Optimal design of nonlinear TMD with Bingham-type damping for base-excited structures

ABSTRACT This paper presents an optimal design procedure for a nonlinear TMD with Bingham-type damping that can lead to a more economic and realistic design of the damper. The optimization problem is solved in the Genetic Algorithm (GA) framework. Considering small nonlinearities, the nonlinear TMD design using GA is validated through standard equivalent linearization method. The efficacy of the TMD designs is presented through a numerical simulation study on four different single-degree-of-freedom structure-TMD systems subjected to recorded earthquake ground motions. Results indicate that the optimally designed nonlinear TMD with Bingham-type damping can effectively reduce the size of the TMD damping element at the cost of a very slight degradation in control performance as compared to the linear TMD. The improved performance of the nonlinear TMD with Bingham-type damping over the linear TMD that develops post-design nonlinearities is also shown. Further, a robust design procedure of the nonlinear TMD using GA is presented that can cater to perturbations in the natural frequency of the primary structure. Thus, the optimal design procedure using GA for the nonlinear TMD offers several advantages as compared to the statistical linearization approach.