Coupled Lamb waves propagation along the direction of non-principal symmetry axes in pre-stressed anisotropic composite lamina

Abstract

Based on the linear three-dimensional elastic theory and the mechanics theory of incremental deformation, using the Legendre orthogonal polynomial expansion (LOPE) method, the wave equations of Lamb wave propagation in the non-principal symmetry axes direction of anisotropic composite lamina was firstly derived when the initial stresses were applied in the horizontal and vertical directions. Subsequently, the coupled equations of Lamb wave propagation were numerically solved. In order to verify the accuracy of the process, the dispersion curves of phase velocity in an isotropic aluminum plate and anisotropic composite lamina without loaded initial stresses were beforehand calculated by LOPE method to compare with those obtained from the commercial software of DISPERSE® and available data. Then, a series of cases referring to unidirectional fiber reinforced composite lamina were further implemented to study the effects of horizontal initial stress and vertical initial stress on the fundamental Lamb wave modes. The results show that the phase velocity of the A0 mode is more sensitive to the implementation of initial stresses compared with the S0 mode and SH0 mode. Finally, the effect of fiber orientation was illustrated in details.