Frequency domain prediction of peak nonlinear wave heights of structure-TLD systems

Prediction of peak wave heights early in the TLD design process is critical to ensure proper tank freeboard is allocated. If insufficient freeboard is allocated, the performance of the TLD may be adversely affected by the waves impacting with the tank ceiling. A frequency domain model is developed to predict the spectral response of the first two TLD sloshing modes. A probability density function of the wave height envelop for the first two sloshing modes is derived and employed to predict the peak wave height expected during a specified duration of time. Scale-model structure-TLD tests and nonlinear simulations are employed to evaluate the proposed frequency domain model. The model predicts the RMS response of the second order sloshing mode within a relative error of 15% when compared to simulations. The error increases when the water depth ratio is small. The predicted peak structural responses are in excellent agreement with those that are simulated or measured. The predicted peak TLD wave heights show a maximum error of 20% for all the cases considered. The peak factor relating the peak wave height to the RMS response of the fundamental sloshing mode increases with a decreasing liquid depth and increasing RMS response amplitude. The proposed model enables a rapid estimation of the peak wave response without resorting to computationally expensive nonlinear time domain simulations.