Vibration Analysis of a Rotating Disk with a Crack

<table>Variations in the dimensionless natural frequencies for mode shapes (a) <svg height="13.45" id="M354" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 32.674999 13.45" width="32.674999" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="21.867746" y="0">)</tspan>
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</svg> and (b) <svg height="13.45" id="M355" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 32.674999 13.45" width="32.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="21.867746" y="0">)</tspan>
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</svg> versus the angular speed <svg height="7.1875" id="M356" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜔</tspan>
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</svg> for three different values of the dimensionless radial crack length <svg height="14.7125" id="M357" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 29.512501 14.7125" width="29.512501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="6.2765059" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="9.7523403" y="0">𝑅</tspan>
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<text transform="matrix(1,0,0,-1,-52.95,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
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</svg>.</table>

International Scholarly Research Notices

Vibration Analysis of a Rotating Disk with a Crack

Figure 12