A Ball-Track-NES for the vibration control of flexible structures under seismic excitation

Abstract

Track Nonlinear Energy Sinks (T-NESs) are gravity-based dynamic absorbers oscillating over properly designed curved tracks. Due to the resulting nonlinear restoring forces, they exhibit effective control performance even when the natural frequencies of the host structure shift due to damage. Among the available configurations for gravity-based devices, ball absorbers present a cost-effective option characterized by space efficiency and minimal maintenance requirements. Nevertheless, a comprehensive literature survey reveals that, due to the greater mathematical modeling complexity, fewer works on ball absorbers are available than their translational counterparts. Moreover, all existing papers addressing ball absorbers focus on circular tracks; to the best of the author’s knowledge, not a single paper on Ball Track Nonlinear Energy Sinks (BT-NES) can be found. Hence, this work introduces an original approach dealing with the optimum track shape of BT-NESs installed in flexible structures under seismic excitations. A nonlinear 2D model is developed to capture the motion of a heavy ball on an arbitrarily shaped track installed on the top floor of generic multi-degree of freedom (MDOF) structures modeled through the Finite Element (FE) method. Instead of imposing a fixed shape curvature, a generic rational function obtained from the Padé expansion of the circle equation is integrated into the optimization. The scheme allows for exploring a diverse set of arbitrary curvatures to describe the BT-NES track shape. The application case featured a typical soft-story building subjected to earthquake loadings. The BT-NES exhibited effective control performance, reducing the building’s ISDR by almost 30%.