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AE301WingVibration18SupplementMomentOfInertia - 1.8...

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1.8. Supplement for Moment of Inertia Formula Strength of Materials Approach - use image processing on a wing section digital photo 1. The applied bending moment applied to a section of a wing is a function of the distance, x, from the wing tip The applied moment is larger as x increases due to larger moment arm, x, and due to additional aerodynamic loads as the wing area is added at x. 2. The moment bends the wing about a z-axis through the wing profile. The wing section at each x has a particular profile and material to resist the bending. The 2D profile can be modeled as a number of filaments that carry the load. Some filaments are in tension and some are in compression depending on the location of the bending axis, z.
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The angle of the bending axis through the wing section is determined by the applied moment’s direction. 3. The static balance requires that the total sum of all moments from each filament (assume differential filament size) balance with the applied moment about the z axis The bending axis location is such that there is a static balance between filaments in tension and filaments in compression with each contributing to a net moment that counteracts the applied moment. 4. The moment from one filament is the force (in the x direction) times the moment arm about the bending axis. With the bending axis being at y=0, the filaments below the axis (y>0) are in tension and the filaments above the axis (y<0) are in compression. Since a moment is the product of moment arm, y, and filament’s force, each filament will resist the applied moment (negative y has negative force so the product is positive).
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