Nonlinear Finite Element Model for Sloped Wall Tuned Liquid Dampers Controlling the Nonlinear Seismic Response of Structures

In many engineering fields, tuned liquid dampers (TLDs) are becoming cost-effective and low-maintenance vibration absorbers. The sloped wall TLDs inclined wall enables more liquid to participate in sloshing, which increases the sloshing force that opposes the inertial force of the structure and makes it a more efficient vibration controller than the conventional flat-bottom TLDs. When a structure experiences a strong excitation, its safety becomes uncertain because of the deterioration of structural stiffness, hence, it needs to be equipped with adequate damping arrangements. The suppression of the nonlinear vibration of the structures equipped with sloped wall TLDs associated with nonlinear sloshing has been investigated in this paper. The Eulerian-Lagrangian-based nonlinear finite element scheme for the TLD and the nonlinear spring-mass scheme for the structure are combined and employed for the numerical modeling of the present problem. Compared to the linear sloshing frequencies, the obtained nonlinear sloshing frequencies are closer to the existing experimental result, justifying the accuracy of the nonlinear model. For the TLD with the nonlinear sloshing model, the optimal tuning ratio is found to be slightly less than unity (i.e., 0.986–0.996), whereas, by the linear sloshing model, the predicted optimal tuning ratio remains higher than unity. The loss of energy during yielding causes less amount of energy to be transferred to the TLD tank resulting in a lower hydrodynamic base shear and corresponding poor response reduction.