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

<table>Nondimensional natural
frequencies <svg height="16.637501" id="M95" style="vertical-align:-4.68874pt" version="1.1" viewbox="0 0 42.912498 16.637501" width="42.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6375)">
<g transform="translate(72,-58.69)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,60.28)">
<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">1</tspan>
<tspan style="font-size: 8.75px; " x="13.854416" y="0">)</tspan>
</text>
<text transform="matrix(1,0,0,-1,-48.41,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">ℎ</tspan>
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</svg> of the
imperfect plate versus the amplitude of the imperfection having the shape of
mode (0,1).</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells 