Porosity-Dependent Free Vibration Characteristics of Functionally Graded Plates Modeled via a Non-Polynomial Higher-Order Shear Deformation Theory

Functionally Graded Materials (FGMs) offer a continuous transition in material properties, enhancing thermal and mechanical performance in demanding applications. This study investigates the free vibration behavior of porous FGM plates using a non-polynomial Higher-Order Shear Deformation Theory (NPHSDT) and Finite Element Method (FEM). A C⁰ continuous 9-noded isoparametric element is employed to model complex deformation profiles without requiring shear correction factors. Porosity distributions, arising from manufacturing processes or intentional design, are incorporated into the material model to assess their influence on stiffness and dynamic characteristics. The effects of porosity volume fraction, gradient index, aspect ratio, and boundary conditions are systematically examined. Results reveal that ceramic-rich and low-porosity configurations enhance stiffness and natural frequencies, whereas metallic-rich and highly porous structures exhibit reduced rigidity and stability. The proposed framework provides an efficient and accurate tool for analyzing the vibration response of next-generation porous FGM structural components. Keywords: FGM; Finite element method; HSDT; Free Vibration; porous FGM