Models To Derive the Resonant Frequency of a Liquid in a Rectangular Tank With a Curved Bottom

Abstract

This thesis investigates the resonant frequency of a partially-filled rectangular tank of water with a curved bottom that is subject to a horizontal harmonic excitation. The primary goal was to find a model that can accurately find the resonant frequency to study the change in the natural frequency when the parameters of the curved base and system were changed. The EOM model, the h ̅ model, and the ω ̅_n model were derived all from the same linear assumptions and approximation for the velocity potential. Frequency sweeps were done for several curved base systems and compared to each of the models’ predictions. It was found that the h ̅ and ω ̅_n models both agreed well with the data generally, while the EOM model did not. An additional investigation was done on this system to understand the presence of nonlinearities and damping and their significance to the problem. It was found that while several nonlinearities exist like additional harmonic frequency content and surface tension, they are not significant in determining the resonant frequency. Furthermore, the accuracy in the h ̅ and ω ̅_n models show that the linear assumptions and simplifications made for the velocity potential equation were feasible to a degree. Despite this, it is clear that this approximation of the velocity potential needs further work as the EOM model utilizes it fully and is inaccurate.