Nonlinear post-buckling and vibration of 2D penta-graphene composite plates

  • Nguyen Dinh DucEmail author
  • Pham Tien Lam
  • Tran Quoc Quan
  • Pham Minh Quang
  • Nguyen Van Quyen
Original Paper


The newly developed penta-graphene is a two-dimensional (2D) carbon allotrope with promising mechanical properties. This paper investigates the nonlinear post-buckling and vibration of imperfect three-dimensional penta-graphene composite plates resting on elastic foundations and subjected to uniform external pressure and axial compressive load. The elastic constants of the single-layer penta-graphene are fully determined by the density functional theory by fitting the equation of strain energy to the density functional theory energy. Specifically, the elastic constant \(C_{66}\) which has not been considered by other authors is also determined. The motion and compatibility equations are derived based on the classical plate theory taking into account von Karman geometrical nonlinearity, initial geometrical imperfection and Pasternak type elastic foundations. For nonlinear post-buckling, the Bubnov–Galerkin method is applied to obtain the load–deflection amplitude curves while the Runge–Kutta method and harmonic balance method are used to obtain the deflection amplitude–time curves and the amplitude–frequency curves for nonlinear vibration. Numerical results show the effects of geometrical parameters, initial imperfection and elastic foundations on the nonlinear post-buckling and vibration of the imperfect 2D penta-graphene plates. The present results are also compared to others to validate the accuracy of the applied method and approach.



This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2018.04. The authors are grateful for this support.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Advanced Materials and Structures Laboratory, VNUHanoi - University of Engineering and TechnologyHanoiVietnam
  2. 2.National Research Laboratory, Department of Civil and Environmental EngineeringSejong UniversityGwangjin-guKorea
  3. 3.PIAS, Phenikaa UniversityHanoiVietnam
  4. 4.JAISTNomiJapan
  5. 5.NTT Institute of High TechnologyNguyen Tat Thanh UniversityHo Chi Minh cityVietnam

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