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

<table>Nondimensional natural frequencies <svg height="16.174999" id="M107" style="vertical-align:-4.68874pt" version="1.1" viewbox="0 0 30.299999 16.174999" width="30.299999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.175)">
<g transform="translate(72,-59.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑇</tspan>
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<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">(</tspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">0</tspan>
<tspan style="font-size: 8.75px; " x="7.2904158" y="0">,</tspan>
<tspan style="font-size: 8.75px; " x="9.4784164" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="13.854416" y="0">)</tspan>
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</svg> of the
imperfect plate versus the amplitude of the imperfection having the shape of
mode (2,0,C).</table>

Mathematical Problems in Engineering

fig8

Figure 8

Figure 8: Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells 