嵌入可变形基体中的预应力石墨烯片的振动分析
Vibration analysis of a pre-stressed graphene sheet embedded in a deformable matrix
摘要：
通过基于非局部Kirchhoff板理论的理论公式，研究了初始单轴应力和周围弹性基体对单层石墨烯片（SLGS）横向振动响应的影响. SLGS的周围弹性矩阵被建模为Pasternak型的基础。用瑞利法求解了预应力SLGS动力学的椭圆型偏微分方程。分析的数值结果表明，SLGS的振动响应对模型控制参数的变化具有不同程度的敏感性。数学模型中各控制参数的Pareto图表明，地基的剪切模量对SLGS的基本固有频率影响最大。小尺度效应被发现有更显着的效果上的SLGS的振动响应时，它是完全固定在四个边缘。
英文摘要：
The effect of the initial uniaxial stress and a surrounding elastic matrix on the transverse vibration response of a single-layered graphene sheet (SLGS) is investigated through a theoretical formulation that is based on the nonlocal Kirchhoff plate theory. The surrounding elastic matrix of the SLGS is modeled as a foundation of the Pasternak-type. The elliptic partial differential equation governing the dynamics of the pre-stressed SLGS is solved with the Rayleigh method. Numerical results from the analyses reveal different level of sensitivity of the vibration response of the SLGS to changes in the control parameters of the model. Pareto charts of the effect of the control parameters in the mathematical model show the shear modulus of the foundation to have the most dominant influence on the fundamental natural frequency of the SLGS. The small-scale effect is found to have more pronounced effect on the vibration response of the SLGS when it is fully clamped at the four edges.
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