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研究了包含表面效应及Casimir力的纳米阵列弯曲行为。通过表面能模型引入表面效应,基于Euler-Bernoulli梁模型,运用最小势能原理推导了控制纳米阵列弯曲变形的一组基本方程并进行了数值求解,主要计算分析了纳米梁根数N=7、N=20、N=50的纳米阵列。结果表明:在表面效应和Casimir力作用下,纳米阵列的弯曲变形量较小,不足以使纳米阵列相互粘附;与阵列始末两端的纳米梁变形相比,纳米阵列中间部分纳米梁的变形可忽略不计。因此,对于包含数量较多纳米梁的纳米阵列,仅需要关注阵列始末两端的纳米梁变形即可。本研究结果对纳米阵列及以纳米阵列为元件的纳米器件的设计和使用具有一定的指导意义。
The bending behavior of nano-array including surface effect and Casimir force was studied. Based on the Euler-Bernoulli beam model, a set of basic equations governing the bending deformation of nano-arrays are deduced by using the principle of minimum potential energy. Numerical calculations are carried out. The main results are as follows: N = 7, N = 20, N = 50 nano-array. The results show that under the effect of surface and Casimir force, the bending deformation of the nano-array is small, which is not enough to make the nano-arrays adhere to each other. Compared with the deformation of the nano-beams at the both ends of the array, the deformation of the nano- can be ignored. Therefore, for a nanoarray that contains a large number of nano-beams, only the deformation of the nano-beams at the both ends of the array needs to be taken into consideration. The results of this study are of guiding significance for the design and use of nanoarrays and nanoarrays with nanoarrays as their components.