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<p>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.</p>
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