Free vibration analysis of multidirectional FG porous annular sector plates based on three-dimensional elasticity using GDQ with RSM-derived predictive frequency formulas

Annular sector plates are widely used in advanced engineering systems, where their dynamic characteristics play a crucial role in structural performance. Tailoring material distributions and introducing controlled porosity provide an effective approach for tuning their vibration response, particularly the natural frequencies, without modifying the structural geometry or base constituents. In this study, for the first time, the free vibration behavior of multidirectional functionally graded (FG) porous annular sector plates with material properties varying along the thickness, radial, and circumferential directions is investigated based on three-dimensional elasticity theory, and the governing equations are solved using the generalized differential quadrature (GDQ) method to obtain highly accurate results even for relatively thick plates. The accuracy of the proposed formulation is verified through comparisons with available results in the literature and finite element simulations performed in Abaqus. Furthermore, response surface methodology (RSM) is employed to develop predictive relations describing the influence of key parameters on the natural frequencies. The proposed framework combines the flexibility of GDQ-based numerical analysis with the simplicity of RSM-derived predictive formulas, while the use of three-dimensional elasticity ensures high accuracy of the obtained vibration responses. The results are presented and discussed through graphical representations, providing insight into the natural frequency characteristics of these structural elements.