Flexural Vibration Test of a Beam Elastically Restrained at One End: A New Approach for Young’s Modulus Determination

<table>The flexural vibration test of partially restrained aluminum beam with <svg height="12.4375" id="M88" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 77.387497 12.4375" width="77.387497" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, and <svg height="12.4375" id="M90" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 87.349998 12.4375" width="87.349998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>. (a) Dynamic response detected by the force sensor at sample rate <svg height="12.2625" id="M91" style="vertical-align:-0.02728pt" version="1.1" viewbox="0 0 39.537498 12.2625" width="39.537498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><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(.017,-0,0,-.017,11.044,12.162)"><path d="M513 0l-137 -2q-16 18 -164 198q-19 22 -31 22q-7 0 -16 -3v-111q0 -49 11.5 -61t60.5 -17v-26h-223v26q50 4 61.5 17t11.5 61v472q0 50 -10 61.5t-56 15.5v24q57 6 144 35v-471q37 7 63 35q31 31 71 88q16 23 10.5 31.5t-40.5 12.5v26l204 9v-25q-51 -8 -75 -19.5
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</svg>. (b) Identified resonance frequencies: <svg height="17.262501" id="M92" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 87.974998 17.262501" width="87.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
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<g transform="matrix(.012,-0,0,-.012,10.975,17.2)"><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>
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</svg>; <svg height="17.262501" id="M93" style="vertical-align:-4.0404pt" version="1.1" viewbox="0 0 87.974998 17.262501" width="87.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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Advances in Materials Science and Engineering

fig3

Figure 3

Figure 3: Flexural Vibration Test of a Beam Elastically Restrained at One End: A New Approach for Young’s Modulus Determination 