220 H. Brand et al. 22.3.1.1 Excitation The strategy for exciting the material was motivated by a need to excite high frequency modes while remaining within the linear regime of the material response. An additional challenge met by the excitation strategy was preserving the integrity of the (low amplitude) deflection signal as a contributor to the temporal phase. Because of the material’s viscous properties, the modal hammer, used in past materials studies with this method, was not a viable option for exciting high frequency modes. A shaker provided a suitable alternative because the input loading could be controlled at a desired frequency. The input signal could then be removed and the decaying response of the specimen observed. Still, an additional obstacle remained, the response was on a micrometer scale and any slight system vibrations of a shaker apparatus could provide input signals comparable to the materials response. Therefore, a suspended shaker was use constructed with a linear stage in order to minimize other possible vibration sources. 22.3.1.2 Imaging Image resolution is traditionally a trade-off between frame rate, in most imaging systems. The challenge with using an imager-based technique to observe the response of stiff polymers is that it requires both high resolution and high sampling rate, and therefore limits our ability to compromise either one for the other. For this reason, a high-speed camera with a high-magnification lens was used. However, this posed an additional challenge, in that the boundary of specimen was relatively smaller than the surface of the specimen in the field of view of the imager. The imager-based technique observes local changes in phase, in which phase changes at the boundary or edge of the specimen encodes the motion response. The challenge in this application of the technique was that the moving surface of the object was more prevalent then the edge of the specimen in the imager field of view. The temporal phase observed on the surface of the specimen as it is moving does not necessarily relate to the specimen motion response. This means that the surface could potentially contribute more unrelated motion effects to the temporal phase which would exacerbate modal extraction as a principal component. The specimen was marked in order to increase the significance of the motion response on the temporal phase from the point of view of the imager. 22.3.1.3 Illumination The relatively close proximity of the lens to the specimen required for high frequency response observation provide a challenge to illuminating the specimen. Other challenges arose from the relative high frame rate of the imager. This required the light source to deliver a significant amount of energy back to the image sensor. This also meant that any oscillations in illumination due to oscillations in the illumination power circuit would be observed over the time series image data and contribute to changes in phase comparable to the contributions of the motion of the specimen. It was found that if the oscillations remained consistent, the contributions to temporal phase were statistically independent to that of the specimen motion response. 22.4 Analysis Additional challenges within this study arose from the fact that specimen displacements are quite small, resulting in difficulty detecting motion and modal properties with video. After testing the specimen at a 1.47 kHz frequency, it was found that imager-based modal analysis techniques are able to detect vibrational responses in this range. Four modes were extracted using the modal analysis algorithm. As shown by Fig. 22.3, the program extracted the resonant frequency of the specimen at 1.47 kHz indicated by the strong single peak from the power spectral density in component 1. For this same component, the estimated mode corresponding to this excitation clearly depicts the damping of the specimen as the input to the shaker was turned off. Using this modal information, the damping ratio was calculated with the Hilbert transform method, which will be discussed later.
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