This paper presents a comprehensive study on bending, vibration and buckling behaviours of the zigzag and armchair nanobeams. Based on a third order shear deformation beam theory and the doublet mechanics, a finite element model is proposed and employed to solve the problems of zigzag and armchair nanobeams with various boundary conditions for the first time. The verification is performed by comparing the numerical results with those from the previous studies with respect to various boundary conditions. A number of numerical examples on zigzag and armchair nanobeams with four boundary conditions have been carried out. The effects of material length scale parameters, aspect ratio, nanobeam model and boundary conditions on the displacements, natural frequencies and buckling loads of nanobeams are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies.

本文对之字形和扶手椅纳米梁的弯曲，振动和屈曲行为进行了全面的研究。基于三阶剪切变形梁理论和双重力学，提出了有限元模型，并首次解决了各种边界条件下的锯齿形和扶手椅形纳米束问题。通过将数值结果与先前关于各种边界条件的研究结果进行比较来进行验证。已经对具有四个边界条件的之字形和扶手椅形纳米束进行了许多数值算例。材料长度比例参数的影响，详细研究了纳米高宽比，纳米束模型和边界条件，研究了纳米束的位移，固有频率和屈曲载荷。一些新的结果（尚未在公开文献中提供）可供将来的研究参考。