Convergence behavior and steady state response of a rib-stiffened, layered plate structure subjected to high frequency acoustic loading

Abstract

An existing 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. The solution methodology, which is found to be numerically unstable under certain conditions, contains an Ansatz for 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. In order to provide a remedy while retaining the positive aspects of the solution methodology, we determine the set of admissible propagating (and attenuating) waves via an eigenvalue analysis. Several approaches exist to determine the admissible waves of structures with periodicity. The Wave Guide Finite Element (WFE) method leads to a two parameter, nonlinear eigenvalue problem, which is difficult to solve. The Scale Independent Element (SIE) formulation results in a two-parameter quadratic eigenvalue problem and overcomes the numerical issues of the WFE method. This study examines available methods in determining the admissible waves and compares them with those established using the dispersion relation. The computed admissible waves are then compared with the aforementioned Ansatz.