具有随机粗糙表面的变截面杆中的扭转波传播  

Propagation of TorsionalWave in Variable-Section Rods with Random Rough Surface

作　　者：秦臻[1] 袁乐 贺宇翔 李翔宇 QIN Zhen;YUAN Le;HE Yuxiang;LI Xiangyu(School of Mechanics and Aerospace,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都611756

出　　处：《四川轻化工大学学报（自然科学版）》2023年第2期23-30,共8页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(12072297)。

摘　　要：建立了含有随机粗糙表面的轴对称变截面杆的数字模型,研究了扭转波在变截面粗糙杆中的传播规律。首先,利用摄动法和快速傅里叶变换求解了含有粗糙面离散序列的扭转波动方程,得到了离散形式的半解析解。其次,利用MATLAB将离散解数值化,并通过ABAQUS对变截面粗糙杆进行有限元模拟对比,验证了解的有效性。再次,通过系统计算,得到了影响摄动法精度的小参数的适用范围。最后,系统地讨论了粗糙面的统计参量对扭转波传播特性的影响规律。结果表明:无量纲高度均方根越大,扭转波幅值均值越小;无量纲相关长度越大,扭转波幅值均值越大,但均不会超过扭转波在光滑杆中的幅值。A numerical model of an axisymmetric variable cross section rod containing a random rough surface is established,and the propagation law of torsional waves in a variable cross section rough rod is studied.Firstly,the torsional wave equation containing a discrete sequence of rough surfaces is solved using the perturbation method and the fast Fourier transform,and a semi-analytic solution in discrete form is obtained.Secondly,the discrete solution is numerically solved by using MATLAB,and the validity of the solution is verified by comparing finite element simulations of variable cross section rough bars by ABAQUS.Thirdly,the applicable range of small parameters affecting the accuracy of the perturbation method is obtained by systematic calculations.Finally,the influence law of the statistical parameters of the rough surface on the propagation characteristics of torsional waves is discussed systematically.The results show that the larger dimensionless root mean square of height,the smaller the mean value of torsional wave amplitude;the larger dimensionless correlation length,the larger the mean value of torsional wave amplitude,but none of them will exceed the amplitude of torsional wave in a smooth rod.

关 键 词：随机粗糙表面 变截面杆 扭转波 摄动法 快速傅里叶变换 ABAQUS 

分 类 号：O326[理学—一般力学与力学基础]