Interpreting material anisotropy through the fractional wave equation

In the fields of structural health monitoring and non-destructive evaluation (NDE), guided waves are often used for detection of material and structural defects. In this research, we have developed a comprehensive understanding of the generalized superelliptical form of the 2D scalar wave (Helmholtz) equation to predict structural features in anisotropic materials. The exponent of the terms in the superelliptical wave equation was systematically varied, while simultaneously varying the ratio of the wave velocities in two orthogonal directions, to develop 3D maps of wave propagation characteristics in the wavenumber domain as a function of frequency. These wave profiles were then interpreted to reveal structural features and material anisotropy. To validate these predictions, an experimental scheme was designed where a piezoelectric sensor excites a thin specimen, and the ensuing guided wave propagation features were captured on several materials using a laser Doppler vibrometer. The resulting responses in the wavenumber domain were compared against the predicted profiles and a good agreement was observed. Thus, the understanding developed from the superelliptical wave equation and its relationship to a material's anisotropic structure were experimentally validated on an isotropic material, a uniaxial fiber reinforced composite, and three biaxial composites with different ratios of fiber and matrix stiffnesses. The proposed framework based on guided wave propagation of ultrasonic waves is shown to be a valuable tool to identify structural anisotropy.