Soil-Dependent Optimization of TMD- and Inerter-Based Devices for Seismic Retrofit of Multi-Story Structures

Distributed passive vibration control systems (VCSs) offer an attractive solution for improving the seismic response of multi-story buildings, particularly in seismic retrofit applications and when soil–structure interaction (SSI) effects are explicitly considered. This study presents a soil-dependent optimization framework of distributed Tuned Mass Damper (TMD) and Tuned Mass Damper Inerter (TMDI) systems applied to a ten-story building. The proposed framework determines the optimal number, tuning, damping and spatial distribution of these VCS, including non-collocated inerter configurations for TMDI layouts, while also examining different auxiliary mass ratios. Soil–structure interaction effects are explicitly incorporated by considering four soil classes (A–D) in accordance with Eurocode 8, enabling a systematic evaluation of soil-dependent vibration control effectiveness. Structural performance is evaluated using normalized performance criteria associated with peak absolute floor displacements, floor accelerations and inter-story drifts. The results indicate that distributing control devices along the height of the structure enhances seismic mitigation for both TMD and TMDI configurations, with performance improvements becoming more pronounced as the number of devices increases. Moreover, TMDI systems consistently achieve superior response reduction compared to TMDs across all soil classes, highlighting their potential as a robust, efficient, and lightweight passive vibration control solution for seismic retrofit applications involving SSI effects.