Development of a chaotic nonlinear tuned mass damper for optimal vibration response

In this article an efficient method is developed for optimal design of a nonlinear tuned mass damper (N-TMD) system. Using several horizontal linear springs coming into action sequentially, system nonlinearity can be achieved with ease as a novel method. Friction force between tuned mass and the structure is variably produced by a vertical linear spring that follows a specified controlling curved path allowing reduction of the desired tuned mass. Chaotic behavior of the introduced tuned mass is investigated in terms of the existing parameters in the system. Lyapunov characteristic exponents are determined to demonstrate the chaotic behavior of the system. It is confirmed by comparison that the proposed scheme is able to retrofit structures in a superior way than some other devices such as multiple tuned mass damper systems. The optimization procedure is performed by sequential Simplex algorithm, while Newmark’s beta method for step by step integration is used to find the dynamic response of the structure.