Bending and buckling behavior of the macro CNTRCs (carbon nanotubes reinforced composites) beam was studied considering the scale effect of CNTs (carbon nanotubes). Based on the EMT (Eshelby-Mori-Tanaka) method and using nonlocal theory to characterize the scale effect of CNTs, the nonlocal EMT constitutive model was established. According to the Timoshenko beam theory, the static differential equations and boundary conditions of CNTRCs beams were derived through Hamilton principle. Bending response and ultimate buckling load of CNTRCs beams at S-S (simply supported) edges were obtained and compared with the literature to verify the correctness of the proposed model and solution method. Influences of the scale effect parameters and volume fraction of CNTs and the slenderness ratio of composite beams on the bending response and ultimate buckling load of S-S CNTRCs beams were analyzed. Results show that the equivalent stiffness of the CNTRCs beam is weakened by considering the scale effect of CNTs, and the volume fraction of CNTs and the scale effect parameter both have a great impact on the bending response and ultimate buckling load of the CNTRCs beam with a large slenderness ratio.

FG-CNTRC demonstrate significant engineering value in advanced equipment manufacturing due to their exceptional mechanical properties and designable characteristics. The critical problem of nano-reinforcement scale effects on mechanical response mechanisms was addressed through integration of nonlocal theory with the Eshelby-Mori-Tanaka method, resulting in the development of a nano-to-macro multiscale constitutive model. Based on mathematical characterization of spatially gradient-distributed CNTs (carbon nanotubes), the thermo-mechanical coupling effects from environmental temperature and visco-Pasternak substrates were incorporated. Vibration governing equations for nanocomposite structures were established through Kirchhoff plate theory and energy variational principles, with characteristic frequencies of simply-supported plates subsequently solved. The influence mechanisms of CNTs′ characteristic parameters and thermo-mechanical coupling effects on the natural frequency of structural systems was analyzed. Results demonstrate that the constitutive model effectively characterizes the stiffness-weakening effect induced by CNTs′ scale effects. This effect simultaneously suppresses the stiffness enhancement from substrate elastic parameters while significantly increasing sensitivity to temperature variations. Moreover, the critical volume fraction for structural reciprocating vibration shows positive correlation with substrate damping parameters.