Robust multimodal control of a large‐scale tensegrity dome using multiple tuned mass dampers

Abstract

Tensegrity domes are reticulated prestressed structures composed of bars in compression and cables in tension. These structures are flexible lightweight systems with low structural damping, and thus, they are sensitive to vibrations induced by strong wind and earthquakes. The present work deals with the robust multimodal control of a large-scale tensegrity dome of Geiger's type. Assuming random excitations and linear behavior of the structure around an equilibrium prestressed configuration, the control is achieved in the low-frequency range using multiple tuned mass dampers (MTMDs). The optimal MTMD parameters, ensuring optimal performances, are obtained using a root mean square displacement (RMSD)-based approach. The optimization strategy is firstly applied, in a deterministic context where the structural parameters uncertainties are not included, to control the fundamental resonant frequency of the dome structure and then extended to perform multimodal control using multiobjective optimization. In addition, in real-life situations, it's very hard to describe actual engineering structures in precise model yielding to unavoidable internal and external uncertainties. To deal with these uncertainties, it has been shown that the proposed multimodal control is also able to carry out robust control in presence of structural uncertainties. The proposed optimization strategy applied to the dome structure is compared to other optimization strategies, from the open literature. The obtained results showed the efficiency of the proposed methodology of the passive control in both contexts, that is, the deterministic and the non-deterministic where uncertainties are considered.