A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam

<table>The first six vibration mode shapes of a rotating beam (<svg height="13.55" id="M476" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 58.587502 13.55" width="58.587502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜂</tspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.00672" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.258221" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="40.50972" y="0">0</tspan>
</text>
</g>
</g>
</svg>, <svg height="15.4875" id="M477" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 38.887501 15.4875" width="38.887501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.4875)">
<g transform="translate(72,-59.61)">
<g>
<path d="m -71.95,70.71 9.25,0" 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,-71.95,59.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
<tspan style="font-size: 12.50px; " x="12.715551" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.755939" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="11.1625" id="M478" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 48.412498 11.1625" width="48.412498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1625)">
<g transform="translate(72,-63.07)">
<text transform="matrix(1,0,0,-1,-71.95,63.39)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="28.806911" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,-36.88,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">∘</tspan>
</text>
</g>
</g>
</svg>).</table>

Mathematical Problems in Engineering

fig10

Figure 10

Figure 10: A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam 

Figure 10 | A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam 