Modal approach for dynamical analysis of sandwich plates

The dynamic equation of a sandwich plate is presented under the hypothesis of linear logitudinal displacement fields in each layer and an hysteretic structural damping of the viscoelastic core. A model approach is adopted to investigate sandwich plate dynamical behaviour. First, the elastic eigemodes are used in the characterisation of the modal damping. Then, the dynamical analysis is established using the model dynamic recombination method and the result of modal damping characterisation. The numerical results obtained show that the eigenmodes are not orthogonal with respect to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coeffcients vary according to the ratio of the core thickness to the total thickness of the sandwich plate following a second order polynomial function. The model approach with hysteretic modal damping characterisation is proposed in establishing dynamical respones. The results show the dynamical respones due to the use a hysteretic diagonal modal damping matrix are good agreement with those abtained when a full modal damping matrix is considered.