Derivation of circumferential guided waves equations for a multilayered laminate composite hollow cylinder by state-vector and Legendre polynomial hybrid formalism. (1st January 2021)

• Record Type: Journal Article
• Authors: Zheng, Mingfang; Ma, Hongwei; Lyu, Yan; Lu, Chao; He, Cunfu
• Is Part Of: Composite structures. Volume 255(2021)
• Publication Date: 2021-01-01
• Subjects: Anisotropic laminate hollow cylinder -- Circumferential guided waves -- Dispersion curve -- State vector -- Legendre polynomial; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112950
• Languages: English
• ISSNs: 0263-8223

Abstract

Highlights: A spectral method is proposed to solve circumferential guided waves (CGW) in CFRP pipe. The explicit expressions of CGW in the viscoelastic/elastic CFRP pipe are derived. The proposed method has an exponential rate of convergence. The dispersion curve and mode shape of CGW in the CFRP hollow cylinders are analyzed. Abstract: A new spectral method based on the hybrid formula system of the state-vector and Legendre polynomials are used to derive the explicit expressions of circumferential guided waves in the anisotropic multilayer composite cylinders with an arbitrary lay-up. In this hybrid method, the state vector was utilized to transform the wave equation, boundary conditions, and interface continuous conditions in the cylinder coordinate system to form the dispersion equation in terms of the state matrix. Then, following the principle of the Galerkin method, projecting the dispersion state matrix equations onto the weight functions consisting of Legendre polynomials, the system of algebraic equation is obtained. The dispersion curves and mode shape can be obtained by solving the eigenvalues and eigenvectors of the system of algebraic equations. This hybrid method uses the orthogonal and recursive properties of the Legendre polynomial to simplify the integral expressions involved in all the matrices and yields the closed-form solutions. Numerical verification, including the cases of isotropic and anisotropic viscoelastic/elastic multilayer cylinders, was conducted to evaluate the performance of the proposed method. The results show that the proposed method overcomes the cumbersome of the traditional Legendre polynomial method to treat the interface displacement and stress continuity. The results also confirm that the hybrid method has the exponential convergence.