Interpreting material anisotropy through the fractional wave equation.

Area of Science:

• Physics
• Materials Science
• Engineering

Background:

• Guided waves are crucial for structural health monitoring and non-destructive evaluation (NDE).
• Detecting material and structural defects often relies on analyzing wave propagation.
• Anisotropic materials present unique challenges in wave propagation analysis.

Purpose of the Study:

• To develop a comprehensive understanding of the generalized superelliptical wave equation for predicting structural features in anisotropic materials.
• To establish a framework for interpreting wave propagation characteristics to reveal material anisotropy.
• To experimentally validate the predictive capabilities of the superelliptical wave equation.

Main Methods:

• Systematically varied the exponent in the superelliptical wave equation and the ratio of wave velocities in orthogonal directions.
• Developed 3D maps of wave propagation characteristics in the wavenumber domain as a function of frequency.
• Employed a piezoelectric sensor to excite guided waves and a laser Doppler vibrometer to capture wave propagation in various materials.

Main Results:

• Interpreted wave profiles to reveal structural features and material anisotropy.
• Observed good agreement between predicted wave profiles and experimental results in the wavenumber domain.
• Successfully validated the framework on isotropic, uniaxial, and biaxial composite materials.

Conclusions:

• The superelliptical wave equation provides valuable insights into the relationship between wave propagation and material anisotropy.
• The proposed framework is a powerful tool for identifying structural anisotropy using guided ultrasonic waves.
• Experimental validation confirms the utility of this approach for material characterization in NDE applications.