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How does it look like?

Fig. 1: Input panel for generic cross-sections.

Fig. 2: Solver panel for pipes.

Fig. 3: Output panel.

What are guided waves? What is GUIGUW?

Guided ultrasonic waves (GUWs) provide a highly efficient method for the non-destructive evaluation (NDE) and the structural health monitoring (SHM) of waveguides such as beam-like or plate-like structures. Compared to ultrasonic bulk waves, the use of GUWs provides: (a) longer inspection range, (b) larger versatility owing to dispersive and multimodal nature and (c) complete coverage of the waveguide cross-section. These advantages can be fully exploited only once the complexities of guided wave propagation are unveiled and managed for the given test structure.

These complexities include the existence of multiple modes that can propagate simultaneously, and the frequency-dependent velocities and attenuation (dispersive behavior). For example, the knowledge of the wave velocity is important for mode identification. Similarly, the knowledge of those mode–frequency combinations propagating with minimum attenuation losses helps maximizing the inspection coverage.

To date, Semi-Analytical Finite Element (SAFE) formulations are among the available tools for modeling GUWs propagation.

SAFE algorithms are efficient tools to extract the spectrum (dispersion curves) of waveguides with geometrical and mechanical properties constant along the wave propagation direction. The key point of these formulations is the hybrid displacement field adopted to describe the motion of a propagative guided wave. A transient wave is described, in fact, coupling a mono- or bi-dimensional finite element mesh over the waveguide cross-section and harmonic functions along the wave propagation direction. Then, a displacement-based variational scheme leads the governing wave equation to be defined by a system of algebraic equations, with wave frequency and wavenumber as unknowns. The waveguide modal spectrum is next obtained solving the homogenous part of the wave equation by using standard routines for eigenvalue problems. The main advantages in the calculation of waveguides spectrum via SAFE formulations are: no missing roots; capability to handle waveguides of arbitrary cross-section; possibility to model high degree anisotropic waveguides with no extra effort; fast and reliable high frequency computation.

The unique characteristics of SAFE formulations can also be exploited for the construction of the time–transient response of waveguides excited by a time-varying load. Time–transient response is essential to actuators design, quantitative non-destructive evaluation of cracks size and location as well as for structural health monitoring purposes. In brief, the SAFE formulated time–transient response at a point can be obtained by means of the inverse Fourier transform, that turns into the time domain the waveguide frequency response calculated as a summation of the modal data contribution at that point weighted with the spectrum of applied load. The advantages Compared to analytically based time–transient responses, generally limited to isotropic waveguides with standard cross-section geometries, SAFE-based formulations can also handle waveguides with high anisotropy and arbitrary cross-section. In respect to a 3D finite element (FE) guided waves simulation, SAFE-based time–transient response presents enormous computational, time and memory saving. This is true, in particular, for high frequency computations, where the wavelengths are small and an accurate prediction by FE procedures involves an intensive three-dimensional discretization, as well as for simulations of long propagation, where, even for modest frequency values, the required number of finite elements to support the simulation could be too large.