A Finite Element Plate Formulation for the Acoustical Investigation of Thin Air Layers

Double wall systems consisting of thin plates separated by an air gap are common light-weighted wall structures with high transmission loss. Generally, these plate-like structures are modeled in a finite element analysis with shell elements and volume elements for the air (fluid) layer. An alternative approach is presented in this paper, using shell elements for the air layer as well. First, the element stiffness matrix is obtained by removing the thickness dependence of the variational form of the Helmholtz equation by use of a power series. Second, the coupling between the acoustical shell element and the elastic structure is described. To verify the new shell element, a simple double wall system is considered. Comparing the predicted sound field with the results from a commercial FE software (with a single layer of volume elements) a very good agreement is observed. At the same time, employing the new elements with a third-order power series (4 DOFs per node), the calculation time is reduced