In vibration-based high cycle fatigue testing, a base-excited plate is driven at a high frequency resonant mode until failure. In one vibration-based method involving a cantilevered square plate, a mode often referred to as the “two-stripe” mode is sometimes used because it exists at high frequencies and produces large uniaxial bending stresses along the free edge that are suitable for fatigue testing. The purpose of this work is to precisely investigate how the dimensions of a more generally rectangular plate influence performance when driven at the two-stripe mode. Included are the results of many thousands of modal analysis simulations. From these simulations, general trends with respect to resonant frequencies, frequency isolation, and stress fields in the plate are examined. Results of select geometries were then experimentally validated using a 1000 lb shaker. It is generally shown that, compared to square plates, rectangular plates with 1.37 length-to-width ratio exhibit more favorable stress distributions and frequency isolation. Recommendations are also given for how to quickly select preferable plate dimensions when planning a test based around the operating frequencies of the test setup.

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Digital Image Correlation (DIC) is a non-contacting, camera-based technique that calculates full-field displacements and strains by comparing digital images taken before and after an object is deformed. During a vibration-based fatigue test, DIC has an advantage over strain gages in that it is non-contacting and does not accumulate damage during the test. In this work, DIC was implemented to build strain-velocity calibration curves as an alternative to strain gages. First, a curve fit was applied to DIC displacements and strains along the free edge of the plate using an approximate solution for the mode shape of a cantilevered plate. In total, the curve fits were applied to three sets of DIC data: (i) the raw strains calculated with DIC; (ii) the in-plane U-displacements from which the raw DIC strains were computed; and (iii) the out-of-plane W-displacements observed in the direction of motion. Second, classical plate theory was used to calculate strains by taking derivatives of each of the applied curve fits. Third, the peak strains from each curve fit were used to build the strain-velocity calibration curves. Further, a Monte Carlo Method uncertainty analysis was performed to estimate the uncertainty of the curve fitted DIC and strain gage measurements. Of the three curve-fits, the DIC strains derived from the out-of-plane displacements provided the most precise measurements relative to a strain gage at all excitation levels used to build the calibration curves.

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