Application of state vector formalism and Legendre polynomial hybrid method in the longitudinal guided wave propagation analysis of composite multi-layered pipes

In this research, we applied a polynomial hybrid approach for modeling 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. (C) 2020 Elsevier B.V. All rights reserved.