Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of fluid-loaded functionally gradient plates
Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of fluid-loaded functionally gradient plates
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计算载液功能梯度板反射和透射系数的勒让德正交多项式法
DOI：
10.1016/j.wavemoti.2021.102754
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发表时间：
2021-05-13
期刊：
影响因子：
2.4
通讯作者：
Lee, Yungchun
中科院分区：
文献类型：
--
作者：
Gao, Jie;Lyu, Yan;Lee, Yungchun
基于勒让德正交多项式级数展开和分波理论，提出一种勒让德正交多项式法（LOPM）来计算载液功能梯度材料（FGM）板液/固界面处平面波的反射和透射系数。 FGM 板的位移解通过勒让德正交多项式级数近似拟合。推导了 FGM 板的应力和控制微分方程。根据液/固界面的边界条件和控制微分方程，建立线性独立方程来计算反射系数和透射系数。同时，还得到了Legendre正交多项式的展开系数。幂函数建立了力学参数沿厚度方向的梯度模型。 LOPM的反射和透射系数的角谱与传递矩阵法的计算结果非常吻合。通过分析反射系数谱的收敛性，确定了勒让德正交多项式截断阶数的临界值。可以同时展示FGM梯度模型与反射系数角谱、频谱和位移/应力分布之间的映射关系，为FGM力学性能的超声无损检测提供了理论基础，扩展了LOPM的应用。 (C) 2021 Elsevier B.V. 保留所有权利。
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.