Several Related Models for Multilayer Sandwich Plates

Mathematical models for multilayer sandwich plates consisting of alternating stiff and compliant layers are derived. Two main types of models are described. First an initial model (analogous to the three-layer Rao-Nakra model) is derived under Kirchhoff plate assumptions for the stiff layers and Mindlin shear-deformable displacement assumptions for the compliant layers. The second type of model can be obtained from the original model by dropping the in-plane and rotational inertia. The resulting model is a generalization of the well-known model of Mead and Markus. Well-posedness and continuous parameter dependence results are described. Some variations of the initial model corresponding to thin compliant layers are described and shown to be regular perturbations of the initial model.