Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

Awrejcewicz, Jan; Kudra, Grzegorz; Mazur, Olga

doi:10.1007/s11071-021-06765-w

Cited by 11 publications

(7 citation statements)

References 32 publications

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“…Furthermore, several works have addressed the analysis of the nonlinear dynamical behavior of graphene, with chaos being the main nonlinear behavior discovered [11][12][13][14][15][16][17]. In [14], they investigated the nonlinear dynamics of some graphene structures.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, simulations were used to study the impact of the quoted effects on the global dynamics of the introduced model. Recently, [15] has established an improved model of a graphene sheet based on a particular mathematical approach described in their work. The chaotic behavior of the proposed model was analyzed based on the variation of the excitation parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Given the wide field of application of graphene, it is important to research if that widespread phenomenon is able to occur in its dynamics. So, in order to give a response to that research question, we will investigate in this work the global dynamics of a graphene sheet under periodic loads introduced by Awrejcewicz in [15]. Let's recall that, in their investigation, after obtaining a mathematical model of the material using the Bubnov-Galerkin method, they used nonlinear dynamical analysis tools to demonstrate that the model exhibits chaotic dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The remaining parts of this contribution are structured as follows: In section 2, the model of the singlelayered graphene sheet under periodic loads established by Awrejcewicz et al [15] is recalled. Its properties are investigated, and its Hamiltonian energy is determined using Helmholtz theory.…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical expression of the graphene structure of figure 1 has been established recently by Awrejcewicz and collaborators [15], as given in equation (1). From the work of [15], the values of the coefficients are given as follows:…”

mentioning

confidence: 99%

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Complex dynamics, released energy, and multistability in a single-layered graphene sheet under periodic loads

et al. 2023

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Graphene was found in 2004. It's a carbon allotrope built around a single layer of atoms organized in a two-dimensional (2D) honeycomb lattice nanostructure. In the contribution, the complex behavior of a graphene sheet under periodic loads is investigated using the usual nonlinear analysis tools. From the dynamic states and the material's symmetry investigations, it is found that the graphene model considered in this work can exhibit the simultaneous existence of up to six different patterns by varying initial conditions for fixed parameters. The Helmholtz theorem is also used to calculate the Hamilton energy of excited graphene. As a result, when the damping coefficient and the nonlocal parameter were close to zero, the system's energy was null. This supports the fact that when graphene is in its resting state, vibrations are null inside the material. In contrast, when the damping coefficient and the nonlocal parameter were simultaneously increased, the energy of the graphene sheet increased until it reached a peak value, justifying the oscillations observed in the material. The dependency of the material on the initial condition is also used to support the coexistence of the energy found.

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