Optimization of multiple tuned mass dampers for vibration control of a nonlinear beam

This research focuses on optimizing tuned mass dampers (TMDs) to achieve maximum vibration suppression in beam structures. We thoroughly investigate both the linear and nonlinear dynamic behaviors of an Euler-Bernoulli beam system. The complex mathematical model of the coupled beam-TMDs system is precisely developed using Hamilton’s principle. A key contribution of this study is its exploration of the incremental effect of adding absorbers, determining optimal parameters as each TMD is progressively integrated. Another novel aspect is the simultaneous optimization of each TMD’s position, stiffness, and damping coefficient. We utilize the particle swarm optimization (PSO) method to achieve this, with the objective of minimizing the area under the system’s response curve. This provides critical insights into improving the dynamic performance and robustness of both linear and nonlinear beam systems.