78 R.K. Giles and T.J. Kennedy 0 0.5 1 1.5 2 2.5 3 −0.8 −0.6 −0.4 −0.2 0 0.2 a b Time (s) Time (s) Command Displacement (cm) 00.511.522.53 −0.1 −0.05 0 0.05 0.1 Acceleration (g) Fig. 10.3 (a) Command displacement (cm) for the Quanser Shake Table II. (b) Corresponding command accelerations (g) Noncontact, three-dimensional measurement of the column motion was performed using a three-camera Xcitex ProCapture system. The cameras were arranged to capture the three-dimensional movement of the column. Each camera operated at a sampling speed of 125 frames per second. Recordings were individually calibrated within Xcitex ProAnalyst software to remove lens distortion and merged in pairs to allow for the two-dimensional images to be interpreted as threedimensional measurements. The ProAnalyst software is able to track each point individually over the entire length of the record. Four points on each column and a fixed point on the shake table were tracked for each trial. Figure 10.2 shows the four column points and the table point tracked and overlaid on the image of the column at rest. An accelerometer on the shake table was synchronized to the image data to confirm the desired command accelerations. Positional data was exported from the ProAnalyst software and displacement measurements of the column relative to the shake table surface were calculated. The data was also filtered using an eight pole elliptical filter with a 50 Hz cutoff frequency. The filter served to reduce the small amount of jitter inherently present due to the motion tracking. Anti-alias filtering is not possible with optical systems and therefore oversampling above the expected behavior of the rocking is required to produce accurate results. 10.5 Results and Discussion Thirty-two experiments were performed and processed for this analysis. As the cameras are located in fixed positions external to the shake table system, the motion of the table was removed from the motion of the column to generate displacement values relative to the shake table. Figures 10.4, 10.5, 10.6 and 10.7 show typical results for the tracking of the top tracking point (i.e. Point 1 in Fig. 10.2) in all three directions—xis the axis of the table motion, yis the gravitational axis, andz is out of plane. These figures have been plotted in the same scale to emphasize the differences between the records. The tracked motion of the table is shown in each plot for reference. The rocking motion in the x-axis is greater than the other directions as expected from the desired experimental focus on rocking in one direction. To investigate the differences apparent in the experiments, the free rocking of each record was examined further. The rocking records were processed to determine when the forced motion of the table ended and free rocking began. The value for the angular displacement and angular velocity were determined for the initiation of the free rocking. These values served as initial conditions for comparison to the analytical free rocking model. The values for the angular displacement and angular velocity at the end of the table motion showed great variety. Each experiment was excited using the same command displacements as confirmed by the tracking of the table during each trial. Nevertheless, the excitation had varied effects on the forced motion of the column in each trial. The differences are due to slight, uncontrollable, experimental conditions. However, the free rocking of the columns shows similar behavior once it begins. After determining the start of free rocking, the peaks of the motion were located. The initial six peaks were used to calculate the damping ratio using the logarithmic decrement method. A histogram of the damping ratios is presented in Fig. 10.8. Figure 10.9 plots the calculated damping ratio against a lognormal distribution. Both Figs. 10.8 and 10.9 indicate that four of the experiments do not fall within the same distribution of damping coefficients. These four do however appear similar to one another and Fig. 10.6
RkJQdWJsaXNoZXIy MTMzNzEzMQ==