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I am working on a project and we need to calculate the torsional stiffness of a wing in order to analyze flutter and divergence. However, the dimensions of the cross section vary along the semi-span, so the torsional stiffness changes. How can I calculate this in this situation?

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Basically, you can take two different paths as a starting point.

  1. From the FEM model of the wing, from the axis (I assume it is the y-axis), where the torsion movement occurs, you can find the value of Iyy. Then, by looking at the mode shapes and finding first torsional mode shape frequency, you can calculate kt from the formula wn=sqrt(kt/Iyy) from the frequency you see for the 1.torsion mode. Of course, since other modes also have a contribution, even if it is not a completely correct answer, it may work at the beginning.

  2. Twist can be read by applying unit moment from tip of the wing. Then kt can be calculated from the formula: unit moment=kt * theta. It's not the exact equivalent stiffness of course, but it's a simple starting point.

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