Optimal design and numerical studies of negative stiffness device–TMD controlled systems using PSO algorithm

In recent years, research on negative stiffness devices (NSDs) for vibration control has increased. This study examines the combination of NSDs with tuned mass dampers (TMDs) and explores the NSD-TMD as a nonlinear energy sink (NES). The particle swarm optimization (PSO) algorithm was employed to determine the optimal parameters for the TMD, NSD-TMD, and NES systems. The optimization procedure proves that the PSO algorithm is suitable for solving the optimization problem of the complex systems with strong nonlinearity. The overall procedure is effective and demonstrates strong convergence. The force transmissibility curves of the optimized systems were compared, revealing that the NSD-TMD achieved the best vibration performance, while the NES system demonstrated the target energy transfer (TET) property. Another interesting characteristic of the NSD-TMD system is that it does not necessarily require a large additional mass or damping factor to achieve optimal performance. An actual vertical vibration control scenario for a pedestrian bridge was analyzed using various control strategies. Human-induced force excitations were simulated using a code-defined method. The acceleration responses of an uncontrolled pedestrian bridge and the three optimized control systems were compared in both time and frequency domains. Results further verified the force transmissibility curves. The NSD-TMD system outperformed the other two systems, particularly in reducing the first-order response. Conversely, the NES system proved less effective for controlling human-induced vibration with harmonic force excitations.