Modelling wave propagation in two-dimensional structures using finite element analysis

A method is described by which the dispersion relations for a two-dimensional structural component can be predicted from a finite element (FE) model. The structure is homogeneous in two dimensions but the properties might vary through the thickness. This wave/finite element (WFE) method involves post-processing the mass and stiffness matrices, found using conventional FE methods, of a segment of the structure. This is typically a 4-noded, rectangular segment, although other elements can be used. Periodicity conditions are applied to relate the nodal degrees of freedom and forces. The wavenumbers-real, imaginary or complex-and the frequencies then follow from various resulting eigenproblems. The form of the eigenproblem depends on the nature of the solution sought and may be a linear, quadratic, polynomial or transcendental eigenproblem. Numerical issues are discussed. Examples of a thin plate, an asymmetric laminated plate and a laminated foam-cored sandwich panel are presented. For the last two examples, developing an analytical model is a formidable task at best. The method is seen to give accurate predictions at very little computational cost. Furthermore, since the element matrices are typically found using a commercial FE package, the meshing capabilities and the wealth of existing element libraries can be exploited. (C) 2008 Elsevier Ltd. All rights reserved.