应用数学和力学2026，Vol.47Issue(4)：415-425,11.DOI:10.21656/1000-0887.460048
基于有限元和微分求积法的石墨烯等效纳米板动力特性研究
Dynamic Characteristics Analysis of Equivalent Graphene Nanoplatelets Based on Finite Element and Differential Quadrature Methods
摘要
Abstract
The nonlocal continuum theory effectively integrates microscopic structural features and macroscop-ic mechanical responses by introducing a cross-scale correlation mechanism,providing a new theoretical para-digm 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 par-tial integro-differential equations,and significantly increase the computational complexity.A novel finite ele-ment-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 influ-ential 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 vi-bration 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.关键词
非局部连续介质理论/FE-DQ方法/石墨烯/等效纳米板/动力特性Key words
dynamic characteristic/FE-DQ method/graphene/equivalent nanoplatelet/nonlocal continuum theory分类
数理科学引用本文复制引用
吴雪彬,白镇滔,刘秦龙,李东波..基于有限元和微分求积法的石墨烯等效纳米板动力特性研究[J].应用数学和力学,2026,47(4):415-425,11.基金项目
国家重点研发计划课题(2023YFF0906001) （2023YFF0906001）
国家自然科学基金(52378195 （）
52008332) （）
