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

• Published in: Engineering with computers Vol. 38; no. 3; pp. 2583 - 2607
• Main Authors: Ma, Lianghua, Liu, Xiaoliang, Moradi, Zohre
• Format: Journal Article
• Language: English
• Published: London Springer London 01.06.2022; Springer Nature B.V
• Subjects: Annular plates; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Differential equations; Dynamic models; Dynamical systems; Frequency response; Generalized differential quadrature method; Graphene; Hamilton's principle; Harmonic excitation; Math. Applications in Chemistry; Mathematical and Computational Engineering; Nonlinear dynamics; Original Article; Perturbation; Quadratures; Systems Theory; Thickness ratio; GPLRC annular plate; Quasi-harmonic motion; Poincaré section; Von Karman nonlinearity; Chaotic responses
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-020-01210-9

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