764 T. Marinone et al. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Time (sec) Displacement (in) DOF 141 Time Response Comparison - Single Beam with Conical Spring Contact Analytical Test 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Time (sec) Displacement (in) DOF 81 Time Response Comparison - Single Beam with Conical Spring Contact Analytical Test Fig. 71.22 Comparison of experimental and analytical displacements for single beam with conical spring contact – DOF81 (top) and DOF 141 (bottom) for transient portion of time response (0–0.2 s) The results shown in Figs. 71.22 and 71.23 demonstrate that the analytical model accurately predicts the response when compared to the experimental data for the first 0.2 s of the response. The test results measured at ‘a’ space were expanded to ‘n’ space using the linear transformation matrix previously developed and were compared to the ‘n’ space analytical solution. Figure 71.24 shows the MAC and TRAC (the TRAC now consists of all 146 DOF). Note that the y-axis scale for the MAC and TRAC plots is 0.0–1.0. As seen in Fig. 71.24, the time response has been expanded and is accurate in comparison to the full field solution. In addition, the time response at DOFs that would be hard to traditionally measure (rotational DOF, DOF with minimal response, or DOF that are not easily accessible for instrumentation) can be obtained. Furthermore, this reduces the need for instrumentation as a subset of measurement points can be used to compute the full field solution instead of attempting to measure the response at every location. Figure 71.25 displays the correlation between the analytical model and experimental data for DOF 62, a rotational DOF located near the clamped end. Although this would be very difficult to measure traditionally, the expansion shows a high level of correlation. Table 71.10 lists the solution times for the full space and reduced space analytical models as well as the average MAC and TRAC comparing the experimental results to the analytical models. As in the previous case, the reduced order model can accurately predict the system response with significant computational savings. Also note that for the experimental case the expanded results improve the MAC and TRAC by smoothing the experimental error. Again, the additional time required to expand the time solution is negligible compared to the full field solution.
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