Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer

The natural frequencies and loss factors of a rectangular three-layered plate with a viscoelastic core layer and laminated face layers are considered. The equations of free vibration of the plate together with the corresponding boundary conditions are derived for a non-symmetric plate with general anisotropy of the face layers. A first order shear deformation theory is used to describe the deformation of the faces. Simplified forms of these equations, for a symmetric plate or for specially orthotropic face layers, are then discussed. Equations are also given for a model with no shear deformation in the face layers and all but transverse inertia terms neglected (simplified model). Results of numerical examples are presented for simply supported plates with specially orthotropic face layers. Complex eigenvalues are found numerically, and from these, both frequencies and loss factors are extracted. Comparison is made between the shear deformation and the simplified models, in the case of high modulus composite face layers.