Analysis of Porosity-Dependent Wave Propagation in FG-CNTRC Beams Utilizing an Integral Higher-Order Shear Deformation Theory

This paper seeks to study and investigate the wave dispersion behavior in porous functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) beams. The beams comprise four patterns of single-walled carbon nanotubes (SWCNTs) distributed in the polymer matrix. The mixture rule is used to estimate the CNTR beams’ material properties. Innovative to this study are three porosity models describing the porosity distributions within the matrix and a three-unknown integral higher-order shear deformation theory (HSDT) modeling analytically the CNTRC beams with a novel shape function expressing the distributions of shear stresses and strains. The equations of motion for CNTRC beams are derived based on Hamilton’s principle. The stiffness and mass matrices are formulated by a generalized solution of harmonic wave propagation to express the wave dispersion relations. Numerical comparisons with previously published works verify the applicability of this mathematical model. The paper studies the effects of CNTs patterns through the polymer matrix, porosity models, and volume fractions of the porosity and CNTs. Based on the analytical results, augmenting the porosity and CNTs volume fractions leads to faster phase and group velocities. Furthermore, the impact of CNTs volume fractions, porosity models, and porosity volume fractions becomes more pronounced as the wavenumber increases.