ABSTRACT

In this study, the free torsional vibration of the nanorod with noncircular cross-section based on the nonlocal strain gradient theory is investigated. The rectangular cross-section has been selected. The governing partial equation of the torsional vibration of the noncircular nanorod is derived using Hamilton’s principle. Using a Galerkin method, and by consideration of the rectangular shape function in series, the natural frequency of noncircular nanorod is obtained. The obtained results indicate the convergence of the nondimensional natural frequency of the nanorod by enhancement of the number of the rectangular shape function. Furthermore, the nondimensional natural frequency of the noncircular nanorod for different nondimensional nonlocal parameter and nondimensional material length scale parameter is studied. Eventually, the effects of both nonlocal parameter and material length scale parameter on the nondimensional natural frequency, which causes torsional stiffness softening and torsional stiffness hardening of the nanorod, is also illustrated.

摘要

在这项研究中，基于非局部应变梯度理论研究了具有非圆形横截面的纳米棒的自由扭转振动。已选择矩形横截面。非圆形纳米棒扭转振动的控制部分方程是利用汉密尔顿原理推导出来的。采用Galerkin方法，考虑串联矩形函数，得到非圆形纳米棒的固有频率。所得结果表明通过增加矩形形状函数的数量可以收敛纳米棒的无量纲固有频率。此外，研究了不同无量纲非局部参数和无量纲材料长度尺度参数下非圆形纳米棒的无量纲固有频率。最终，