5/30/2023 0 Comments Half wing vector![]() The work by Bogert, Haugse, and Gehrki also included a criterion for selecting the most suitable mode shapes for the application of the method. The knowledge of the modal coordinates allows the reconstruction of the displacement field. The modal coordinates are computed by fitting the reconstructed strain field on to the measured one at discrete locations. The displacement and strain fields are expressed in terms of known shape functions (the mode shapes and the spatial derivatives of the mode shapes, respectively) and unknown weights (the modal coordinates). The Modal Method, developed by Foss and Haugse and Pisoni, Santolini, Hauf, and Dubowsky in 1995, can reconstruct the displacement field of any structure using its mode shapes and some strain measurements at discrete locations. After reconstructing the bending and twist deformation of the wing through the Ko’s Displacement Theory, the results were compared with the experimental ones obtained with a photogrammetric approach, and a very good degree of accuracy was obtained. performed a ground test of a full-scale wing using a fiber optic strain-sensing system. Two measurement lines were set along the wingspan to rebuild the deflections and cross-sectional twist, then the data were compared with those computed from a finite element model. The Ko’s Displacement Theory was applied to the deformed shape analysis of the wing of the Ikhana UAV. Using more than one sensing line along the span of a wing structure, it is also possible to evaluate the cross-sectional twist angle due to torsion. Double integration of the curvature provides the deflection shape at the same discrete locations. Through axial strain measurements at discrete positions along a line, it is possible to evaluate the curvature. The Displacement Theory of Ko, Tran, and Richards is based on the classical Bernoulli–Euler beam theory. Further numerical analyses show that the Modal Method is influenced by the set of mode shapes included in the analysis and that excellent reconstructed deflections can be obtained with a reduced number of sensors, thus assessing the approach as an efficient shape-sensing tool for aircraft structures real applications. The Modal Method is shown to be more accurate than Ko’s Displacement Theory, especially for the evaluation of the deflection field. For a given common set of surface strain measurement points, Ko’s Displacement Theory and the Modal Method are compared in terms of accuracy of the reconstructed half-wing deflection and twist angle. Then, the multirotor UAV is presented and a finite element model of its half-wing is used to simulate the static response to straight-and-level flight conditions. The approaches are summarized in order to set the framework for the numerical comparative investigation. ![]() An object of the shape-sensing analysis is the half-wing of a multirotor UAV. The aim of this paper is to compare two approaches to shape sensing that have been shown to be more efficient, especially for aircraft structures applications, in terms of required input strain measurements: the Ko’s Displacement Theory and the Modal Method. Shape sensing is the reconstruction of the displacement field of a structure from some discrete surface strain measurements and is a key technology for structural health monitoring.
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