TY - JOUR

T1 - Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of fluid-loaded functionally gradient plates

AU - Gao, Jie

AU - Lyu, Yan

AU - Song, Guorong

AU - Liu, Mingkun

AU - Zheng, Mingfang

AU - He, Cunfu

AU - Lee, Yungchun

N1 - Funding Information:
This work is supported by national Natural Science Foundation of China (Nos. 11872082 , 11972052 , 51875010 , 51905099 ).
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

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U2 - 10.1016/j.wavemoti.2021.102754

DO - 10.1016/j.wavemoti.2021.102754

M3 - Article

AN - SCOPUS:85105708514

SN - 0165-2125

VL - 104

JO - Wave Motion

JF - Wave Motion

M1 - 102754

ER -