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OA

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.