初始应力与非线性弹性耦合作用下弹性波的传播特性研究

糜鸿锐; 李文强; 胡恒山

doi:10.21656/1000-0887.470002

初始应力与非线性弹性耦合作用下弹性波的传播特性研究

doi: 10.21656/1000-0887.470002

1. 昆明理工大学建筑工程学院，昆明 650500;
2. 哈尔滨工业大学航天科学与力学系，哈尔滨 150001

基金项目:

云南省基础研究计划(202501CF070160)；国家自然科学基金(12272107)

详细信息

作者简介:
糜鸿锐（2003—），男，硕士生（E-mail: mhr170124@163.com）;李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）；胡恒山（1963—），男，教授，博士，博士生导师（E-mail: hhs@hit.edu.cn).

通讯作者:
李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）

中图分类号: O34
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出版历程
- 收稿日期: 2026-01-04
- 修回日期: 2026-02-12
- 网络出版日期: 2026-07-03
- 刊出日期: 2026-06-01

Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves

1. Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, P.R. China;
2. Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P.R. China

Funds:

The National Science Foundation of China(12272107)

摘要

摘要: 初始应力场与介质的非线性特性会影响弹性波在固体介质中的传播行为，准确表征受初始应力介质中弹性波的传播规律对于应力无损检测、结构健康监测及地球物理勘探等具有重要的意义.目前研究对初始应力相关的几何非线性（有限变形）与物理非线性如何影响弹性波的传播还缺乏清晰认识.本研究基于声弹性理论，建立了耦合有限的初始变形与物理非线性的弹性波传播理论框架，并通过摄动近似方法获得体波相速度的近似解析解，为快速计算受初始应力介质中弹性波的传播提供有效手段.此外，通过求解平面波的特征方程并进行对比分析，系统揭示了初应力场与非线性弹性耦合效应作用下的弹性波传播规律.研究结果表明，初始应力对弹性波传播的影响是几何非线性效应与物理非线性效应竞争的结果.在拉伸初始应力作用下，几何非线性会使弹性波速度提高，而物理非线性会使弹性波速度降低.物理非线性效应使得初始应力产生更显著的体波相速度改变及横波各向异性，在7075-T651铝合金材料中，横波各向异性程度A_S可达到2%～3%.
- 初始应力 /
- 声弹性理论 /
- 弹性波传播 /
- 几何非线性与物理非线性 /
- 摄动理论
Abstract: The propagation of elastic waves in solids is influenced by initial stresses and material nonlinearity. Accurately characterizing the propagation of elastic waves in initially stressed media is crucial for stress nondestructive testing, structural health monitoring, and geophysical exploration. However, the distinct roles of stressrelated geometric nonlinearity and material nonlinearity remain unclear. A theoretical framework based on acoustoelasticity and coupling finite initial deformation with material nonlinearity was developed. Approximate analytical solutions for the phase velocities of body waves were derived with the perturbation theory, to give an efficient approach for the rapid calculation of elastic wave propagation in initial stress media. Furthermore, the characteristic equation was solved for plane waves, the coupled effects of initial stress and nonlinear elasticity were systematically analyzed. The results show that, the effects of initial stresses stem from the competition between geometric and physical nonlinearity. Under tensile initial stresses, geometric nonlinearity will increase wave speeds, while physical nonlinearity will decrease them. Physical nonlinearity induces more pronounced changes in phase velocity and velocity anisotropy of shear waves. For the 7075-T651 aluminum alloy, the shear wave anisotropy reaches 2%~3%.
- initial stress /
- acoustoelastic theory /
- elastic wave propagation /
- geometrically and physically nonlinearity /
- perturbation theory

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参考文献(33)

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初始应力与非线性弹性耦合作用下弹性波的传播特性研究

doi: 10.21656/1000-0887.470002

作者简介:
糜鸿锐（2003—），男，硕士生（E-mail: mhr170124@163.com）;李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）；胡恒山（1963—），男，教授，博士，博士生导师（E-mail: hhs@hit.edu.cn).

通讯作者:
李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）

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Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves

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留言板

初始应力与非线性弹性耦合作用下弹性波的传播特性研究

doi: 10.21656/1000-0887.470002

作者简介: 糜鸿锐（2003—），男，硕士生（E-mail: mhr170124@163.com）;李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）；胡恒山（1963—），男，教授，博士，博士生导师（E-mail: hhs@hit.edu.cn).

通讯作者: 李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）

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出版历程

Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves

计量

出版历程

目录

作者简介:
糜鸿锐（2003—），男，硕士生（E-mail: mhr170124@163.com）;李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）；胡恒山（1963—），男，教授，博士，博士生导师（E-mail: hhs@hit.edu.cn).

通讯作者:
李文强（1994—），男，讲师，博士，硕士生导师（通信作者. E-mail: wqli@kust.edu.cn）