4 Stereo-DIC Measurements of Thermal Gradient Effects on the Vibratory Response of Metals 41 4.4 Conclusions The work described here has combined, for the first time, high frequency vibratory loading (up to about 1300 Hz) at elevated temperature (up to 600 ıC) with the full-field optical diagnostics of stereo-DIC. This combination has provided high quality experimental data suitable for the validation of numerical results. Using this combined loading experimental set-up with induction heating and shaker-induced vibration, the thermo-acoustic behavior of a rectangular plate of Hastelloy-X was explored. By investigating the first 9 resonant modes at both room temperature and high temperature, and measuring mode shapes for each of the resonant frequencies using stereo-DIC, the influence of temperature on the thermomechanical vibratory response of the plate was assessed. A decrease in resonant frequencies was seen with increasing temperature, although the first 9 mode shapes themselves were similar. Companion finite element numerical simulations that accounted for the temperature dependence of elastic modulus also produced very similar mode shapes, although the influence of temperature on modal frequencies was not as significant as observed experimentally. As a model process for validating simulation results based on this type of experimental data collection an image decomposition technique based on 2D Tchebichef polynomials [13] was used. The image decomposition, which allows comparison between numerics and experiments using the fitted Tchebichef coefficients rather than the entire images, confirmed quantitatively the qualitative observation that as temperature increased the resonant mode shapes remained very similar. Overall, the results of this combined thermal-mechanical study point to the conclusion that the simulation is a good representation of the experiment both at room temperature and at high temperature (in fact a little better at high temperature as the signal to noise ratio in that experiments is larger). Acknowledgements This effort was sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF under grant numbers FA8655-11-3083 and FA9550-12-1-0386. The U.S. Government is authorized to reproduce and distribute reprints of Governmental purpose notwithstanding any copyright notation thereon. Major Matt Synder (EOARD) and Dr. David Stargel (AFOSR) respectively are the program officers for these grants. EAP is the recipient of a Royal Society Wolfson Research Merit Award. The collaboration that was central to this study was supported by a Royal Academy of Engineering Distinguished Visiting Fellowship awarded to JL. References 1. 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