40 R. Berke et al. Fig. 4.6 A schematic diagram summarizing the results with the Tchebichef kernels shown along the top row with the corresponding coefficients from both room (darker color) and high (bright color) temperature tests shown in the bar charts from both the experiment (red) and simulation (blue) The column in which the larger bars appear for a particular mode provide an indication of the dominant components of the deformation. Note that negative values simply indicate that the out-of-plane deformation was in the opposite orientation to the Tchebichef kernels. So, for instance examining mode 3 again, it can be seen that the simulation reproduces the decrease in the sixth coefficient with increasing temperature observed in the experiment but predicts a significant value for the second coefficient which is not present in the experiment. The dominant role of the second coefficient in mode 2 can also be observed. When the first coefficient is ignored, which represents the ‘piston term’ or average magnitude, the figure shows a trend in which the higher magnitude bars are found along the diagonal from top left to bottom right, i.e., the higher order, more complex kernels are used to represent the higher order modes, which is entirely expected. The higher order modes also tend to require more kernels to represent them, which is again expected due to their more complex shape. Overall, the figure supports the conclusion that the simulation is a good representation of the experiment and permits the more complex modal shapes to be visualized in terms of the simpler kernel shapes.
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