Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="325434.fig.006a" src="https://static.hindawi.com/articles/mpe/volume-2014/325434/figures/325434.fig.006a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>1st natural frequency</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="325434.fig.006b" src="https://static.hindawi.com/articles/mpe/volume-2014/325434/figures/325434.fig.006b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>2nd natural frequency</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="325434.fig.006c" src="https://static.hindawi.com/articles/mpe/volume-2014/325434/figures/325434.fig.006c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>3rd natural frequency</td></tr></table></td></tr></table>

<table>Comparison of the lowest three natural frequencies of the rotor systems with and without an unbalanced mass (<svg height="12.025" id="M149" style="vertical-align:-3.24916pt" version="1.1" viewbox="0 0 23.237499 12.025" width="23.237499" 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="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><path d="M751 650l-6 -28q-53 -1 -69 -12.5t-24 -38.5q-23 -85 -43 -192l-13 -69q-34 -181 -130 -262q-79 -65 -185 -65t-171 57q-87 77 -54 258l42 232q12 58 0.5 73t-75.5 19l8 28h263l-6 -28q-63 -5 -78 -18t-26 -74l-41 -226q-25 -135 22 -201t139 -66q99 0 161.5 68t91.5 217
l11 57q28 149 28 193q0 28 -19 38t-79 12l6 28h247z" id="x1D448"></path></g>
</svg> = 0.493 kg) at two different locations.</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model 