Influence of Uncertainties on the Dynamic Buckling Loads of Structures Liable to Asymmetric Postbuckling Behavior

<table>Comparison of the scatter of buckling load with
the Melnikov load <svg height="15.1375" id="M105" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 54.412498 15.1375" width="54.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,10.912,14.938)"><path d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" id="x1D459"></path></g>
<g transform="matrix(.017,-0,0,-.017,19.45,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,34.137,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg>  and two values of <svg height="12.375" id="M106" style="vertical-align:-3.43848pt" version="1.1" viewbox="0 0 27.5875 12.375" width="27.5875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,9.663,12.112)"><path d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
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</svg>.</table>

Mathematical Problems in Engineering

fig18

Figure 18

Figure 18: Influence of Uncertainties on the Dynamic Buckling Loads of Structures Liable to Asymmetric Postbuckling Behavior 