An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="672648.fig.005a" src="https://static.hindawi.com/articles/sv/volume-2014/672648/figures/672648.fig.005a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Flat bottom</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="672648.fig.005b" src="https://static.hindawi.com/articles/sv/volume-2014/672648/figures/672648.fig.005b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>V-shaped bottom</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="672648.fig.005c" src="https://static.hindawi.com/articles/sv/volume-2014/672648/figures/672648.fig.005c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Arc-shaped bottom</td></tr></table></td></tr></table>

<table>Various shape tuned liquid dampers (length unit: mm).</table>

Shock and Vibration

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Figure 5

Figure 5: An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts 