Wave based method for the vibrations of moderately thick plates including corner stress singularities

摘要

The simulation of plate vibrations in the low frequency range is commonly carried out with the Finite Element Method (FEM) or the Boundary Element Method (BEM), while the Statistical Energy Analysis (SEA) is used in the high frequency range. There is a gap between the low and high frequency range where neither the FEM or BEM are efficiently applicable nor the SEA leads to accurate results. A deterministic method called the Wave Based Method (WBM) is able to tackle the so-called mid frequency gap due to a higher computational efficiency. Among other applications, the WBM has been used to calculate the plate vibrations using the Kirchhoff plate theory, which is limited to thin plates. In this paper, the Mindlin plate theory is used, since it is applicable for moderately thick plates. Compared to the original WBM a different selection of wave functions is used, distinguishing between the traveling and the evanescent waves. This leads to more accurate results. Furthermore, special purpose functions to treat corner stress singularities are derived.