A Static and Free Vibration Analysis of Porous Functionally Graded Beams

Abstract

In this work, the static and free vibration analysis of functionally graded (FG) porous beams is investigated using a new higher-order shear deformation model (HSD). The porosity that develops naturally during the fabrication of a material is arbitrary in nature. Therefore, in the present study, a variation is considered taking into account three distribution patterns, namely (i) even distribution, (ii) uneven distribution, and (iii) the logarithmic-uneven pattern. Furthermore, the impact of several micromechanical models on the bending and free vibration behavior of the beams was investigated. Different micromechanical models were used to examine the mechanical properties of functionally graded beams, the properties of which change continuously throughout the thickness following a power law. Using the HSD model, the equations of motion are obtained using Hamilton's principle. To obtain displacements, stresses, and frequencies, the Navier type solution method was employed, and the numerical results were compared to those published in the literature. The impact of porosity and volume fraction index, different micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams were investigated.