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作者:

Jie, Gao (Jie, Gao.) | Yan, Lyu (Yan, Lyu.) | Guorong, Song (Guorong, Song.) | Mingkun, Liu (Mingkun, Liu.) | Mingfang, Zheng (Mingfang, Zheng.) | Cunfu, He (Cunfu, He.) | Yungchun, Lee (Yungchun, Lee.)

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摘要:

Based on the Legendre orthogonal polynomial series expansion and the partial wave theory, a Legendre orthogonal polynomial method (LOPM) is proposed to calculate the reflection and transmission coefficients of plane waves at the liquid/solid interface of a liquid-loaded functionally gradient material (FGM) plate. The displacement solutions in FGM plate are fitted approximately by Legendre orthogonal polynomial series. The stresses and the governing differential equations of the FGM plate are derived. Based on the boundary conditions of the liquid/solid interface and the governing differential equations, the linearly independent equations are set up to calculate the reflection and transmission coefficients. Meanwhile, the expansion coefficients of the Legendre orthogonal polynomials are also obtained. The power function establishes the gradient model of the mechanical parameters along the thickness direction. The angular spectrums of reflection and transmission coefficients from LOPM are in well agreement with the calculation results from the transfer matrix method. By analyzing the convergence of the reflection coefficient spectrum, the critical value of the truncated order of Legendre orthogonal polynomials is determined. The mapping relationship between the FGM gradient models and the reflection coefficient angular spectrum, also the frequency spectrums and the displacement/stress distributions can be demonstrated simultaneously, which provides the theoretical fundamentals of the ultrasonic non-destructive testing for the mechanical properties of FGM and extends the application of the LOPM. (C) 2021 Elsevier B.V. All rights reserved.

关键词:

Reflection and transmission coefficients Legendre orthogonal polynomials Displacement and stress distribution FGM plate Truncated order

作者机构:

  • [ 1 ] [Jie, Gao]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 2 ] [Yan, Lyu]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 3 ] [Guorong, Song]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 4 ] [Mingkun, Liu]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 5 ] [Cunfu, He]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 6 ] [Yungchun, Lee]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China
  • [ 7 ] [Mingkun, Liu]Beihang Univ, Sch Instrumentat & Optoelect Engn, Beijing, Peoples R China
  • [ 8 ] [Mingfang, Zheng]Dongguan Univ Technol, Sch Environm & Civil Engn, Dongguan 523808, Peoples R China
  • [ 9 ] [Yungchun, Lee]Cheng Kung Univ, Dept Mech Engn, Tainan, Taiwan

通讯作者信息:

  • [Yan, Lyu]Beijing Univ Technol, Fac Mat & Mfg, Beijing, Peoples R China

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来源 :

WAVE MOTION

ISSN: 0165-2125

年份: 2021

卷: 104

2 . 4 0 0

JCR@2022

ESI学科: PHYSICS;

ESI高被引阀值:72

JCR分区:2

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