Investigation study of isotropic porous FG spherical shells using a refined higher-order shear deformation theory

Billel Rebai , Messas Tidjani , Touam Lakhemissi , Mustapha Meradjah , Abdelouahed Tounsi , Ayed Eid Alluqmani , Jabr Aljedani , Mohammed A. Balubaid , S.R. Mahmoud

Abstract

This study presents a comprehensive vibration analysis of isotropic porous functionally graded material (FGM) spherical shells using a refined higher-order shear deformation theory (HSDT). Four distinct porosity distribution patterns even, uneven, logarithmic-uneven, and mass-density based are investigated to determine their influence on the dynamic behavior of FGM shells. The material gradation is modeled using power-law, trigonometric, and Viola-Tornabene four-parameter functions, while five different micromechanics models (Voigt, Reuss, Tamura, Mori-Tanaka, and LRVE) are employed to calculate effective material properties. Analytical solutions are obtained using Navier's technique for simply supported boundary conditions. The effects of gradient index, porosity coefficient, radius of curvature, and vibration mode numbers on the fundamental frequencies are systematically analyzed. Results reveal that each porosity distribution pattern uniquely affects the dynamic response, with mass-density porosity showing the strongest positive correlation to frequency enhancement. The findings provide valuable insights for designing FGM shell structures with tailored dynamic characteristics for various engineering applications.

Key Words

FGM; free vibration analysis; HSDT; micromechanics models; Navier's solution; porosity distribution; porous structures; spherical shells

Address

Billel Rebai, Messas Tidjani, Touam Lakhemissi — Faculty of Sciences & Technology, Department of Civil Eng., University Abbes Laghrour, Khenchela, Algeria
Mustapha Meradjah — Department of Civil Engineering, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria; Multiscale Modeling and Simulation Laboratory, University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria Equipe Mixte "Nano-biomatériaux et Ingénierie Numérique pour des Applications Pharmaceutique", Agence Thématique de Recherche en Sciences et Technologie (ATRST), Algeria
Abdelouahed Tounsi — Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Ayed Eid Alluqmani — Department of Civil Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, Saudi Arabia Jabr Aljedani, S.R. Mahmoud8: GRC Department, Applied College, King Abdulaziz University, Jeddah, Saudi Arabia
Mohammed A. Balubaid — Department of Industrial Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

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