In this article, the free torsional vibration of the noncircular microwire is obtained via modified couple stress theory. The noncircular cross section is considered to be equilateral triangle. The governing equations are derived using Hamilton’s principle, and the natural frequencies of the clamped-clamped and clamped-free microwires are obtained based on a Galerkin method. The natural frequency for analyzing of the results is considered to be dimensionless. The effects of the different parameters including the dimensionless material length scale parameter, the dimensionless edge length of the triangle, and mode number on the dimensionless natural frequency of the microwire are evaluated. Ultimately, the influence of the Poisson’s ratio on the natural frequency of the microwire under various boundary conditions is investigated.

中文翻译：

---

基于修正偶应力理论的三角微丝自由扭转振动

在本文中，非圆形微丝的自由扭转振动是通过修正的耦合应力理论获得的。非圆形截面被认为是等边三角形。使用哈密顿原理推导出控制方程，并基于伽辽金方法获得夹紧和未夹紧微丝的固有频率。用于分析结果的固有频率被认为是无量纲的。评估了包括无量纲材料长度尺度参数、三角形的无量纲边长和模式数在内的不同参数对微丝的无量纲固有频率的影响。最后，研究了泊松比在各种边界条件下对微丝固有频率的影响。