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.