Effect of porosity distribution on free vibration of functionally graded plates: an accurate application of HSDT theory

This study investigates the natural vibration characteristics of porous plates with three different patterns of porosity distributions. The analysis employs a 2D Higher Shear Deformation Theory (HSDT), which simplifies the model by reducing the number of unknown displacement variables to four compared to other theories. Material properties vary smoothly across the plate thickness according to Voigt's power law of volume fraction mixing. The shape function employed in this theory meets the zero shear stress conditions on both surfaces of the FG plate, eliminating the need for shear correction factors. The governing equations, derived from Hamilton's principle, are solved using the Navier solution method. The study explores the influence of various parameters on natural vibration, including porosity distribution, slenderness ratios(h/a), material index (p), and geometric coefficient (a/b) in functionally graded porous plates. The accuracy and effectiveness of the present theory, considering different porosity distributions (FGU, FGA, FGS), have been validated and compared with other studies in the literature. All the examples considered showed excellent agreement. Based on these findings, it is clear that the proposed theory is effective in predicting the frequencies of functionally graded porous plates. The results highlight significant effects of these parameters on the plates' vibration characteristics, contributing novel insights that advance understanding in this field and set a benchmark for future research.