A unified formulation for guided-wave propagation in multi-layered mixed anisotropic-isotropic hybrid aerospace composites

A unified approach was formulated to predict guided-wave propagation in a material regardless its degree of anisotropy, thereby having one solution method for both isotropic and anisotropic material. The unified approach was based on the coupled eigenvalue problem derived from Chirstoffels equation for a lamina. The eigenvalue problem yielded a set of eigenvalues, and corresponding eigenvectors that were used to obtain the stress-displacement matrix. The dispersion curves were obtained by applying the traction free boundary conditions to the stress-displacement matrix, and searching for sign changes in the complex determinant of the matrix. To search for sign changes, hence the velocity-wavenumber pairs which yielded a solution to the problem, the real and imaginary part of the complex determinant had to change sign simultaneously. A phase angle approach was, therefore, developed and successfully applied. A refinement algorithm was applied to refine the accuracy of the solution without increasing the computational time significantly. A high accuracy was required to calculated the correct partial-wave participation factors. The obtained partial-wave participation factors were used to calculate the modeshape through the thickness for each velocity-wavenumber pair. To identify the different wave types, A0, S0, SHS0, SHA0, a modeshape identification was applied successfully. The unified approach was evaluated for hybrid aerospace composites. In addition, the two most common solution methods: (i) the global matrix method; and (ii) the transfer matrix method were applied, and a comparative study between the different methods was performed.