包含表面效应及Casimir力的纳米阵列弯曲变形分析

Bending of nano-arrays with surface effects and Casimir forces

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。

Mechanical behavior of nano-arrays with surface effects and Casimir forces are considered. The surface effects are introduced by surface energy model. A set of coupled nonlinear equations of nano-arrays are arisen and numerically solved based on Euler-Bernoulli beam model by using the principle of minimum potential energy. Results obtained demonstrate that the combination of surface effects and Casimir force would not cause stiction in nano-arrays. No matter what the number of beams in the arrays, the deflections of the intermediate nano-beams are negligibly small which compared to the first and the last nano-beams. Therefore, we only need to focus on the deformations of the first and the last nano-beams for studying a large parallel array. Results reported are helpful for the characterization of the mechanical properties of nano-arrays and for the design of nano-arrays-based devices and systems.