Reconstruction of the area-moment-of-inertia of a rotor blade using a shifting point-load and the end-slope

Abstract

The main focus of this study was to develop an inverse model that could be used to determine the changes in sectional areamoment-of-inertia of a helicopter rotor blade from the knowledge of a shifting point-load and the end-slope data. In this investigation, the cross-sectional area-moment-of-inertias of a rotor blade model with n segments are reconstructed using a shifting point-load and the corresponding end-slope data. The end-slope data used in this inverse problem were numerically generated using the finite element method. The end-slope data and the loading were then used in the inverse problem to reconstruct the cross-sectional area-momentof-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of segments, and a shifting point-load was applied to the mid-point of each segment. The beam equation was then integrated to create a set of linear equations in terms of loading and end-slopes. Next, the resulting set of equations was solved simultaneously to recover the area-moment-of-inertia for each segment. A series of numerical experiments were performed to check the validity and sensitivity of the inverse model. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a helicopter rotor blade can be reconstructed with good accuracy from the knowledge of the shifting point-load and end-slopes.