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Abstract

The properties of ultrasonic nonlinear surface wave in the quasilinear region are investigated. In this work the governing equation of particle displacement potential is employed for surface wave in isotropic elastic solid with quadratic nonlinearity. Then, the quasilinear solution of the nonlinear surface wave is obtained by the perturbation method, and the absolute nonlinear parameter of the surface wave is derived. Subsequently, the main components of the second harmonic surface wave solution are discussed. A finite element model for the propagating nonlinear surface wave is developed, and simulation results of the nonlinear surface wave displacements agree well with the theoretical solutions, which indicates that the proposed theory is effective. Finally, the properties of wave propagation and the characteristic of the nonlinear parameter for the surface wave are analyzed based on the theoretical solutions. It is found that the second harmonic surface wave consists of cumulative and non-cumulative displacement terms. The cumulative displacement term is related to the self-interaction of the longitudinal wave component of the surface wave. However, its amplitude is larger than that of the pure longitudinal wave when the initial excitation conditions and propagation distances are the same. The nonlinear parameters for surface and longitudinal waves are related to each other, and an explicit relationship is found, which can be determined by the second-order elastic coefficients of the material. The propagation properties of nonlinear surface waves and the measurement method of absolute nonlinear parameters are also discussed, which will benefit the practical application of nonlinear surface waves.

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Authors and contacts

Corresponding author:Jia Lu,jia-lu@mail.tsinghua.edu.cn; Zhang Shu-Zeng,sz_zhang@csu.edu.cn;

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 51805554) and the Fundamental Research Fund for the Central Universities of Central South University, China (Grant No. 2021zzts0175).

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DownLoad: Full-Size Img PowerPoint

材料	$ {\rho _{\text{0}}} $/ (kg·m³)	$\lambda $/ GPa	$ \mu $/ GPa	$A$/ GPa	$B$/ GPa	$C$/ GPa
Al^[24]	2700	51	26	–350	–155	–95
Al2024^[26]	2780	56.9	27.7	–305	–146	31
Al6061^[27]	2705	59.5	26.1	–337	–129.5	16.5
Al7075^[28]	2800	54.9	26.5	–351.2	–149.4	–102.8

DownLoad: CSV

序号	传播距离r/m	频率f/MHz	基波幅值${A_1}$/nm	二次谐波幅值
序号	传播距离r/m	频率f/MHz	基波幅值${A_1}$/nm	${A_2}$/nm	$A_2^{\text{C}}$/nm	$u_{\text{l}}^{\left( 2 \right)}$/nm
1	0.2	1	1	2.91×10^–3	3.05×10^–5	3.80×10^–4
2	0.2	0.2	1	1.16×10^–4	6.11×10^–6	1.52×10^–5
3	0.2	1	5	7.28×10^–2	7.62×10^–4	9.48×10^–3
4	0.5	1	1	2.91×10^–2	1.22×10^–4	3.80×10^–3

DownLoad: CSV

材料	${\beta _{\text{l}}}$	${\beta _{\text{r}}}$	${\bar \beta _{\text{r}}}$	$ {\bar \beta _{11}} $	${\delta _{\text{R}}}$
Al	14.670	24.672	4.740	1.166	22.191
Al2024	9.680	15.799	3.044	0.674	13.892
Al6061	9.695	14.753	2.860	0.733	14.444
Al7075	13.723	22.271	4.293	1.024	21.227

DownLoad: CSV

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Vol. 71, Issue 16 - 2022-08-20

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