Higher-order shear deformation model for free vibration analysis of imperfect functionally graded plates

This paper presents a higher-order shear deformation model for the free vibration analysis of functionally graded plates, considering potential porosities that may form within functionally graded materials (FGMs) during fabrication. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. Various porosity distribution patterns, including both uniform and non-uniform, are examined. The study primarily focuses on investigating the free vibration behavior of porous FGM plates. A power-law formulation is employed to model the distribution of Young's modulus across the plate's thickness, while the Poisson’s ratio is kept constant. The equations of motion are derived using Hamilton’s principle based on the higher-order shear deformation model without shear correction factors. A Navier solution method is applied to determine frequencies, and the numerical results are validated against available literature. A detailed parametric study evaluates the effects of the volume fraction index, porosity fraction index on the natural frequencies of imperfect FGM plates.