Efficient boundary element calculations using thin-plate acoustic elements

Abstract

Thin-plate elements are commonly used to represent structural components whose thicknesses are much smaller than the structural wavelength. This simplifies the analysis, because otherwise several elements are required to represent correctly the strain distribution through the thickness, leading to much larger models. Thin-plate elements also have advantages when they are used in acoustic boundary element calculations. By using dipole sources at the midline of the elements to generate the basis functions for the acoustic analysis, the boundary condition can be enforced such that the opposite sides of the plate are forced to move together. The surface velocity boundary condition then only has to be enforced over one side of the elements (even though both sides are in contact with the acoustic medium). Mechanical radiation impedance calculations can also be simplified because the dipole source basis functions create the same pressure field on opposite sides of the plate elements and thus impart no force to the structure. The only exception is for ‘‘self-element’’ terms, where the dipole sources create equal, but opposite, surface pressures. Several example problems are used to validate the calculations, including a vibrating strip, a transversely oscillating disk, and a cantilever plate.