Stability and vibration analysis of shear deformable FG-CNTRC beams resting on elastic foundations

This paper presents novel work on the buckling and vibration analysis of shear-deformable functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams on variable elastic foundations (VEFs). By integrating two-parameter VEF models with a quasi-three-dimensional higher-order shear deformation theory (3D-HSDT). The effective material characteristics of FG-CNTRC beams are described by the rule of mixture. The problem is solved analytically using Navier's technique after the equations of motion are derived using Hamilton's principle. The validity and efficiency of the suggested models and methodology are confirmed by comparing the findings with the results of the available literature. A detailed analysis is conducted on the impact of length-to-thickness ratio, elastic foundation (EF) characteristics, and carbon nanotube (CNT) distribution patterns on the natural frequencies and buckling loads of FG-CNTRC beams, and some benchmark findings are also demonstrated. The results showed that the factors taken into consideration had a significant effect on the FG-CNTRC beams' buckling loads and natural frequencies.