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

<table>Variation of natural frequencies with power law exponent <svg height="10.325" id="M273" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg> of fluid-filled FGM type I &amp; II cylindrical shells on elastic foundations for <svg height="10.8125" id="M274" 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="11.1" id="M275" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.099998 11.1" width="35.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
<tspan style="font-size: 12.50px; " x="9.6773224" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.71771" y="0">5</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M276" 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>, <svg height="11.0125" id="M277" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 84.8125 11.0125" width="84.8125" 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>
<tspan style="font-size: 12.50px; " x="23.405617" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="39.609505" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="45.861004" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="48.986755" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="55.238255" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="61.489754" y="0">2</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.225" id="M278" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.1875 14.225" width="89.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.225)">
<g transform="translate(72,-60.62)">
<text transform="matrix(1,0,0,-1,-71.95,60.99)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐺</tspan>
<tspan style="font-size: 12.50px; " x="12.640533" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.680922" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="30.932423" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="34.05817" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="43.085339" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="53.862923" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="60.114426" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-5.57,66.16)">
<tspan style="font-size: 8.75px; " x="0" y="0">7</tspan>
</text>
</g>
</g>
</svg>, and <svg height="14.225" id="M279" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 89.625 14.225" width="89.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.225)">
<g transform="translate(72,-60.62)">
<text transform="matrix(1,0,0,-1,-71.95,60.99)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="31.282507" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="34.408257" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="43.435421" y="0">×</tspan>
<tspan style="font-size: 12.50px; " x="54.213009" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="60.464508" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-5.22,66.16)">
<tspan style="font-size: 8.75px; " x="0" y="0">7</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig2

Figure 2

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