Regular and Chaotic Dynamics of Flexible Plates

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left"><svg height="14.0375" id="M51" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 16.5375 14.0375" width="16.5375" 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,-.012,10.138,13.838)"><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> <br/><svg height="18.0625" id="M52" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 58.262501 18.0625" width="58.262501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.912,14.938)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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<g transform="matrix(.017,-0,0,-.017,23.312,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,37.999,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,46.159,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,50.035,10.862)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
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</svg></td><td align="center">Poincaré map <br/><svg height="16.4125" id="M53" style="vertical-align:-3.49493pt" version="1.1" viewbox="0 0 60.362499 16.4125" width="60.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
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<g transform="matrix(.012,-0,0,-.012,12.162,16.212)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
<g transform="matrix(.017,-0,0,-.017,16.85,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,22.732,12.138)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
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<g transform="matrix(.012,-0,0,-.012,34.825,16.212)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g><g transform="matrix(.012,-0,0,-.012,38.882,16.212)"><path d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" id="x2B"></path></g><g transform="matrix(.012,-0,0,-.012,45.867,16.212)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
<g transform="matrix(.017,-0,0,-.017,54.425,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg></td><td align="center">Fourier power <br/>spectrum <svg height="15.0875" id="M54" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 30.887501 15.0875" width="30.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68
l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" id="x1D446"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,14.103,12.138)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g><g transform="matrix(.017,-0,0,-.017,24.949,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg></td><td align="center">Curves of equal <br/>deflections</td><td align="center">2D Morlet wavelet</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">0.4</td><td align="center"><img alt="937967.table.002a" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002a.jpg"/></td><td align="center"><img alt="937967.table.002b" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002b.jpg"/></td><td align="center"><img alt="937967.table.002c" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002c.jpg"/></td><td align="center"><img alt="937967.table.002d" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002d.jpg"/></td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left"><b>0.5</b></td><td align="center"><img alt="937967.table.002e" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002e.jpg"/></td><td align="center"><img alt="937967.table.002f" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002f.jpg"/></td><td align="center"><img alt="937967.table.002g" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002g.jpg"/></td><td align="center"><img alt="937967.table.002h" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002h.jpg"/></td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left">0.745</td><td align="center"><img alt="937967.table.002i" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002i.jpg"/></td><td align="center"><img alt="937967.table.002j" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002j.jpg"/></td><td align="center"><img alt="937967.table.002k" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002k.jpg"/></td><td align="center"><img alt="937967.table.002l" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002l.jpg"/></td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left">0.749</td><td align="center"><img alt="937967.table.002m" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002m.jpg"/></td><td align="center"><img alt="937967.table.002n" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002n.jpg"/></td><td align="center"><img alt="937967.table.002o" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002o.jpg"/></td><td align="center"><img alt="937967.table.002p" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002p.jpg"/></td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left">0.75</td><td align="center"><img alt="937967.table.002q" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002q.jpg"/></td><td align="center"><img alt="937967.table.002r" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002r.jpg"/></td><td align="center"><img alt="937967.table.002s" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002s.jpg"/></td><td align="center"><img alt="937967.table.002t" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002t.jpg"/></td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left">0.95</td><td align="center"><img alt="937967.table.002u" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002u.jpg"/></td><td align="center"><img alt="937967.table.002v" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002v.jpg"/></td><td align="center"><img alt="937967.table.002w" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002w.jpg"/></td><td align="center"><img alt="937967.table.002x" src="https://static.hindawi.com/articles/sv/volume-2014/937967/figures/937967.table.002x.jpg"/></td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Applied dynamic characteristics (<svg height="18.0625" id="M50" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 58.262501 18.0625" width="58.262501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M615 290q0 -148 -114 -245q-65 -57 -125 -57q-39 0 -62 27t-29 70q-31 -41 -72 -69t-74 -28q-49 0 -82.5 43t-33.5 124q0 97 55 174.5t148 124.5l15 -24q-59 -45 -94 -113t-35 -146q0 -58 19.5 -88.5t48.5 -30.5q33 0 62 34.5t45 101.5q16 73 20 135l80 17l5 -6
q-11 -37 -23.5 -100t-12.5 -92q0 -47 16.5 -71.5t44.5 -24.5q62 0 95.5 67t33.5 160q0 107 -63 152l1 9q14 14 45 14q29 0 57.5 -44t28.5 -114z" id="x1D714"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.912,14.938)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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<g transform="matrix(.017,-0,0,-.017,23.312,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,37.999,10.862)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,46.159,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,50.035,10.862)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
q53 0 90 28q4 31 4 66q0 51 -9.5 95.5t-39 80.5t-75.5 36z" id="x39"></path></g>
</svg>).

Shock and Vibration

Regular and Chaotic Dynamics of Flexible Plates

Table 2