Free vibration analysis of porous functionally graded plates using a novel shape function

Introduction/purpose: This study introduces a novel analytical framework to comprehensively investigate the natural vibration characteristics of porous functionally graded (FG) plates. The research aims to combine an innovative shape function methodology with a sophisticated porosity model within an advanced higher-order shear deformation theory (HSDT). Methods: Material properties follow power-law distributions across the thickness, with voids incorporated via a refined porosity formulation. The governing equations for simply supported plates are solved analytically using the Navier technique. A parametric study examines the effects of power-law index, geometric ratios, and porosity distribution. Results: Results show exceptional agreement with established theories, revealing significant relationships in which both the power-law index and porosity distribution critically influence natural frequencies. New insights are provided into their coupled effects on vibrational behavior. Conclusion: This work offers fundamental understanding for optimizing porous FG plate design in advanced engineering applications such as aerospace and structural systems, where weight reduction and vibration control are crucial. It delivers practical guidelines for engineering design and material selection.