The Natural Response of Uniform and Nonuniform Plates in Air and Partially Submerged in a Quiescent Water Body

Abstract

The free vibration of three aluminum plates (.4 m wide, 1.08 m long) oriented horizontally is studied experimentally under two fluid conditions, one with the plate surrounded by air, called the Air case, and the other with the bottom plate surface in contact with a large undisturbed pool of water, called the Half-Wet case. Measurements of the out-of-plane deflection of the upper surfaces of the plates are made using cinematic Digital Image Correlation (DIC) over the center portion of the surface and optical tracking of the center point. Three plate geometries and boundary conditions are studied: A uniform plate with 6.35 mm thickness pinned at the two opposite narrow ends (designated UP), a uniform plate with 4.83 mm thickness simply supported at one narrow end and clamped at the opposite end (UC), and a stepped plate with thickness varying from 12.7 mm to 6.35 mm along its 1.08 m length pinned at two opposite narrow ends (SP). The plate's free response is induced using an impact hammer at three locations along the center-line of the plate. Video frames of the motion of the upper surface of the plate are collected from stereoscopic cameras and processed using DaVis-Strainmaster and MATLAB to extract full-field displacements as a function of time. Two-degree-of-freedom displacements of the plate center are also collected by tracking a target attached to the center of the plate's lower surface. Time and frequency response plots are presented for comparison between the Half-Wet and Air cases and analysis of their dynamics. It is found that the added mass of the water results in lower measured natural frequencies and modified mode shapes. In the Air case, these results are compared to mode shapes/frequencies produced in Creo Simulate and found to agree. Further experiments are discussed.