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

<table>(a) Top view and (b)
cross-section of an imperfect circular plate of radius <svg height="7.1750002" id="M15" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" 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">𝑎</tspan>
</text>
</g>
</g>
</svg> and thickness <svg height="10.95" id="M16" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
</text>
</g>
</g>
</svg>. (c) The particular case of a spherical imperfection,
with radius of curvature <svg height="10.325" id="M17" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑅</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells 