Dynamic Characteristics Analysis of Equivalent Graphene Nanoplatelets Based on Finite Element and Differential Quadrature Methods

WU Xuebin; BAI Zhentao; LIU Qinlong; LI Dongbo

doi:10.21656/1000-0887.460048

Volume 47 Issue 4

Apr. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(4): 415-425

WU Xuebin, BAI Zhentao, LIU Qinlong, LI Dongbo. Dynamic Characteristics Analysis of Equivalent Graphene Nanoplatelets Based on Finite Element and Differential Quadrature Methods[J]. Applied Mathematics and Mechanics, 2026, 47(4): 415-425. doi: 10.21656/1000-0887.460048

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Dynamic Characteristics Analysis of Equivalent Graphene Nanoplatelets Based on Finite Element and Differential Quadrature Methods

doi: 10.21656/1000-0887.460048

WU Xuebin¹,
BAI Zhentao²,
LIU Qinlong^1,2,
LI Dongbo^{1,2
,
,}

1. School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, P.R.China;
2. College of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, P.R.China

Funds:

The National Science Foundation of China(52378195；52008332)

Received Date: 2025-03-11
Rev Recd Date: 2025-04-29

Available Online: 2026-04-30

Abstract

Abstract

The nonlocal continuum theory effectively integrates microscopic structural features and macroscopic mechanical responses by introducing a cross-scale correlation mechanism, providing a new theoretical paradigm for solving multi-scale mechanical problems. However, due to the incorporation of long-range interaction integral terms in the constitutive relationship, its control equations exhibit the characteristics of high-order partial integro-differential equations, and significantly increase the computational complexity. A novel finite element-differential quadrature coupling algorithm (FE-DQ) was established and applied to the study of the free vibration characteristics of graphene equivalent nanoplatelets. Based on the parameterized calculation, the influential mechanisms of key variables such as characteristic sizes and non-local parameters on the non-local effects of buckling loads were revealed through systematic parametric studies. The results show that, the scale effect of buckling loads exhibits a significant nonlinear attenuation characteristic and is positively correlated with the size of the non-local parameter. With the gradual increase of the structural size, the non-local effect on the free vibration frequency will gradually weaken; conversely, with the continuous increase of the non-local parameter value or the rise of the vibration modal order, the non-local effect on the free vibration frequency will intensify significantly. The research provides a reference for the study of structural dynamic characteristics on a nanoscale in related fields.
- dynamic characteristic,
- FE-DQ method,
- graphene,
- equivalent nanoplatelet,
- nonlocal continuum theory

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References(26)

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