Analysis of Longitudinal Guided Wave Propagation in the Functionally Graded Hollow Cylinder Using State-Vector Formalism and Legendre Polynomial Hybrid Approach
Analysis of Longitudinal Guided Wave Propagation in the Functionally Graded Hollow Cylinder Using State-Vector Formalism and Legendre Polynomial Hybrid Approach
复制标题
使用状态向量形式和勒让德多项式混合方法分析功能梯度空心圆柱体中的纵向导波传播
DOI：
10.1007/s10921-021-00764-y
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发表时间：
2021
影响因子：
2.8
通讯作者：
He Cunfu
中科院分区：
文献类型：
--
作者：
Gao Jie;Lyu Yan;Zheng Mingfang;Liu Mingkun;Liu Hongye;Wu Bin;He Cunfu
提出了一种分析功能梯度材料(FGM)中空柱中导波传播行为的数值方法。基于三维线弹性理论，将位移和应力分量的状态矩阵形式引入到微分方程组中。结合边界条件，可建立色散特征方程。同时，考虑到勒让德级数的正交完备性，避免了先验方程的穷举求根，并利用其递归性质将冗余的积分算子转化为解析表达式。此外，它不仅不需要对FGM进行分层，还可以引入一元非线性回归来模拟任意的梯度分布，并利用递归性质将冗余的积分算子转化为解析表达式。需要指出的是，系数矩阵只由零项和常数项组成，这些项与弹性常数和归一化波数有关。为同时提取色散曲线、位移分布和应力分布提供了一种快速有效的方法。同时，该方法可以摆脱穷举寻根算法，从而同时区分不同的模式和频散曲线。最后实现了功能梯度材料空心圆柱体纵向导波频散曲线的典型非分层计算。通过与勒让德多项式方法得到的数据进行比较，进一步证明了该方法的准确性。研究了铁基氧化铝功能梯度材料圆柱体的几个数值算例，并讨论了多项式逼近的收敛问题。然后分析了周向波数、梯度变化、径厚比对色散特性的影响。此外，还详细讨论了在给定频率下F(1，1)振型的位移和应力分布特征。结果表明，状态矢量法和勒让德多项式混合方法是求解功能梯度材料弹性圆柱体波动问题的有力工具，为功能梯度圆柱体的梯度结构特性的无损评价和定量表征奠定了理论基础。
A numerical approach for analyzing the guided wave propagation behavior in a functionally graded material (FGM) hollow cylinder is presented. Based on the three-dimensional linear elasticity theory, the state matrix form of displacement and stress component is introduced into the differential governing equation. Combining with boundary conditions, the dispersion characteristic equations can be constructed. Meanwhile, taking the orthogonal completeness of Legendre series into consideration, the exhausting root findings of transcendental equation can be avoided, and it transforms the redundant integral operators into analytical expressions by means of its recursive properties. Moreover, it is not only unnecessary to stratify FGMs, and introducing the univariate nonlinear regression to modelling the arbitrary gradient distribution, and transforming the redundant integral operator into an analytical expression by means of recursive property. It should be pointed out that the coefficient matrix consists only zero and constant terms, which are related to the elastic constants and normalized wave number. And it provides a fast and effectively approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Meanwhile, the proposed method can get rid of the exhausted root-finding algorithm, and accordingly distinguish the different modes and the dispersion curves simultaneously. Finally, the typical non-stratified computation of dispersion curves of longitudinal guided wave for FGM hollow cylinder is realized. The accuracy of the proposed method is further demonstrated through comparison with the available data from Legendre polynomial method. Several numerical cases about iron based alumina FGM cylinder are studied, and the convergence of the present polynomial approach is discussed. Then the effect of the circumferential wave number, gradient variation, diameter-thickness ratio on the dispersion characteristics are illustrated. Moreover, the distribution characteristics of displacement and stress profiles of F(1,1) mode at a given frequency are discussed in detail. It is shown that the state-vector formalism and Legendre polynomial hybrid approach is a powerful tool in solving wave motions in FGM elastic cylinder, which lays a theoretical foundation for the non-destructive evaluation and quantitative characterization of the gradient structure characteristics of functionally graded hollow cylinder.