Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures

<table>Ninth-order mode shape (a) and associated KFD trajectory (b) for Damage Scenario II (where <svg height="11.675" id="M29" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 15.0625 11.675" width="15.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.675)">
<g transform="translate(72,-62.66)">
<text transform="matrix(1,0,0,-1,-71.95,62.83)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
</text>
</g>
</g>
</svg> denotes the normalized <svg height="7.1624999" id="M30" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
</g>
</g>
</svg>-coordinate).</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures 