Previous studies were concerned with transverse vibrations of axially moving nanowires; however, their statics as well as lateral and transverse vibrations and potential instabilities for the most general form of the translational motion in the presence of axially, laterally, and transversely distributed and pointed loads have not been explained yet. To scrutinize this interesting problem simply, but effectively, the authors develop a fairly comprehensive cable-like model for three-dimensionally moving pretensioned wire-like nanostructures in vacuum under static loads accounting for both nonlocality and surface energy. By decomposing the total deformations into the statics and dynamics parts, the continuum-based governing equations pertinent to purely linear static and dynamic states are presented for the first time. The explicit expressions of static deformations and potential divergence instability of the movable nanowire with general translation motion are displayed and discussed. Subsequently, Galerkin methodology based on admissible modes is employed for dynamic analysis of laterally loaded nanowires in the movable manner. The influences of crucial factors on the free vibration response as well as dynamic instability are investigated for various types of motions.

先前的研究涉及轴向移动的纳米线的横向振动。但是，对于在轴向，横向和横向分布的尖锐载荷的情况下最平常形式的平移运动，它们的静力学，横向和横向振动以及潜在的不稳定性尚未得到解释。为了简单而有效地研究这个有趣的问题，作者开发了一种相当全面的电缆状模型，用于在静态载荷下考虑了非局部性和表面能的情况下，在真空中三维移动预拉伸的线状纳米结构。通过将总变形分解为静态和动态部分，首次提出了与纯线性静态和动态状态有关的基于连续体的控制方程。显示并讨论了带有一般平移运动的可移动纳米线的静态变形和电位发散不稳定性的明确表达。随后，基于可允许模式的Galerkin方法被用于以可移动方式对横向加载的纳米线进行动态分析。对于各种类型的运动，研究了关键因素对自由振动响应以及动态不稳定性的影响。