Fluid-loaded elastic slab excited by line and point loads

Abstract

The plate equations are not sufficient to predict the response for high wave-number excitations. In order to determine the difference between plate and elastic slab results, and the range of validity of the plate equations, the following problems were solved: an infinite slab excited by a line load and a point load. The space above the slab contains an acoustic medium and below the slab there is a vacuum. It was proven that the point-loading case was formally identical to the line-loading case. The only difference was in the use of Hankel transforms instead of Fourier transforms. Full elastic slab equations were solved for this acoustic medium/elastic slab coupling problem with analytical and numerical techniques. Far-field-radiated pressure and surface interface displacement results indicated that full elastic slab equations predict lower radiated pressure and higher interface trapped wave amplitude compared to thin plate results for high-frequency excitations. The upper nondimensional frequency limit for the validity of the thin plate equations was determined to be ωh/cl≊0.17. By introducing structural damping, one is able to determine the interface displacements in the vicinity of the excitation. [Work supported by Mechanics Division, ONR.]