Parametric‐Free Vibration Analysis of Porous Functionally Graded Euler–Bernoulli Beams Considering Material Properties, Porosity, and Boundary Conditions

Functionally graded materials (FGMs) provide a continuous variation of material properties and have been widely used in engineering structures to improve structural performance and vibration characteristics. However, it must be clarified how material properties, porosity and boundary conditions, axial stiffness, and axial‐bending coupling stiffness simultaneously influence the free vibration behavior of porous functionally graded beams. This study attempted to develop an analytical framework based on the Euler–Bernoulli beam theory for accurately predicting the free vibration characteristics of porous functionally graded beams. In this study, the analytical formulation was validated using the differential quadrature method (DQM) through a comparison with previously published results, and the effects of ceramic and metallic elastic moduli, ceramic and metallic densities, porosity, mode shape, power‐law index, and boundary conditions on the dimensionless natural frequencies were comprehensively investigated. Although previous studies have mainly analyzed porous FGM beams without fully considering the influence of axial stiffness and axial‐bending coupling stiffness, the results also indicate that neglecting axial stiffness and axial‐bending coupling stiffness led to a significant overestimation of the dimensionless natural frequencies. The dimensionless natural frequency increases by up to 37% when these values are neglected. It is also concluded that the effect of porosity on frequency is not constant and depends on power‐law index.