Higher Period Stochastic Bifurcation of Nonlinear Airfoil Fluid-Structure Interaction

<table>Response surface of the pitch angle <svg height="7.1750002" id="M384" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.175)">
<g transform="translate(72,-66.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
</text>
</g>
</g>
</svg> at <svg height="10.9125" id="M385" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 58.775002 10.9125" width="58.775002" 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">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="9.8648672" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.905256" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="28.156755" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.408257" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="40.659756" y="0">0</tspan>
</text>
</g>
</g>
</svg> as function of the random frequency ratio <svg height="12.35" id="M386" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 10.7625 12.35" width="10.7625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.35)">
<g transform="translate(72,-62.12)">
<g>
<path d="m -71.95,70.71 8.51,0" 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,-71.95,62.31)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜔</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig8

Figure 8

Figure 8: Higher Period Stochastic Bifurcation of Nonlinear Airfoil Fluid-Structure Interaction 