On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation

In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton's principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio (l(GPL)/w(GPL)) of the GPLs. Moreover, utilizing GPLs in the shapes close to square (l(GPL)/w(GPL) = 1) presents higher frequency of the annular plate. Also, increase in l(GPL)/t(GPL) indicates that using GPLs with lower thickness relative to its length provides better frequency response

Automated summary

A mathematical model was developed for the nonlinear frequency and chaotic responses of graphene nanoplatelets-reinforced composite annular plate subject to external harmonic load, using Hamilton's principle and von Karman nonlinear theory. The study utilized generalized differential quadrature method and perturbation approach to accurately solve the nonlinear governing equation. Results showed that the chaotic motion and nonlinear frequency of the annular plate are hardly influenced by the length to thickness ratio of graphene nanoplatelets, and using GPLs with shapes close to square could lead to higher frequency response.