Shape Optimization of Rectangular Plates for Vibration-Based Fatigue Testing

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 with 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.