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建立了单层石墨烯等效非局部薄板的一种新的有限元模型,并运用有限元法分析不同边界条件下单层石墨烯振动的小尺度效应.给出了基于弹性应变梯度理论下Kirchhoff板的振动方程.发展了一种4节点24自由度的板单元,用于离散化求解考虑微纳结构尺度效应的高阶微分方程.在研究四边简支板振动时,考虑应变梯度的非局部弹性有限元数值计算结果与理论分析结果相一致.用有限元方法研究了不同尺寸、振动波长、振动模态阶数、边界条件类型以及非局部参数的单层石墨烯振动.
A new finite element model of single layer graphene equivalent nonlocal thin plate is established and the small scale effect of single layer graphene vibration under different boundary conditions is analyzed by finite element method.According to the elastic strain gradient theory Kirchhoff Plate vibration equation. A four-node, 24-degree-of-freedom plate element is developed to discretize the higher-order differential equations that take into account the scaling effect of the micro-nano structure. The numerical results of the elastic FEM are consistent with those of the theoretical analysis.The single-layer graphene vibration of different sizes, vibrational wavelengths, order of vibration modes, boundary condition types and non-local parameters are studied by finite element method.