基于改进模量比寻根算法的黏弹性多层空心圆柱超声导波特性分析  

Characteristic analysis of ultrasonic guided waves in viscoelastic multilayer hollow cylinder based on an improved modulus ratio root-finding algorithm

作　　者：黄梓琦 刘宏业[1] 田振华 刘增华[3] HUANG Ziqi;LIU Hongye;TIAN Zhenhua;LIU Zenghua(School of Optical-Electrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;Department of Mechanical Engineering,Virginia Polytechnic Institute and State University,Blacksburg 24061,USA;School of Information Science and Technology,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]上海理工大学光电信息与计算机工程学院,上海200093 [2]弗吉尼亚理工大学机械工程系,黑堡24061 [3]北京工业大学信息科学技术学院,北京100124

出　　处：《无损检测》2024年第12期34-43,共10页Nondestructive Testing

基　　金：国家自然科学基金项目(52175513,51705325)。

摘　　要：基于勒让德正交多项式展开法和Kelvin-Voigt模型,推导了黏弹性多层正交各向异性空心圆柱中纵向导波的特征方程,并提出了一种改进的模量比寻根算法来求解该方程,详细阐述了频散方程的物理意义。为了验证理论模型和所开发程序的可靠性,首先进行了大径厚比黏弹性单层管的频散曲线和衰减曲线计算,并与已发表的数值结果进行了比对。随后以3层黏弹性空心圆柱为例,研究了径厚比和黏性常数对频散曲线及衰减曲线的影响。最后,进行了三维复波数-频率频散曲线的计算,并对非传播模态进行了阐释。Based on Legendre orthogonal polynomial expansion method and the Kelvin-Voigt model,the characteristic equation for longitudinal guided waves in a viscoelastic multilayer orthotropic anisotropic hollow cylinder is derived,and an improved modulus-ratio root-seeking algorithm is proposed for solving this equation,and the physical significance of the dispersion equations is elaborated.In order to verify the reliability of the theoretical model and the developed program,the calculation of dispersion curves and attenuation curves for a large outer radius-to-thickness ratio viscoelastic single-layer tube is firstly carried out and compared with the published numerical results.Subsequently,the effects of the outer radiusto-thickness ratio and the viscosity constant on the dispersion and attenuation curves are investigated using a three-layer viscoelastic hollow cylinder as an example.Finally,the calculation of three-dimensional complex wave number-frequency dispersion curves is carried out and the non-propagating modes are analyzed.

关 键 词：黏弹性 勒让德多项式 纵向导波 频散曲线 衰减曲线 

分 类 号：TG115.28[金属学及工艺—物理冶金]