Free vibration of axially loaded functionally gared carbon nanotube-reinforced composite curved beams

This study analyzes the free vibration of axially graded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) curved beams. The theoretical framework employed is based on higher-order shear deformation theory. The governing equations are formulated using the Lagrange equation. A Ritz procedure is implemented to compute the beams’ natural frequencies and critical buckling loads under diverse boundary conditions. Several numerical examples are presented to substantiate the efficacy of the proposed theory and method. Furthermore, the study explores the influences of boundary condition, curvature, slenderness ratio, distribution pattern, and fractional volume of the reinforcing materials on the free vibration and buckling behaviors of the FG-CNTRC curved beams.