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

<table>Crack identification on the ninth-order mode shape for Damage Scenario II. (a) Affine transformed mode shape <svg height="13" id="M100" style="vertical-align:-0.1881pt" version="1.1" viewbox="0 0 20.1 13" width="20.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13)">
<g transform="translate(72,-61.6)">
<text transform="matrix(1,0,0,-1,-71.95,61.84)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.45,67.01)">
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
</text>
</g>
</g>
</svg> and its original counterpart <svg height="11.975" id="M101" style="vertical-align:-0.1881pt" version="1.1" viewbox="0 0 22.1 11.975" width="22.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.975)">
<g transform="translate(72,-62.42)">
<text transform="matrix(1,0,0,-1,-71.95,62.66)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-59.45,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">∗</tspan>
</text>
</g>
</g>
</svg>; (b) KFD trajectory showing a singular peak attributed to the crack.</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures 