Optimization of the individual stiffness and damping parameters in multiple-tuned-mass damper systems

The characteristics of multiple tuned-mass dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers, and several papers have included some parameter optimization. In this paper, we propose an efficient numerical algorithm to optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system directly. We formulate the parameter optimization as a decentralized H2 control problem where the block-diagonal feedback gain matrix is composed of the stiffness and damping coefficients of the TMDs. The gradient of the root-mean-square (RMS) response with respect to the design parameters is evaluated explicitly, and the optimization can be carried out efficiently. The effects of the mass distribution, number of dampers, total mass ratio, and uncertainties in system parameters are studied. Numerical results indicate that the optimal designs have neither uniformly spaced tuning frequencies nor identical damping coefficients, and that optimization of the individual parameters in the MTMD system yields a substantial improvement in performance. We also find that the distribution of mass among the TMDs has little impact on the performance of the system provided that the stiffness and damping can be individually optimized.

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