In this study, the effect of shear deformation on the atomic size-dependent free vibration of nanoframes is investigated. The equations of motion of axial and bending vibrations are obtained via the variational algebra according to nonlocal elasticity theory. Axial and bending behaviors are expressed by using simple rod theory and first-order shear deformation beam theory, respectively. By combining the nonlocal finite element solutions for the equations of motion, an eigenvalue formulation for the free vibration of nanoframe is developed. In the presentation of numerical results, firstly, some comparison studies are carried out to show the accuracy of the present analysis. Then, the variations of nondimensional frequencies of three different nanoframe structures are investigated with respect to various parameters, and the results are discussed in detail. The focus of this study is to better understand the dynamic behavior of nanostructures that are within the scope of nano-electro-mechanical systems (NEMS) technology and can be modelled with discrete members.

在这项研究中，研究了剪切变形对纳米框架原子尺寸相关的自由振动的影响。根据非局部弹性理论，通过变分代数得到了轴向振动和弯曲振动的运动方程。轴向和弯曲行为分别用简单杆理论和一阶剪切变形梁理论来表达。通过结合运动方程的非局部有限元解，开发了纳米框架自由振动的特征值公式。在数值结果的呈现中，首先进行了一些比较研究以证明本分析的准确性。然后，研究了三种不同纳米框架结构的无量纲频率随各种参数的变化，并对结果进行了详细讨论。这项研究的重点是更好地了解纳米结构的动态行为，这些纳米结构属于纳米机电系统 (NEMS) 技术的范围，并且可以使用离散成员进行建模。