Finite Element Formulation for Vibration Analysis of Multi-layer Laminated Beam

A new approach is developed for finite element modeling of muiti-layer laminated beams. Within the beam element, the laminate is decomposed as muttiple basic layers, such as base beam layers of metal like, soft-core layers of adhesives, and soft coating layers of polymers, and mass and stiffness matrices of these basic layers are assembled together to generate those matrices for the beam element. By associating displacements of the soft layers to those of base beam layers, the method overcomes the aspect ratio limitation which is always a problem for the conventional finite element method because soft layer is usually much thinner than base beam layers in the laminates. In the conventional finite element method, modal strain energy method is usually used for structural damping analysis, which becomes quite inaccurate when the damping of the structure becomes high. This method allows the direct consideration of complex modulus of any layer so that it offers much more accurate damping analysis for such structures.