Finite Element Simulation of the Vibration Provided by Sandwich Rigid Panel with a Resilient Material In Between under Heavyweight Impact

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Item</td><td align="left">Value</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Force integration (<svg height="11.175" id="M2" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.6625 11.175" width="11.6625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M667 650l-9 -28q-53 -5 -76 -17t-64 -59q-51 -61 -175 -225q-21 -29 -27 -55l-27 -136q-13 -65 -0.5 -80t83.5 -22l-7 -28h-280l8 28q64 4 81 19t30 83l25 128q6 35 -7 65l-98 231q-17 41 -32.5 52t-68.5 16l8 28h252l-6 -28l-40 -4q-27 -3 -33 -12.5t2 -31.5
q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" id="x1D44C"></path></g>
</svg>)</td><td align="left">19.92 N·s<svg height="0.125" id="M3" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 5.7874999 0.125" width="5.7874999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
</svg></td></tr><tr><td align="left">Maximum impact force (<svg height="15.4" id="M4" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 33.887501 15.4" width="33.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.637,15.187)"><path d="M797 0h-214v26q46 5 58 17.5t12 63.5v167q0 116 -88 116q-48 0 -112 -52q3 -18 3 -42v-195q0 -46 11 -58t53 -17v-26h-214v26q48 5 59.5 17t11.5 60v172q0 115 -88 115q-47 0 -109 -52v-235q0 -47 10 -59.5t48 -17.5v-26h-211v26q50 5 62.5 17t12.5 60v207q0 48 -9 59.5
t-52 18.5v23q79 14 139 41v-81q3 2 29 20.5t44 29.5q45 28 81 28t66 -22t46 -61q25 20 83 57q39 26 76 26q59 0 93 -40t34 -113v-193q0 -49 10.5 -60.5t54.5 -16.5v-26z" id="x6D"></path></g><g transform="matrix(.012,-0,0,-.012,20.383,15.187)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.012,-0,0,-.012,25.606,15.187)"><path d="M474 0h-214v26q32 4 39 12t-5 28l-74 117q-39 -58 -64 -106q-16 -25 -10 -35t44 -16v-26h-186v26q46 6 64 17t48 49t85 120l-87 136q-23 36 -40 47t-58 16v26h199v-26q-31 -4 -36.5 -12.5t9.5 -29.5l59 -93q37 56 58 94q13 23 7 30t-40 11v26h183v-26q-47 -5 -65 -13.5
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</svg>)</td><td align="left">1563.83 N</td></tr><tr><td align="left">Average impact force (<svg height="18.3125" id="M5" style="vertical-align:-5.04861pt" version="1.1" viewbox="0 0 27.4125 18.3125" width="27.4125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.637,15.188)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
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q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78
q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g>
</svg>)</td><td align="left">996.08 N</td></tr><tr><td align="left">Velocity at impact (<svg height="11.375" id="M6" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 12.7375 11.375" width="12.7375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" id="x1D449"></path></g>
</svg>)</td><td align="left">4.427 m/s</td></tr><tr><td align="left">Average acceleration (<svg height="18.6" id="M7" style="vertical-align:-5.04861pt" version="1.1" viewbox="0 0 29.299999 18.6" width="29.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.525,15.475)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.012,-0,0,-.012,17.534,15.475)"><path d="M478 437v-26q-39 -5 -53 -17.5t-35 -57.5q-68 -149 -142 -347h-28q-47 128 -138 350q-17 43 -30.5 54.5t-53.5 17.5v26h205v-26q-40 -4 -46.5 -14.5t6.5 -42.5q41 -115 95 -247q43 101 89 238q12 36 3.5 48.5t-50.5 17.5v26h178z" id="x76"></path></g><g transform="matrix(.012,-0,0,-.012,23.043,15.475)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
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q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g>
</svg>)</td><td align="left">398.43 <svg height="18.612499" id="M8" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 33.625 18.612499" width="33.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M797 0h-214v26q46 5 58 17.5t12 63.5v167q0 116 -88 116q-48 0 -112 -52q3 -18 3 -42v-195q0 -46 11 -58t53 -17v-26h-214v26q48 5 59.5 17t11.5 60v172q0 115 -88 115q-47 0 -109 -52v-235q0 -47 10 -59.5t48 -17.5v-26h-211v26q50 5 62.5 17t12.5 60v207q0 48 -9 59.5
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<g transform="matrix(.012,-0,0,-.012,27.225,7.613)"><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>
</svg></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The calculated values of the waveform of the impact force.

Shock and Vibration

tab2

Table 2

Table 2: Finite Element Simulation of the Vibration Provided by Sandwich Rigid Panel with a Resilient Material In Between under Heavyweight Impact 