INVESTIGATING THE IMPACT OF POROSITY DISTRIBUTION AND GRADING PARAMETER ON THE FREE VIBRATION OF FUNCTIONALLY GRADED BEAMS

Abstract

This study focuses on investigating the free vibration of porous functionally graded (FG) beams 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 hyperbolic 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/non-porous FG beams under simply supported boundary conditions at both ends. 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. The analysis provides significant insights into the behavior of different porous materials and can be useful for designing and selecting materials with porosities.