Applied Mathematics and Mechanics >
Mathematical framework of nonlinear elastic waves propagating in pre-stressed media
Received date: 2024-05-25
Online published: 2024-09-27
Supported by
the National Natural Science Foundation of China(12134002);Project supported by the National Natural Science Foundation of China (No. 12134002)
Copyright
Acoustic nonlinearity holds potential as a method for assessing material stress. Analogous to the acoustoelastic effect, where the velocity of elastic waves is influenced by third-order elastic constants, the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants. Despite this, there has been a notable absence of research exploring this phenomenon. Consequently, this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials. It delves into the impact of pre-stress on higher-order material parameters, and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress. This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.
Jiangcheng CAI, Mingxi DENG . Mathematical framework of nonlinear elastic waves propagating in pre-stressed media[J]. Applied Mathematics and Mechanics, 2024 , 45(10) : 1705 -1716 . DOI: 10.1007/s10483-024-3176-7
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