Vibration Analysis of a Rotating Disk with a Crack

<table>Mode shape <svg height="13.45" id="M161" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="21.867746" y="0">)</tspan>
</text>
</g>
</g>
</svg> for a rotating disk (<svg height="11.1" id="M162" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 45.787498 11.1" width="45.787498" 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">𝜔</tspan>
<tspan style="font-size: 12.50px; " x="11.977874" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.018263" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="30.269764" y="0">0</tspan>
</text>
</g>
</g>
</svg> Hz) with a radial crack of length <svg height="14.8375" id="M163" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 68.4375 14.8375" width="68.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8375)">
<g transform="translate(72,-60.13)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<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>
</text>
<text transform="matrix(1,0,0,-1,-52.95,60.27)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
</text>
<text transform="matrix(1,0,0,-1,-44.97,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="18.291889" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="21.417639" y="0">6</tspan>
</text>
</g>
</g>
</svg>. (a) The symmetric mode with a natural frequency of 76 Hz and (b) the antisymmetric mode with a natural frequency of 75.4 Hz.</table>

International Scholarly Research Notices

Vibration Analysis of a Rotating Disk with a Crack

Figure 4