Analysis of the Free Vibration of Porous Functionally Graded Beams with Different Boundary Conditions and a Novel Two-Variable Model

This study introduces a new approach to the vibration analysis of porous functionally graded (PFG) beams by utilizing a two-dimensional elasticity solution. Polynomial and trigonometric series are used to enhance the kinematics of a beam with only two variables along the thickness and axial axes, respectively. The beams' characteristic equations are then derived using Lagrange's equations. Material characteristics, porosity, and boundary conditions all have an effect on natural frequencies, which is explored in this parametric study.