Wave propagation analysis of composite beams reinforced with nonlinear FG-CNT distributions supported on Kerr elastic foundation utilizing an improved integral first-order shear deformation theory

Functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) has demonstrated a substantial promise for developing advanced lightweight structures and multifunctional composites, a crucial part of modern life, such as in the automotive, aerospace, marine, and medical industries. This work investigates the wave propagation behavior of FG-CNTRC beams resting on an elastic foundation with four configuration patterns of single-walled carbon nanotubes (SWCNTs). The key innovations in this study include nonlinear distributions of FG-CNTs based on exponential power-law models to achieve an optimal distribution of CNTs within the matrix, a Kerr substrate to illustrate the impact of the surroundings, and an improved integral first-order shear deformation theory (FSDT) to analytically formulate the dispersion of the waves with a novel correction function describing the distribution of shear stresses and strains. The rule of mixture is employed in estimating the elastic material's properties, and the governing equations of motion are derived using Hamilton's principle. The results are compared to those found in the literature for validation of the models. The parametric investigation includes the influence of the CNT's dispersion patterns and volume fraction on wave propagation responses. In addition, the study examines the effects of the Kerr foundation and the nonlinear models on wave dispersion behavior. Analytical findings suggest that the arrangements of CNTs manipulate the rigidities of the beams, affecting the dispersion relations. Also, increasing the volume fractions of CNTs improves the stiffness of the beams, corresponding to faster wave velocities. Further, the nonlinear distributions of FG-CNTs greatly influence the wave propagation, depending on the wave type and the patterns of CNTs. Moreover, the foundation presence boosts wave velocities and influences only the bending waves.