Mathematical Modeling of an Active-Fiber Composite Energy Harvester with Interdigitated Electrodes

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="971597.fig.007a" src="https://static.hindawi.com/articles/sv/volume-2014/971597/figures/971597.fig.007a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Frequency response curves for <svg height="15.4" id="M160" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 35.924999 15.4" width="35.924999" 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>
<g transform="matrix(.012,-0,0,-.012,12.675,15.187)"><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,-.012,22.42,15.187)"><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,-.012,27.644,15.187)"><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
t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" id="x78"></path></g>
</svg> at different load resistances</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="971597.fig.007b" src="https://static.hindawi.com/articles/sv/volume-2014/971597/figures/971597.fig.007b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Variation of <svg height="17.9125" id="M161" style="vertical-align:-2.92166pt" version="1.1" viewbox="0 0 35.924999 17.9125" width="35.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,13.625)"><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>
<g transform="matrix(.012,-0,0,-.012,12.675,5.463)"><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(.008,-0,0,-.008,20.263,8.325)"><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>
<g transform="matrix(.012,-0,0,-.012,12.675,17.7)"><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,-.012,22.42,17.7)"><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,-.012,27.644,17.7)"><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
t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" id="x78"></path></g>
</svg> as a function of <svg height="11.3125" id="M162" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.075 11.3125" width="11.075" 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="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117
t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
</svg></td></tr></table></td></tr></table>

<table>Analytical and FE harvested voltage at different excitation frequencies and load resistances: analytical prediction (continuous and dashed lines) and FE model (circles).</table>

Shock and Vibration

fig7

Figure 7

Figure 7: Mathematical Modeling of an Active-Fiber Composite Energy Harvester with Interdigitated Electrodes 