Nonlinear Modeling of Series-Type Pendulum Tuned Mass Damper-Tuned Liquid Damper

The nonlinear response of a series-type pendulum tuned mass damper-tuned liquid damper (TMD-TLD) system is investigated in this study. The TLD is mounted on the pendulum TMD in series to remove the need for costly viscous damping elements. Since the response of the TMD is greater than that of the primary structure, the TLD experiences a significant base motion, leading to a highly nonlinear response that is difficult to model. The nonlinear pendulum TMD equation of motion is modeled without linearizing assumptions. The TLD is represented by an incompressible smoothed particle hydrodynamics (SPH) model that can capture large sloshing responses. The nonlinear model results are compared to shake table testing for a TMD-TLD system and a linear equivalent mechanical model. Four system configurations are considered. The nonlinear model shows good agreement with the experimental data for the TMD displacement and TLD wave heights in both time and frequency domains. The nonlinear model shows improved agreement compared to the linear model for all cases studied, especially for the TLD wave heights. The impact of simplifying the pendulum TMD equation of motion by the small-angle assumption is investigated for two cases. The results indicate that the simplified pendulum equation does not properly capture the frequency of the TMD in the TMD-TLD system and results in a reduction in calculated TLD wave heights compared to the fully nonlinear equation. It is therefore critical to consider the fully nonlinear pendulum TMD response to capture the TMD-TLD behavior.