Page 88 - 《应用声学》2022年第1期

第 41 卷 第 1 期 Vol. 41, No. 1
2022 年 1 月 Journal of Applied Acoustics January, 2022

⋄ 研究报告 ⋄

非线性兰姆波在阶梯板中传播的有限元仿真 ∗

孔媛媛 1,2 安志武 1,2†

(1 中国科学院大学 北京 100049)
(2 中国科学院声学研究所 声场声信息重点实验室 北京 100190)
摘要：在非线性兰姆波检测中，累积二次谐波是重要的检测信号。该文利用有限元法仿真了非线性兰姆波在
阶梯板中的产生和传播过程，通过二维离散傅里叶变换分析了兰姆波的传播模态和各个模态通过波导横截面
的能流大小，给出了各个模态在阶梯板中的反射、透射系数，总结了其随阶梯板厚度的变化规律。研究发现，随
着台阶增高，散射效应使得兰姆波更难入射波导的薄端，使兰姆波的总透射能量降低，但是随着非线性兰姆波
累积效应的增强，更多的能量会从基波馈入高次谐波，两种效应共同决定了非线性兰姆波的透射和反射系数，
随着阶梯板厚度差的增加，向薄端传播的二次谐波能量先增加后减小，存在一个极大值。该文研究结果对深入
研究非线性导波传播理论和发展非线性导波检测技术提供了借鉴。
关键词：非线性兰姆波；阶梯板；超声检测；导波散射
中图法分类号: G301 文献标识码: A 文章编号: 1000-310X(2022)01-0084-12
DOI: 10.11684/j.issn.1000-310X.2022.01.010

Finite element simulation of nonlinear Lamb wave propagation in

a plate with step discontinuities

KONG Yuanyuan 1,2 AN Zhiwu 1,2

(1 University of Chinese Academy of Sciences, Beijing 100049, China)
(2 State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)
Abstract: In the application of nonlinear Lamb waves, amplitude of cumulative second harmonics is an
important indicator. This paper analyzes the generation and propagation of nonlinear Lamb waves in a plate
with step discontinuities, uses 2D discrete Fourier transform to identify the propagating Lamb modes and their
power flow past the cross-sections of the plate, quantifies their reflection and transmission coefficients and their
variation with respect to the height of the step. It is found that, as the height of the step increases, the scattering
of Lamb waves will reduce the power flux transmitted to the thinner side of the plate and therefore reduces
the total transmitted energy. However, as the accumulation of nonlinear Lamb waves becomes stronger, more
energy will be transmitted from fundamental waves to higher harmonics. The scattering and accumulation of
nonlinear Lamb waves determine the transmission and reflection coefficient of different Lamb modes. As the
height of the step becomes larger, the energy of second harmonics transmitted to the thinner side of the plate
will first increase and then decrease, reaching a maximum at a certain step thickness. This paper provides
guidance to a deeper understanding of nonlinear guided wave propagation and the development of nonlinear
guided wave testing.
Keywords: Nonlinear Lamb wave; Plate with step discontinuities; Ultrasonic testing; Scattering of guided waves

2021-03-08 收稿; 2021-04-07 定稿
国家自然科学基金项目 (11874386)
∗
作者简介: 孔媛媛 (1994– ), 女, 江苏南京人, 硕士研究生, 研究方向: 非线性声学。
† 通信作者 E-mail: anzhiwu@mail.ioa.ac.cn