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...

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Veröffentlicht in:Engineering with computers Jg. 38; H. 3; S. 2583 - 2607
Hauptverfasser: Ma, Lianghua, Liu, Xiaoliang, Moradi, Zohre
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Springer London 01.06.2022
Springer Nature B.V
Schlagworte:
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
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Beschreibung
Zusammenfassung: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
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-020-01210-9