34 Investigation of Crossing and Veering Phenomena in an Isogeometric Analysis Framework 363 In the fourth section, a modal analysis of the test-rig using IGA, with comparison to the results that were previously obtained using a beam-based FE code and commercial FE software. Then a parametric modal analysis is performed to obtain the frequency loci plot, where crossing and veering phenomena reveal. In the last section, the IGA model is updated using the experimental data obtained from the test-rig, to fit the curves with the experiments. 34.2 The Experimental Test-Rig The test-rig considered for investigating crossing and veering is shown in Fig. 34.1. It represents a wing-like structure, where its components can be considered as three thin beams with different orientation and three added masses. The first and the third beam are fixed in space, and they have orthogonal orientation with respect to each other, while the second beam can have a chosen continuous orientation thanks to the rotating device between the first and the second beam. The configuration parameter, in this case, is the angular position of the second beam, where the “0 deg” configuration is considered as the one where the second and third beams are aligned. This parameter defines a coupling condition among the different beams, with the aim of having veering among bending modes. Due to its envelope on a common axis, the ideal theoretical model of beams and lumped added masses have no coupling between bending and torsional eigenspaces, hence the expectation is to have crossing condition among them. This structure can be easily modelled in Finite Elements with beams, used for the actual beams and for the cylindrical parts as well, considering a bulk density in order not to change the mass of those parts. To compute the parametric analysis with the beam structure, an FE code developed by the authors named LUmped Parametric Open Source (LUPOS), is used thanks to its parametric concept. In Fig. 34.2 the model in LUPOS is shown. On this test-rig, Experimental Modal Analysis was performed in order to identify the natural frequencies for 19 configurations, from 0 to 90ı with5ı step, and they will be considered as a reference to further update the material properties modelled in all the different solutions. The three beams are produced in Aluminium alloy, while the beam used as a clamp, and the rotating device are made by Steel. The remaining components which forms the added masses are made by Aluminium. Figure 34.3 shows detailed view of what the three added masses are and what are their aims. Fig. 34.1 The experimental test-rig: (a) actual model with test hardware; (b) full CAD model with configuration parameter
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