Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells

<table>Type of nonlinearity for
mode (0,2) with an axisymmetric imperfection having the shape of mode (0,1).
2:1 internal resonances with modes (0,3), (0,4), and (0,5) occurs,
respectively, for <svg height="10.9125" id="M100" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 35.512501 10.9125" width="35.512501" 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">𝜃</tspan>
<tspan style="font-size: 12.50px; " x="10.014903" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.055292" y="0">0</tspan>
</text>
</g>
</g>
</svg> = 1.74, 5.43,
and 9.92.</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells 