Investigating the fidelity of a pseudo-analytical solution of a rib-stiffened, layered plate structure subjected to high frequency acoustic loading

Abstract

There is a need for a fast and reliable tool to assist in the analysis, design, and optimization of submarine and UUV coatings due to high frequency incident acoustic pressure loading. An existing pseudo-analytical, frequency domain solution for wave propagation in coated, ribbed, three-dimensional elastic layered plates excited by acoustic plane waves provides fast solutions for high frequency excitations. Weidlinger Associates, Inc. (WAI) is developing an analysis software tool which integrates this solution methodology while adding some technical improvements to the formulation. The solution methodology, which is found to be numerically unstable under certain conditions, contains a fundamental ansatz regarding the set of excited wave forms expressed through a particular wave number expansion in the direction of periodicity. Evidence is presented to show that the numerical instability is due to the specific choice of the wave number basis used in the solution. In order to provide a remedy while retaining the positive aspects of the solution methodology, WAI is implementing a pre-processing step to determine the optimal wave number basis: the set of admissible propagating (and attenuating) waves are predetermined via an eigenvalue analysis and then substituted into the wave number basis in computing the pseudo-analytical solution.