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热振动对纳尺度器件动力学特性有着重要的影响.为此,建立了预应力作用下,考虑量子效应的双层矩形石墨烯的等效连续介质模型.计算了不同预应力作用下,不同温度时双层石墨烯的固有频率和均方根振幅.双层石墨烯层间存在范德华相互作用,其同向振动固有频率与相同尺寸单层石墨烯固有频率相等,双层石墨烯存在大于同向振动频率的反向振动频率.考虑量子效应板模型得到的均方根振幅值小于结合能量均分原理板模型得到的结果.且随着温度的降低,两种板模型结果之间的差值增大,量子效应越来越明显.随着预应力的增加,双层石墨烯的固有频率值增加,均方根振幅值降低,量子效应的影响逐渐增加.预应力对同向振动的影响远大于对反向振动的影响.分析了零点能量对双层石墨烯热振动的影响,当计入零点能量后,石墨烯均方根振幅大于结合能量均分原理板模型预测的结果,且在零温时依然存在不为零的振幅.
The thermal vibration has an important influence on the dynamic behavior of nanoscale devices. For this reason, an equivalent continuum model of double-layer rectangular graphene with quantum effect under prestressing effect is established. Under different prestressing forces, When the double-layer graphene van der Waals interaction between the natural vibration frequency with the same size single-layer graphene natural frequency equal double-graphene existence is greater than the same direction The vibration frequency of the reverse vibration frequency.Considering the rms model of the root mean square of the amplitude value is less than the combined energy of the principle plate model results obtained and with the temperature decreases, the difference between the two plate model results by Large and quantum effect is more and more obvious.With the increase of prestress, the intrinsic frequency of double-layer graphene increases, the amplitude of rms decreases, the influence of quantum effect increases gradually.The influence of prestress on co-directional vibration is far greater than The influence of zero energy on thermal shock of double graphene is analyzed. When the zero point energy is taken into account, the amplitude of the root mean square of graphene is larger than that of the split mode Prediction result, and remains non-zero amplitude at zero temperature.