Vibrational Study of Fluid-Filled Functionally Graded Cylindrical Shells Resting on Elastic Foundations

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left"><span style="width: 25.049999px;"><svg height="11.0125" id="M138" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 25.049999 11.0125" width="25.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0125)">
<g transform="translate(72,-63.19)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="7.214231" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="10.690065" y="0">𝑅</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 7.8874998px;"><svg height="7.1374998" id="M139" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1375)">
<g transform="translate(72,-66.29)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">Li [<a href="/journals/isrn/2011/892460/#B32">28</a>]</td><td align="center">Present</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left" rowspan="5">0.05</td><td align="center">0</td><td align="center">0.09295</td><td align="center">0.092968</td></tr><tr><td align="center">1</td><td align="center">0.01610</td><td align="center">0.016102</td></tr><tr><td align="center">2</td><td align="center">0.03930</td><td align="center">0.039271</td></tr><tr><td align="center">3</td><td align="center">0.109824</td><td align="center">0.109811</td></tr><tr><td align="center">4</td><td align="center">0.210284</td><td align="center">0.210277</td></tr><tr><td align="center" colspan="4"><hr/></td></tr><tr><td align="left" rowspan="5">0.002</td><td align="center">0</td><td align="center">0.09293</td><td align="center">0.092929</td></tr><tr><td align="center">1</td><td align="center">0.016101</td><td align="center">0.016101</td></tr><tr><td align="center">2</td><td align="center">0.005453</td><td align="center">0.005452</td></tr><tr><td align="center">3</td><td align="center">0.005042</td><td align="center">0.005041</td></tr><tr><td align="center">4</td><td align="center">0.008534</td><td align="center">0.008533</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Comparison of frequency parameters <svg height="20.4125" id="M135" style="vertical-align:-3.25287pt" version="1.1" viewbox="0 0 141.95 20.4125" width="141.95" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.4125)">
<g transform="translate(72,-55.67)">
<text transform="matrix(1,0,0,-1,-71.95,58.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">Ω</tspan>
<tspan style="font-size: 12.50px; " x="12.765563" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.805952" y="0">𝜔</tspan>
<tspan style="font-size: 12.50px; " x="33.320496" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="42.572716" y="0">√</tspan>
</text>
<g>
<path d="m -17.77,70.71 59.28,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-17.77,58.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="13.190665" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="24.530886" y="0">𝜈</tspan>
</text>
<text transform="matrix(1,0,0,-1,13.05,62.4)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,17.92,58.96)">
<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="13.915839" y="0">𝐸</tspan>
</text>
</g>
</g>
</svg> for an isotropic cylindrical shell with simply-supported boundary condition (<svg height="10.8125" id="M136" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 38.424999 10.8125" width="38.424999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="12.340461" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.38085" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M137" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.112499 10.9125" width="62.112499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan>
<tspan style="font-size: 12.50px; " x="8.8521242" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="12.327958" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="25.043509" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="37.083897" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="43.3354" y="0">0</tspan>
</text>
</g>
</g>
</svg>).

International Scholarly Research Notices

tab2

Table 2

Table 2: Vibrational Study of Fluid-Filled Functionally Graded Cylindrical Shells Resting on Elastic Foundations 