A Finite Element Method for Modelling Waves in Laminated Structures

The generality and complexity of laminated structures raises issues regarding modelling their dynamics and optimising their design. In this paper, a wave and finite element (WFE) method for modelling the dynamic behaviour of plane and axisymmetric laminated structures is described. A small segment of the structure is modelled using conventional finite element (FE) methods, typically using a commercial package. The mass and stiffness matrices are found, periodicity conditions are applied, and an eigenvalue problem is formulated and solved to find the dispersion relations. The frequency dependence of viscoelastic material properties and pre-stress can be taken into account straightforwardly. A hybrid FE/WFE approach for determining transmission characteristics of joints is described. Numerical examples are presented, including anisotropic, plane and cylindrical foam-cored laminated sandwich constructions with pre-stress. The method is simple in application, provides accurate results at low computational cost and is a valuable tool for evaluating the vibro-acoustic behaviour of multi-layer panels and optimising their design.