正交各向异性板中的兰姆波频散曲线

玻璃钢/复合材料 ›› 2018, Vol. 0 ›› Issue (10): 47-50.

正交各向异性板中的兰姆波频散曲线

蔡应龙, 铁瑛^*, 陈江义

郑州大学机械工程学院,郑州450000

收稿日期:2018-04-09 出版日期:2018-10-28 发布日期:2018-10-28
通讯作者: 铁瑛(1972-),女,硕士生导师,副教授,主要从事复合材料无损检测方面的研究,tieying@zzu.edu.cn。
作者简介:蔡应龙(1993-),男,硕士研究生,主要从事复合材料无损检测方面的研究。
基金资助:
国家自然科学基金民航联合基金重点项目(U1333201);国家博士后科学基金面上资助项目(2016M602256)

DISPERSION CURVES OF LAMB WAVE IN ORTHOTROPIC PLATE

CAI Ying-long, TIE ying^*, CHEN Jiang-yi

School of Mechanical Engineering, Zhengzhou University, Henan 450000, China

Received:2018-04-09 Online:2018-10-28 Published:2018-10-28

摘要/Abstract

摘要： 求解了正交各向异性板中的兰姆波频散曲线。利用正交各向异性板中导波的波动方程,通过求解特征值问题获得了位移分量的表达式,并结合板上、下表面应力自由的边界条件,推导出兰姆波在正交各向异性板中的频散方程。根据此频散方程,分析了不同相速度变化范围内波数的取值区间,并以对称模态的频散方程为例,确定频散方程根的合理搜索区间,并用二分法求解出兰姆波的频散曲线。最后分别以各向同性和正交各向异性板作为算例,绘制出了它们的频散曲线,计算结果也表明正交各向异性板中的频散曲线具有与各向同性板不同的特征。

关键词: 正交各向异性板, 兰姆波, 频散方程, 二分法

Abstract: The dispersion curves of Lamb wave in orthotropic plate is solved in this paper. By virtue of wave equation of guided wave in orthotropic plate, the analytical expressions of displacement components in plate is obtained based on the solution of eigenvalue problems. Taking traction free conditions on the top and bottom surface of plate into account, the dispersion equation of Lamb in orthotropic plate is derived. Based on this dispersion equation, the range of wave numbers in different phase velocities is analyzed. Taking the dispersion equation of symmetry mode as an example, the reasonable search interval for the root of the dispersion equation is determined, and the bisection method is used to calculate the dispersion equation. Two kinds of plate, isotropic and orthotropic, are taken as numerical examples. And their dispersion curves are plotted, which are significantly different from those in isotropic plate.

Key words: orthotropic plate, Lamb wave, dispersion equation, bisection method

中图分类号:

TB332

蔡应龙, 铁瑛, 陈江义. 正交各向异性板中的兰姆波频散曲线[J]. 玻璃钢/复合材料, 2018, 0(10): 47-50.

CAI Ying-long, TIE ying, CHEN Jiang-yi. DISPERSION CURVES OF LAMB WAVE IN ORTHOTROPIC PLATE[J]. Fiber Reinforced Plastics/Composites, 2018, 0(10): 47-50.