Free Vibration Analysis of S-FGM-Coated and S-FGM-Undercoated Plates with Classical Boundary Conditions

This work presents free vibration analysis of laminated rectangular plates with classical boundary conditions based on the classical plate theory (CPT). The first involves an S-FGM plate with different boundary conditions. Then involves a two-layer plate in which an S-FGM layer is coated on a homogeneous substrate with classical boundary conditions, simply called an S-FGM-coated plate; the other involves a three-layer plate in which an S-FGM employed for inter-medium layer and different homogeneous materials are in top and bottom layers with classical boundary conditions; this is called an S-FGM-undercoated plate. The Young’s modulus of FGM plates is assumed to vary in the thickness direction and the poisson's ratio remain constant throughout the FGM plate. The material gradations in FGM portion of laminate structures follow sigmoid functions, therefore these plates are called S-FGM. For multi-layer structures, the calculations of the quantities  defined herein become complex, therefore, a method is used to easily and efficiently calculating them in this investigation. The results are first compared with the ABAQUS software, showing an excellent agreement. Then frequency parameters of three plates for different boundary conditions and aspect ratios are graphically presented for a wide range of gradient index.