On the dispersion of cylinder guided waves propagating in a multilayer composite hollow cylinder made of anisotropic materials

Abstract

The formula system of the state-vector and Legendre polynomials hybrid method (SV-LPHM) was applied to produce the dispersion curves and mode shape for the general anisotropic multilayer composite cylinders with whatever the dissimilarities of the layer material properties. According to relevant literature's reports, traditional Legendre polynomial method was only able to deal with the multilayer system where the material properties of adjacent layers are not significantly changed. To overcome the drawback, we introduce the state vector method to reshape the wave equation, boundary conditions and interface continuous conditions of the multilayer hollow cylinder in a consistent manner. Moreover, expanding the displacement field by the Legendre polynomials, and then a complete and concise state matrix form is formed for dispersion equation after complex algebraic transformation. All the matrices involving the mass and stiffness have been deduced analytically by the recurrence relation and orthogonality of the Legendre polynomial. The abovementioned operation overcomes the cumbersome when applying traditional Legendre polynomial method to dealing with the interface displacement and stress continuity. Firstly, we outlined the derivation of the formalism of the hybrid method (SV-LPHM) for guided waves propagating in the anisotropic multilayer hollow cylinder with an arbitrary number of layers. And then we demonstrated the SV-LPHM technique on the composite pipe of isotropic material and anisotropic material, where the key-factors of phase speed, displacement, and stress distribution were assessed and elaborated thoroughly. The results confirm the exponential convergence of the SV-LPHM compared with finite element methods.