Free vibration characteristics analysis of FG-CNTRC Kirchhoff plates on viscoelastic substrates in thermal environment

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.