The homogenization of the energy functional of a sandwich plate, its minimization and its discretization by finite element methods and modeling the viscoelastic core behavior by an hysteretic structural damping lead to the homogenized dynamic equation of a sandwich plate. The vibratory analysis permits the determination of the elastic eigenmodes and the characterization of the modal damping which will serve to the establishment of dynamical responses if we used the modal dynamic recombination method. The numerical results obtained show that the eigenmodes are not orthogonal to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coefficients vary according to the ratio of the core thickness and the total thickness of sandwich plate and follow a second-order polynomial function of this ratio.

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