Impact of porosity distribution and grading parameters on free vibration of functionally graded beams

This study focuses on investigating the free vibration of porous functionally graded (FG) beams based on neutral surface position and the impact of porosity distribution on the properties and performance of materials. To achieve this, the study assumes that the beam’s material characteristics vary continuously along its thickness direction. The volume fraction of constituents is specified using the modified rule of the mixture, which includes porosity volume fraction with changed porosity patterns across the cross-section. The study uses the parabolic shear deformation theory without shear correction factors to derive the equations of motion by applying Hamilton’s principle. The study employs Navier’s method to obtain analytical results for the free vibration of porous FG beams. To verify the proposed formulation, the study compares the results with relevant findings from the literature. The study also examines the relationship between frequency of vibration and grading parameter in homogeneous porosity distributions, as well as the frequency of vibration in beam structures with different porosity patterns. Additionally, numerical examples are provided to investigate the impact of parameters like power-law index, span to depth ratio, porosity distribution pattern, and porosity volume fraction on the natural frequencies of FG beams.