222 H. Brand et al. Fig. 22.4 Flow vectors diagram Fig. 22.5 Region for damping ratio calculation using Hilbert transform From component 2 in Fig. 22.3, strong frequencies components were detected at 120 Hz. These signals are a result of the periodic variations of the light intensity from the LED point light source. Because the light energy is so intense compared to the slight motion of the specimen at 1.47 kHz, this frequency is output by the algorithm as a possible modal property. Due to this known frequency, this signal can be eliminated as a property of the specimen itself, rather we can assert that it is a property of the environment. Components 3 and 4 found in Fig. 22.3 are identified as computational modes. These are outputs from the algorithm that are not attributed to modal properties of the specimen and may relate to noise within the video data or other possible unknown phenomena. Figure 22.4 shows the direction of the motion associated with the pixels that detected movement. This allows us to analyze each component, indicating whether the component contains modal information or simply noise. Component 1 is identified as a viable mode, as Fig. 22.4 shows the red flow vector arrows all pointing in coherent directions. When the algorithm outputs a computational mode, these components will yield flow vectors which point in all different directions incoherently. Following the compilation of the estimated modes and power spectral densities, a Hilbert transform is used to calculate the damping ratios of the specimen. This method utilizes an envelope to determine the decay of the signal. Figure 22.5 shows an example of how the damping ratio is calculated. The original component 1 data is cut down to the regions where the system damps out. This is where the input to the shaker is shut off, allowing the specimen to dissipate its oscillating motion. The cropped region of the data is then input into MATLAB, where a Hilbert transform extracted the damping ratio. The damping ratio relating to this figure is 0.0255% or 2.55% damping. After analyzing 11 tests, the average damping ratio output using this method was 0.023% or 2.3% damping. These damping ratios were compared to damping ratios extracted from accelerometer data with the same method of excitation. The accelerometer data yielded an average damping ratio of 0.026% or 2.6%. This validates the imager-based method for extracting damping ratios.
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