Performance-based optimization of T-NESs considering SSI effects on rectangular embedded foundations

Track-Nonlinear Energy Sinks (T-NESs) are passive vibration absorbers exploiting geometrically nonlinear restoring forces from a mass moving along a curved track, enabling adaptive tuning for structural control under frequency-varying conditions. Despite recent progress in this field, two gaps remain. First, while Soil–Structure Interaction (SSI) has been studied for linear Tuned Mass Dampers (TMDs), it is largely neglected in T-NES design, with only one study reported. This work advances the field by applying the Wolf and Somaini (1986) lumped-parameter model for rigid rectangular foundations embedded in homogeneous, undamped, linear elastic half-spaces, including coupled translational–rocking motions and higher-order soil inertia via the “monkey-tail” component, representing the first comprehensive SSI treatment in T-NES design. Second, although multiple-device TMDs are common, their integration with T-NESs is scarcely explored. Here, multiple T-NESs are optimized atop buildings with embedded foundations within a Reliability-Based Design Optimization (RBDO) framework. Independent track profiles use Padé-expansion rational functions, accounting for stochastic seismic excitation and system uncertainties, with performance assessed via life-cycle cost across three damage limit states. Application to a 10-story building in Concepción, Chile, under four support conditions (fixed base and three soil types) shows that both single and multiple T-NESs reduce life-cycle costs, with multiple devices outperforming the single configuration for stiff soils, but the advantage diminishing as soil stiffness decreases.