Multi-Mode Seismic Vibration Control: Simultaneous Optimization of Tuned Mass Damper Placement, Mass, and Parameters for Global Peak Displacement Mitigation

Passive Tuned Mass Dampers (TMDs) are widely implemented to mitigate the seismic response of multi-degree-of freedom (MDOF) structures. Conventional design methodologies and optimization frameworks predominantly restrict TMD placement to a simplified single-degree-of-freedom (SDOF) target, arbitrarily fix the damper mass, and tune continuous parameters solely to minimize the maximum absolute displacement of the roof. However, this heuristic approach inherently neglects the complexity of real-world structural dynamics, where higher-mode vibrations can cause catastrophic peak drifts on intermediate floors. To address this limitation, this study proposes an expanded mixed-integer nonlinear programming (MINLP) framework that simultaneously optimizes four variables: the discrete installation floor level (p), damper mass (m_d), spring stiffness (k_d), and viscous damping coefficient (c_d). To navigate this highly non-convex search space, a novel integrated metaheuristic optimizer, the Genetic Swarm Whale Integrated Method (G-SWIM) is proposed. G-SWIM functions as a unified loop that applies Genetic Algorithm (GA) exploration, Particle Swarm Optimization (PSO) refinement, and Whale Optimization Algorithm (WOA) exploitation within every single iteration. Powered by a custom vectorized Newmark-β solver, the methodology is evaluated on a 10-story benchmark shear frame subjected to the FEMA P695 far-field ground motion suite. By freeing spatial and mass constraints, the results demonstrate a highly robust, globally optimal passive control strategy that achieves a 52% mean reduction in structural deflection and yields net financial savings of over $4.3 million compared to equivalent brute-force structural stiffening.