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

• Peak nonlinear wave heights are required for tuned liquid damper (TLD) design.
• The structure–TLD system is represented as a linearized equivalent mechanical system.
• A Rayleigh–Stokes model describes the distribution of the peak nonlinear wave height.
• The peak structural response distribution is described using a Rayleigh model.
• The model is evaluated using experimental results and nonlinear simulations.

Linearized equivalent mechanical models are often used to conduct preliminary tuned liquid damper (TLD) design; however, they cannot capture nonlinear behavior resulting from the coupling among sloshing modes. Therefore, these models underestimate the expected peak wave height, a quantity that is necessary to evaluate the required tank freeboard. In this study, a method is presented to estimate the nonlinear peak wave height using an equivalent mechanical model.A linearized equivalent mechanical model of the structure–TLD system is employed to determine the RMS responses of the structural displacement and the TLD fundamental sloshing mode wave height. Davenport’s derivation is used to estimate the probability density function of the peak structural displacement. Subsequently, the probability density function of the peak wave heights is derived using a Rayleigh–Stokes model, which employs an extended second order Stokes wave theory to estimate the nonlinear peak wave heights. Expressions are derived to calculate the mean-peak wave height as a function of the RMS response of the fundamental sloshing mode, and the fluid depth ratio.Structure–TLD system tests and nonlinear simulations are used to evaluate the model. Findings reveal that the Rayleigh model is in agreement with the experimental and simulated peak structural response distributions. In addition, the Rayleigh–Stokes model is in agreement with the experimental and particular simulated peak wave height distributions. Discrepancies are expected to arise when the fluid depth ratio is small, the excitation amplitude is large, and the damping screens are positioned to provide significant damping to the second sloshing mode.