Similar to the MAC, the TRAC is a tool used to determine the degree of correlation between two time traces. For the cases presented here, the TRAC is the correlation for one DOF over all time for the expanded time data [ERTOn] compared to the actual measured data [REFn]. The TRAC is written as ^ ` ^ ` > @ ^ ` ^ ` > @^ ` ^ ` > @ (t) REF (t) REF (t) ERTO (t) ERTO (t) REF (t) ERTO TRAC_RTO n T n n T n 2 n T n (7) The values produced by both the MAC and TRAC will range from 0 to 1; values approaching 1 indicate good correlation. A schematic is shown in Figure 3 showing the MAC and the TRAC correlations. Typically, the TRAC is comparison of the displacement - time response solutions (predicted and reference solutions) while the MAC is comparison between the deformed shape of the structure at each time instant as shown in Figure 3. Figure 3: Schematic showing MAC and TRAC MODEL DESCRIPTION For this study, a simple structure (named as Base-Upright or BU), which has well correlated analytical and experimental modes from previous studies, was used. The structure was assembled from two aluminum plates. The structure was designed to be time-invariant, with well-spaced, directional modes that could be identified easily. Figure 4 shows the BU with the primary dimensions labeled. The base plate is 24 x 24 inches and rigidly bolted to the tied to the ground at the four corners using concrete anchors, while the upright is 24 x 30 inches. Both plates are 3/4” thick aluminum. The base plate and the upright are held together by 0.25 inch thick, 1.5 inch wide, 24 inch long steel L-brackets using 0.5 inch bolts. 205
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