Optimal path shape of friction-based Track-Nonlinear Energy Sinks to minimize lifecycle costs of buildings subjected to ground accelerations

Track Nonlinear Energy Sinks (T-NES) are Pendulum Tuned Mass Dampers (PTMDs) whose nonlinear restoring forces are obtained from curved path shapes. They combine the abilities of traditional spring-based NESs with the operational advantages of PTMDs. T-NES can resonate with broad frequency content, becoming effective even under damage to the host structure originating from strong ground motions. In the published literature, the integration of Friction Dampers (FDs) into T-NESs (so-called T-NES Type II) has only been studied on PTMDs with circular tracks, and in deterministic settings. Herein, a novel Reliability-Based Design Optimization (RBDO) procedure is presented to find the optimal track shape of T-NES Type II in buildings subjected to earthquakes. The objective is to minimize expected life-cycle damage costs corresponding to slight damage, moderate damage, and extensive damage limit states. A set of rational functions encompassing a wide range of generic curvatures is constructed to describe the T-NES track shape. The nonlinear description is used for restoring force and also in the dissipative mechanism. The case study is a medium-rise building located in Chile. The results indicate that, for the studied building, the optimal path is multimodal, and quite different track profiles can significantly reduce oscillation of the host structure.