Parametric investigations on dynamic responses of porous functionally graded al/al2o3 plates: effects of homogenization models and material distributions

This study presents a numerical analysis of the dynamic responses exhibited by functionally graded Al/Al2O3 plates that incorporate porosity. It explores the influence of critical parameters such as the thickness-to-span ratio and the porosity coefficient on the non-dimensional fundamental frequencies. Various micromechanical homogenization models, including Voigt, Mori-Tanaka, LRVE, Tamura, and Reuss, are utilized in conjunction with different material volume fraction distribution profiles: Power-law, Viola-Tornabene four-parameter, and Trigonometric. The research considers four distinct porosity variation patterns: uniform, non-uniform, logarithmic non-uniform, and mass-density. The governing equations are addressed using the Navier solution technique. The findings indicate that the Viola-Tornabene model results in the highest fundamental frequencies, succeeded by the Power-law and Trigonometric models. Among the porosity patterns, mass-density porosity yields the maximum frequencies, whereas uniform porosity leads to the lowest. Furthermore, an increase in the porosity coefficient typically raises the frequencies, with the exception of uniform porosity, while an increase in the thickness-to-span ratio results in a reduction of frequencies across all models. These insights are essential for the optimization of designs for functionally graded porous plates.