Optimum Tuned Mass Damper Parameters for Complex Structures Subjected to Base-Excitation Using Single-Mode Approximation.

This paper addresses the problem of optimal tuning of a tuned mass damper (TMD) attached to a complex structure that is dynamically excited by its base. It proposes new analytical formulae which are based on the reduction of the multiple degree of freedom (MDOF) model of the host-structure into an equivalent single degree of freedom (SDOF) model. As it has been recognized in the literature that the traditional single mode approximation used to perform this reduction is not valid for base-excited systems, we propose an improved version that leads to the definition of two mass ratios instead of one in the traditional approach. Taking into account this new mass ratio, the equal peak method is used to derive analytically the optimal values of stiffness and damping of the TMD for a given mass ratio of the device. The introduction of a second mass ratio leads to the existence of two sets of equations for the optimal parameters, depending on the relative values of the two mass ratios. It is shown, however, that only the first set of equations is of practical use. The application of these new tuning rules is illustrated using a MDOF model of a high-rise building. It demonstrates the efficiency of the approach when the first mode of vibration is targeted. When higher modes are of interest, modal interactions are important, which cause a slight to moderate unbalance of the peaks.