRWD for various configurations and connection levels.