Optimization and performance evaluation of nonlinear pendulum tuned mass damper inerters (NPTMDIs)

Pendulum tuned mass damper (PTMD) is a widely recognized vibration control system, nevertheless, its extensive applications are hindered by concerns regarding the large auxiliary mass and excessive swing angle. To address the above concerns, this paper develops a novel PTMD-like control system, dubbed nonlinear pendulum tuned mass damper inerters (NPTMDIs), by incorporating a nonlinearly arranged inerter, and systematically investigates its optimal design and control effectiveness. In particular, two configurations of NPTMDIs (designated as NPTMDI I and II) are firstly proposed by introducing nonlinearly arranged inerter (NPTMDI I) and clutched inerter (NPTMDI II), respectively, and corresponding analytical models are established. Then, dynamic equilibrium equations of motion of NPTMDI I and II are derived, respectively, and a two-stage optimization scheme is formulated. Based on the optimal parameters, the control effectiveness of NPTMDI I and II are investigated, and compared to that of the traditional PTMD. Finally, case studies are performed to further investigate the control effectiveness of the proposed NPTMDIs in reducing the seismic responses of a 40-storey benchmark building model. The results demonstrate that, compared to the traditional PTMD, the proposed NPTMDIs (especially Configuration I) are more effective in concurrently reducing both the displacement and acceleration responses of the structures. In addition, the incorporation of inerter proves to be effective in reducing the swing angle of the tip mass, with the “ordinary” inerter exhibiting higher effectiveness when compared to the clutched one.