38 B. Witt et al. Fig. 4.10 Examples of imperfect shape expansions 4.4 LDV Direct Methods As mentioned in the previous section, several methods for generating full-field modal strain shapes were utilized. All methods can be grouped into two categories: direct or transformation methods. This section focuses on the direct methods, which can be generated either on an ODS or modal quantity basis. Figure 4.11 shows the two direct methods; the “Direct ODS Method” is the workflow on the left and the “Direct Modal Method” is the workflow on the right. In some cases, it is expected that ODS extracted from sine dwell data near natural resonance frequencies ( " Oa,f) at a-space measurement locations would be less noisy than traditionally fit mode shapes from LDV data (Ea). For example, if a sine-dwell test had a better signal-to-noise ratio than a random vibration test from which modes would be extracted, the Direct ODS Method could be used. The measured " Oa should then be smoothed with a Gaussian filter. Note that a Gaussian filter of sizeσless than approximately one third of the scan point spacing effectively provides no smoothing and leaves shapes in an unfiltered or raw state. Once any desired filtering is applied, the shapes can be run through the strain post-processor to arrive at an ODS-quantity estimation of the strain shapes in a-space, τa. For structures where the ODS well approximate the mode shapes (i.e. resonances well separated), τa will, to the same degree, approximate the τa modal strain shapes we are seeking, although they will be scaled differently. This method most closely aligns with the Polytec Strain Post-Processor that is integrated into the LDV software, which operates on Band Data within a scan file. For applications where a modal test can be conducted and relatively clean mode shapes and natural frequencies (Ea, ω) extracted, the Direct Modal Method can be utilized. The same process of smoothing shapes with a Gaussian spatial filter and post-processing the results for strain are used. In this case, the resultingτa strain shapes are actual modal quantities. Both Direct methods have the benefits of not requiring a FEM of the test object nor needing an expansion process for sufficiently dense measurement grids. However, both are subject to any noise in the measurements and are also highly dependent on the spatial filter parameters used. To demonstrate these effects, Gaussian filters with σ = 0.5–3.5 mm were evaluated. The scan grid on the c-channel faces of interest had a horizontal and vertical spacing of approximately 1.6×2.6 mm, respectively. This means that filter sizes of approximately 0.5 mm or less are providing almost no smoothing. Surface strains (τxx, τyy, τxy) ina-space were calculated for the two c-channel faces (X-surface and Z-surface, see Fig. 4.12), although only τyy results on the X-face are shown here for brevity. Figures 4.13 and 4.14 show the τyy results of the Direct ODS Method and Direct Modal Methods, respectively, for multiple filter sizes. Black indicates noise values that are out of range. Both figures show that filter sizes greater than the nominal spacing of measurement points is necessary to remove spurious noise in the shapes, which is approximately 2.0 mm here. However, it is noted that the Direct ODS Method results for the 1.5 mm filter are noticeably noisier than their Modal counterparts, indicating the ODS for this test structure were not cleaner than the mode shapes, as had been postulated. The test article exhibited nonlinear behavior which is believed to be the reason for this observation. Filter effects near the edges are clearly observed in several shapes, for example ODS 5 and Mode 4; as filter weight increases, the maximum strains at the edges are artificially reduced due to the distribution of the weighting coefficients of the filter. There is a tradeoff between noise reduction and maximum strain accuracy, particularly near edges.
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