Dynamic analysis of porous FG spherical shells: effect of homogenization models
Micòl Amar, Billel Rebai, Mustapha Meradjah, Tidjani Messas, Belgacem Mamen, Abdelouahed Tounsi, Ayed Eid Alluqmani
Abstract
This study presents a systematic comparative analysis of homogenization models for free vibration behavior in isotropic porous functionally graded material (FGM) spherical shells, addressing critical research gaps through rigorous evaluation of five micromechanical schemes Voigt, Reuss, Mori–Tanaka, Tamura, and LRVE coupled with power-law and trigonometric material gradations. A refined higher-order shear deformation theory (HSDT) incorporating five shear functions governs the analytical formulation, solved via Navier’s technique for simply supported boundaries. Comprehensive parametric studies quantify the coupled effects of thickness-to-span ratio, aspect ratio, porosity coefficient, and radius of curvature on non-dimensional fundamental frequencies. Results demonstrate that homogenization model selection critically influences vibrational response, with Voigt and LRVE predicting frequencies 12–15% higher than Reuss models. Porosity distribution dominates stiffness reduction, where mass–density and logarithmic-uneven configurations cause 20–25% greater frequency suppression than even distributions, while trigonometric gradation amplifies curvature sensitivity by 30% versus power-law. These insights provide validated design guidelines for optimizing vibration performance in civil engineering dome structures and pressure vessels, aerospace components, and automotive acoustic enclosures.