Simulating Displacement and Velocity Signals by Piezoelectric Sensor in Vibration Control Applications

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Elastic modulus <svg height="15.25" id="M45" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.200001 15.25" width="17.200001" 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="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.8,15.187)"><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></td><td align="center">55.55 GPa</td></tr><tr><td align="left">Elastic modulus <svg height="15.25" id="M46" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.200001 15.25" width="17.200001" 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)"><use xlink:href="#x1D438"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.8,15.187)"><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><td align="center">25.9 GPa</td></tr><tr><td align="left">Elastic modulus <svg height="15.5375" id="M47" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 24.475 15.5375" width="24.475" 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="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
q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" id="x1D43A"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.375,15.475)"><use xlink:href="#x31"></use></g><g transform="matrix(.012,-0,0,-.012,18.086,15.475)"><use xlink:href="#x32"></use></g>
</svg></td><td align="center">7.7 GPa</td></tr><tr><td align="left">Elastic modulus <svg height="15.6875" id="M48" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 24.475 15.6875" width="24.475" 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)"><use xlink:href="#x1D43A"></use></g>
<g transform="matrix(.012,-0,0,-.012,12.375,15.475)"><use xlink:href="#x31"></use></g><g transform="matrix(.012,-0,0,-.012,18.086,15.475)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></td><td align="center">7.7 GPa</td></tr><tr><td align="left">Poisson ratio <svg height="11.825" id="M49" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 21.2125 11.825" width="21.2125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M509 373q0 -52 -42.5 -118.5t-124.5 -159.5l-94 -107h-27q-22 209 -78 342q-21 48 -41 48q-18 0 -63 -62l-22 21q77 111 125 111q30 0 52 -21.5t38 -75.5q37 -130 52 -285q48 62 74.5 99.5t53.5 87t27 76.5q0 43 -17 60q-5 5 -5 15q0 17 12.5 30.5t28.5 13.5
q21 0 36 -22.5t15 -52.5z" id="x1D708"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.1,11.762)"><use xlink:href="#x31"></use></g><g transform="matrix(.012,-0,0,-.012,14.811,11.762)"><use xlink:href="#x32"></use></g>
</svg></td><td align="center">0.26</td></tr><tr><td align="left">Density</td><td align="center">1881 kg/m<sup>3</sup></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mechanical properties of the uni-directional laminates (S-glass/epoxy).

Smart Materials Research

tab1

Table 1

Table 1: Simulating Displacement and Velocity Signals by Piezoelectric Sensor in Vibration Control Applications 