基于非局部弹性理论的纳米板横向振动

本文利用非局部弹性理论研究了单层石墨烯的纳米板的横向自由振动响应．通过迭代法推导了非局部应力表达，进一步通过哈密顿原理推导了纳米板的控制方程，应用纳维解法得到四边简支纳米板振动固有频率的数值解，并将本文研究结果与已有文献结果进行对比，进一步讨论了小尺寸效应，以及纳米板的三维尺寸和半波数对振动频率的影响．结果表明：非局部效应的存在使得纳米板的等效刚度和固有频率降低；半波数的增加则使得纳米板的固有频率提高．相关分析结果对基于二维纳米材料的新设备的设计和优化具有重要意义．

Transverse Vibration of Nanoplates Based on Nonlocal Elasticity Theory

Transverse free vibration of the nanoplate of the single-layer graphene sheet is studied using the nonlocal elasticity theory. The nonlocal stress is derived via an iterative method and the nonlocal governing equations of motion are established based on Hamilton’s principle. Numerical solutions of natural frequencies for simply supported rectangular nanoplates are obtained by employing Navier’s method. Moreover, the theoretical calculations are compared with those in previous literatures to reveal the effects of small-scale coefficient, three-dimensional sizes and half wave number on the free vibration responses of the nanoplate. It is shown that the existence of nonlocal effect weakens the equivalent stiffness and further decreases the natural frequency of nanoplates. On the other hand, increasing the half wave number leads to the increase of natural frequency. The results are expected to be useful in designing and optimizing the two-dimensional nano-material based new nanodevices.