Abstract In this research, we applied a polynomial hybrid approach for modelling longitudinal guided waves propagating in anisotropic composites multi-layered pipes. Theoretically, dispersion characteristic equations in cylindrical coordinate system were derived by introducing the state vector form of displacement and stress components. In virtue of the orthogonality completeness and recursion properties of Legendre polynomial series, the dispersion curves of longitudinal guided waves for arbitrary multi-layered anisotropic pipes can be obtained efficiently and accurately. As an alternative serial approach, it solves the wave propagation problem of complex anisotropic cylinders, and also avoids the tedious integral operations in the traditional Legendre polynomial method. The reliability of the numerical results of longitudinal guided waves propagating in arbitrary multi-layered anisotropic pipes was investigated based on the state matrix and Legendre polynomial hybrid method. At first, we calculated the multi-layered pipes composed of isotropic materials (steel and aluminum) with different diameter-thickness ratios and circumferential orders, and the results are consistent with the ones from the global matrix method. Then, the numerical analysis for a triple-layered adhesive pipe was implemented. Finally, the composite multi-layered pipes with at most 16 layers, which are the T300/914 in different orientations, were studied. Meanwhile, the effect of the layer number, fiber angle and circumferential order on the propagation characteristics of longitudinal guided waves were analyzed. To demonstrate the generality of this approach, we compared the dispersion curves of flat plate case with the results from the cylindrical case using the same physical properties by making the geometrical diameter to thickness ratio infinity. Furthermore, the displacements and stress distributions were also illustrated at given frequencies.

中文翻译：

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状态向量形式和勒让德多项式混合方法在复合多层管纵向导波传播分析中的应用

摘要 在这项研究中，我们应用多项式混合方法对在各向异性复合材料多层管道中传播的纵向导波进行建模。理论上，通过引入位移分量和应力分量的状态向量形式，推导出柱坐标系下的频散特征方程。利用勒让德多项式级数的正交完备性和递归性，可以高效准确地得到任意多层各向异性管道纵向导波的频散曲线。作为一种替代的串行方法，它解决了复杂各向异性圆柱体的波传播问题，也避免了传统勒让德多项式方法中繁琐的积分运算。基于状态矩阵和勒让德多项式混合方法研究了纵向导波在任意多层各向异性管道中传播数值结果的可靠性。首先，我们计算了由不同径厚比和周向阶数的各向同性材料（钢和铝）组成的多层管，结果与全局矩阵法的结果一致。然后，对三层胶管进行了数值分析。最后，研究了最多16层的复合多层管，即不同取向的T300/914。同时分析了层数、光纤角度和周向顺序对纵向导波传播特性的影响。为了证明这种方法的通用性，我们通过使几何直径与厚度之比无穷大，将平板外壳的色散曲线与使用相同物理特性的圆柱形外壳的结果进行了比较。此外，还说明了给定频率下的位移和应力分布。