Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Abstract

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.