Numerical method for modelling wave propagation in waveguide structures of arbitrary cross-section

The present formulation is based on the Semi-Analytical Finite Element (SAFE) method. This numerical method is used to model ultrasonic wave propagation in waveguides of arbitrary cross-section. A waveguide is a structure that guides waves. Examples of waveguides are shown in Figure 1. It can be seen that a vast majority of structures can be considered waveguides, including plates, tubes, cables, pipes, multilayers and railroad tracks. The method requires the finite element discretization of the cross-section of the waveguide, and assumes 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. The (dispersive) wave solutions are obtained in terms of phase velocity, group velocity (for undamped media), energy velocity (for damped media), attenuation, and crosssectional mode shapes. Response to an arbitrary excitation can be also predicted, both in the time domain and in the frequency domain. Knowledge of these properties is important in any structural health monitoring attempt that uses ultrasonic guided waves, which are gaining increasing interest for monitoring aerospace, civil, naval and mechanical structures. Some results obtained by the proposed SAFE method are shown for several waveguides, including anisotropic viscoelastic layered plates, composite-to-composite adhesive joints and railroad tracks.