Nonlinear simulation of a tuned liquid damper with damping screens using a modal expansion technique

The nonlinear peak response distribution of structure–TLD systems during common wind events

“…A third order nonlinear multimodal model is employed, which captures coupling among the first three sloshing modes. The full model derivation and its experimental evaluation using shake table tests are found elsewhere [7,29,30]. The model has been evaluated for TLDs with h/L > 12%, and has been found to provide acceptable results [7].…”

“…Experimental findings of numerous studies have indicated that equivalent mechanical models, which describe the fluid response using an equivalent spring-mass-dashpot system (an equivalent mechanical system), are suitable for conducting a preliminary TLD design [5][6][7]. Statistical linearization techniques are employed to represent the velocity-squared damping produced by screen drag as amplitude-dependent equivalent viscous damping.…”

A hybrid structural control system using a tuned liquid damper to reduce the wind induced motion of a base isolated structure

“…If the Gaussian distribution is employed for the linearization, the constants used in Eqs. (23) are [10] …”

“…The nonlinear response of the fluid is represented using a modal expansion technique which accounts for the coupling of the sloshing modes through the nonlinear free surface boundary conditions [23,24]. The nonlinear responses of the base isolated structure and the fluid are represented by a system of coupled ordinary differential equations.…”

“…The equation of motion for the mth sloshing mode is of the form q m + 2ω m (ζ w,m + ζ s,m )q m + ω 2 m q m + P mẌ + d m where q m is the response of the mth sloshing mode and the coefficients (P m , d m i , etc.) can be found elsewhere [23,24]. Once the fluid response is determined, the base shear force of the TLD, which must be divided by M s before being used by Eq.…”