Free Vibration Analysis of Porous Functionally Graded Curved Beams Using an Improved First-Order Shear Deformation Theory

This work investigates the free vibration of porous Functionally Graded (FG) curved beams using an Improved First-Order Shear Deformation Theory (IFSDT), considering the thickness-stretching effect. A unified kinematic displacement field and hyperbolic shear shape functions are used, satisfying traction-free shear conditions and capturing shear and normal deformations without the need for correction factors. Five different porosity distribution profiles are considered in the analysis, through which the FG material properties are defined using a power-law distribution. The derivation for simply supported boundaries is achieved through a closed-form Navier solution. Comprehensive parametric analyses are presented to examine the influence of span-to-thickness ratio, curvature ratio, power-law index, porosity level, and porosity distribution pattern on the non-dimensional natural frequencies. Excellent agreement with existing higher-order and quasi-3D theories is observed, confirming the accuracy of the proposed formulation. Results show that increased metal content and porosity decrease stiffness and lower natural frequencies, while higher curvature and core-localized porosity improve rigidity. The model provides accurate and practical solutions for the vibration analysis of porous, FG curved beams.