A new 2D single series model of transverse vibration of a multi-layered sandwich beam with perfectly clamped edges

A new two-dimmensional, single series local model of the transverse vibration of a multi-layer, one-span sandwich beam composed of isotropic layers with ideally (perfectly) clamped ends is proposed in the paper. The model is derived within the local theory of linear elastodynamics and it is composed of two two-dimmensional fields and of two approximations of three-dimmensional fields satisfying exactly the equations of motion as well as the Saint-Venant compatibility equations of the theory. All through-the-thickness boundary conditions of the local theory of elastodynamics as well as all local compatibility equations (for the displacements and stresses) between adjoining layers are fulfiled in the model. Both the cross-sectional warping and the transverse compliance(s) in each layer of the beam are taken into account, thus the model is applicable to the classical three-layer sandwich beam and to a multi-layer sandwich or laminated narrow structure.