Modelling the Dynamics of Laminated Panels Using a Wave and Finite Element Method

The use of laminated panels is increasing because they are stiff, light and offer the engineer flexibility in design. Constructions include composite laminates with various stacking sequences, foam cores, viscoelastic layers etc. The generality and complexity of construction 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, usually using a commercial package. This typically involves a stack of solid elements meshed through the thickness, allowing the shear distribution, in particular in soft layers, to be correctly represented. The mass and stiffness matrices are found, periodicity conditions applied, and an eigenvalue problem solved to find the dispersion relations and hence the characteristics of wave propagation, attenuation and damping. The frequency dependence of viscoelastic material properties and pre-stress can be taken into account straightforwardly. A hybrid FE/WFE approach to determining transmission characteristics of joints is described. Numerical examples are presented, including anisotropic, plane and cylindrical foam-cored laminate 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 vibroacoustic behaviour of multi-layer panels and optimising their design.