Analytical approach for free vibration analysis of porous graphene platelet-reinforced composite beam

This study presents an innovative analytical method for analyzing the free vibrations of porous composite beams reinforced with graphene platelets (GPLs). Using a unified higher-order shear deformation theory, we model the beam with continuously graded material properties. The effective Young’s modulus, Poisson’s ratio, and density are calculated via the Halpin-Tsai micromechanics model. Exact frequency equations are derived through Hamilton’s principle and the governing differential equations for various boundary conditions. This analytical approach allows for a comprehensive parametric study of the effects of beam geometry, GPL distribution patterns, weight fraction, porosity, and boundary conditions on natural frequencies. The detailed development of the equations of motion facilitates applications in similar modeling problems. Our findings provide a valuable reference for validating numerical methods and optimizing the design of advanced composite beams reinforced with nanoparticles for engineering applications.