引用本文: 李志浩, 李翔宇, 朱志武等. 轴对称粗糙圆杆的扭转变形. 力学与实践, 2024, 46(2): 1-8.
Li Zhihao, Li Xiangyu, Zhu Zhiwu, et al. Torsional deformation of round rod with axisymmetric rough surface. Mechanics in Engineering, 2024, 46(2): 1-8.
 Citation: Li Zhihao, Li Xiangyu, Zhu Zhiwu, et al. Torsional deformation of round rod with axisymmetric rough surface. Mechanics in Engineering, 2024, 46(2): 1-8.

## TORSIONAL DEFORMATION OF ROUND ROD WITH AXISYMMETRIC ROUGH SURFACE

• 摘要: 本文旨在研究轴对称表面粗糙圆杆的扭转变形。通过微元法，推导了轴对称表面粗糙圆杆的控制微分方程。结合摄动法和离散傅里叶变换，获得了粗糙圆杆的扭转角摄动解。对比典型粗糙圆杆的材料力学解析解或有限元解，验证了本文摄动解的有效性。通过系统计算，探究了粗糙面的统计参数对于扭转角的影响规律并建立了经验公式。本文的研究成果拓展了材料力学中扭转问题解的范围，并为数学物理方法提供了具体的力学实践。

Abstract: This paper aims to study the torsional deformation of round rods with rough surface. The governing differential equation of round rod with rough surface are derived by the infinitesimal element method. The perturbation solutions of the torsion angle are obtained by combining perturbation method and discrete Fourier transform. The validity of perturbation solution in this paper is verified in comparison with the analytical solution and finite element solution of several round rods with typical rough surface. Systematic computations were conducted to explore the effect of statistical parameters on torsion angle and an empirical formula was established. The present work extends the solution range of torsion problem in Mechanics of Materials and provides a concrete mechanic example for methods of mathematical physics.

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