Analytical Framework for Frequency Response of Porous Tapered Plate Made of Functionally Graded Materials

During the study, functionally graded plate (FGP) with defects such as porosities is considered for natural frequency under conventional boundary conditions (BCs). These defects (porosities), developed during manufacturing process, may change the plate behavior for vibrational response. Different types of porosity distribution rate are considered with power law (P-FG) and sigmoidal law (S-FG) based on functionally graded materials. The examination of plate with tapered thickness in one direction is to be laying on Pasternak foundation. The modulus of elasticity is supposed to vary in thickness direction and several comparisons are studied by applying different power law indexes, thickness parameters, foundation stiffnesses, and BCs. Partial differential equations of motions, which derive by Hamilton’s Principle, are solved by Galerkin’s technique.