Analysis of Static Instability of an Asymmetric, Rotating Sand-Wich Beam

<table>(a) Variation static buckling loads with <svg height="16.450001" id="M93" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 17.174999 16.450001" width="17.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.163)"><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(.012,0,0,-.012,4.637,16.25)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g><g transform="matrix(.012,0,0,-.012,10.777,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> (pinned-pinned). (b) Variation static buckling loads with <svg height="16.450001" id="M94" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 17.174999 16.450001" width="17.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.163)"><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(.012,0,0,-.012,4.637,16.25)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g><g transform="matrix(.012,0,0,-.012,10.777,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> (clamped-free).</table>

Advances in Acoustics and Vibration

fig4

Figure 4

Figure 4: Analysis of Static Instability of an Asymmetric, Rotating Sand-Wich Beam 