A band‐limited reliability‐based robust multimodal optimization of tuned mass dampers

Abstract

Vibrations' mitigation of linear structures, subjected to random excitations, using linear tuned mass dampers (TMDs), has been widely adopted in the field of structural dynamics. Although the TMDs are reliable and constitute a very efficient low‐cost solution, their dynamic parameters should be carefully tuned in order to guarantee optimal performances. Several optimization methods can be used such as the reliability‐based optimization (RBO) of the TMD parameters. Even though the efficiency of the RBO strategy is proven, its main drawback shows up when addressing a multi‐degree of freedom structure. Indeed, only the targeted vibrating mode exhibiting the largest amplitude is controlled whereas the other modes, with relatively smaller vibrating magnitudes, remain uncontrolled. In the present work a new band‐limited BL‐RBO criterion is presented. The new criterion is based on the evaluation of the spectral moments of the structural response, which are required for the failure probability estimation, evaluated on a limited frequency band. The efficiency of the proposed method in controlling a 20‐storey shear building subjected to a seismic excitation has been compared to others from the open literature. It has shown good capabilities in performing a multimodal control of the vibrating structure with uncertainties. The robust multimodal control has been performed using several TMDs (two TMDs per resonant mode), mounted in parallel configuration, and the obtained results showed satisfactory attenuations in the vicinity of the targeted modes.