An improved analytical method to overcome convergence issues in composites guided wave prediction

In this research, at first, several general analytical methods such as global matrix method (GMM), transfer matrix method (TMM) and stiffness matrix method (SMM) were employed to predict the guided waves in composites. It was found that GMM is more stable over other methods. However, GMM has missing roots at high frequency. Other methods such TMM provides spurious roots at high frequency and SMM has some missing roots at low frequency despite having computationally efficient. Therefore, an improved analytical method was implemented to calculate wavenumbers corresponding to propagating, evanescent and complex guided wave mode of composite materials. The evanescent and complex wavenumber guided wave modes are very important in studying the interaction between the guided waves and composite damage. The generic analytical method may not work efficiently for finding threedimensional complex wavenumber, frequency roots in composite materials. Christoffel's equation for composite lamina was used to obtain the eigenvalues and eigenvectors. The eigenvalues and eigenvectors were used to calculate state vectors and field matrix. In this improved analytical method, the exponential part containing wavenumber of the field matrix is expanded as Taylor series expansion with respect to initial wavenumber guess. Then the problem becomes a polynomial eigenvalue problem. Upon solving the eigenvalue problem, it provides wavenumber, frequency solutions for propagating, evanescent and complex guided wave modes. The advantage of the current method is that it is computationally efficient and can provide exact stress mode shapes. As a proof case, the solution was developed first for isotropic (aluminum) materials, and the results were compared with the available analytical solution of the Rayleigh- Lamb equation. Then the solution was extended for unidirectional CFRP composites.