Modeling guided wave propagation for structural health monitoring applications

In this paper a Semi-Analytical Finite Element (SAFE) method for modeling wave propagation in waveguides of arbitrary cross-section is discussed. The method requires the finite element discretization of the cross-section of the waveguide by assuming harmonic motion along the wave propagation direction. The general SAFE technique is extended to account for viscoelastic material damping by allowing for complex stiffness matrices for the material. Phase velocity, energy velocity, attenuation, and cross-sectional mode shapes are obtained by solving an eigenvalue problem. Knowledge of these properties is important in any structural health monitoring attempt that uses ultrasonic guided waves. The proposed SAFE formulation is applied to several examples, including isotropic viscoelastic plates, composite-to-composite adhesive joints and railroad tracks.