Nonlinear multimodal model for an annular tuned sloshing damper equipped with damping screens

Abstract

Annular tuned sloshing dampers equipped with damping screens are studied experimentally and analytically. A nonlinear multimodal model is presented to simulate the coupled response among the lowest order sloshing modes in a tank equipped with damping screens, which leads to velocity-squared damping. Shake table tests are conducted on annular tanks with various inner radii, water depths, screen orientations, and base excitation amplitudes. The proposed model is evaluated by comparing the predicted and measured sloshing forces, energy dissipation per cycle, and wave heights. The predicted sloshing forces and energy dissipation per cycle are in good agreement with the measured results. The wave heights show larger discrepancies, including phase shifts; however, the peak amplitudes are captured with reasonable accuracy for the tests conducted. Secondary resonances lead to multiple peaks in the frequency response plots when higher order sloshing modes become excited through modal coupling. Plots created to indicate which secondary resonances are likely to occur for a given liquid depth ratio indicate that it may not be possible to avoid all secondary resonances. Radial damping screens can be strategically positioned within the tank to provide the desired level of damping to the fundamental sloshing modes, as well as a reasonable amount of damping to higher order modes that are susceptible to secondary resonance excitation. Since existing linearized models for annular tuned sloshing dampers equipped with damping screens do not capture the important nonlinear response characteristics of these devices, the proposed model fills an important research gap necessary to facilitate their effective design.