204 E. Copertaro et al. 50 0 laser at wide angle laser at narrow angle 0 0 0.9 1 0.95 5 max deflection [mm] max deflection [mm] scanning area [mm] relative leakage [-] 10 15 [mm] [mm] 0 0 10 15 5 5 10 15 50 70 31 deg 11 deg 80 100 Fig. 19.6 Wide- and narrow-angle laser geometry (top plot). Trends of relative leakage and scanning area (bottom plots) Fig. 19.6 shows the relative variation of amplitude of m2 as the oscillation becomes larger, with a maximum deflection at the free-end point of 15 mm that corresponds to 15% of the total length of the beam. The trend of the correspondent scanning area is shown as well. As it can be observed, the amplitude of m2 can be assessed within an error of 10%. Such uncertainty is relevant in many applications. Orientating the laser at a narrower angle respect to the y-direction could be effective in reducing it, with the further benefit of a greater sensitivity to that velocity component. However, it also produces a reduction of the scanning area, therefore a lower sensitivity to the rotational degree of freedom. Green curves in Fig. 19.6 refer to a second simulation with the laser positioned at a narrower angle. Using such measurement geometry results in a lower error, this at the cost of a smaller induced scanning area. The previous results indicate that it is possible to optimize the angle of the laser in order to achieve the best compromise between sensitivity to rotation and accuracy in the location of the measurement point. However, it should be noted that in a real-case scenario the rotational degree of freedom can only be assessed qualitatively, since the value of l is unknown. These considerations limit the applicability of such technique in cases where the interest is not in the quantitative values, but in their trends. In upcoming work the method will be exploited in the setup for bending-fatigue tests depicted in Fig. 19.7, and it will concern the assessment of the different sensitivity of the sidebands and the central peak to the incipient damage of the specimen under test, as well as experimental validation. 19.5 Conclusions A 1D numerical model of a cantilever beam was developed for simulating the scanning effect due to the large oscillation of the first bending mode, including a cinematic model for the axial displacement. The movement of the laser spot was found to be an over-imposition of local, harmonic linear scannings, with the one due to the y-displacement of the first mode being prevalent respect to the others. The consequent velocity signal showed left and right sidebands, which were used for calculating the rotational degree of freedom of the second mode according to CSLDV theory. The results were compared to those obtained using multi-point information and it was found that the left sideband can be effectively exploited for the purpose, whilst the right is affected by the super-imposition of more contributions. The discrepancy between the real
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