Numerical modeling and measurement by pulsed television holography of ultrasonic displacement maps in plates with through-thickness defects

Abstract

Abstract. We present a novel numerical modeling of ultrasonic Lamb and Rayleigh wave propagation and scattering by through-thickness defects like holes and slots in homogeneous plates, and its experimental verification in both near and far field by a self-developed pulsed TV holography system. In contrast to rigorous vectorial formulation of elasticity theory, our model is based on the 2-D scalar wave equation over the plate surface, with specific boundary conditions in the defects and plate edges. The experimental data include complex amplitude maps of the out-of-plane displacements of the plate surface, obtained by a two-step spatiotemporal Fourier transform method. We find a fair match between the numerical and experimental results, which allows for quantitative characterization of the defects.

An FC-based spectral solver for elastodynamic problems in general three-dimensional domains

“…The thin-plate scattering applications considered in this section are motivated by a collaboration with our co-authors in [25]; corresponding laboratory experiments were performed by these colleagues at the University of Vigo in Spain. The contribution [25] presents a quantitative characterization of defects in aluminum plates by comparison between experimental and simulated (numerical) scattering patterns of narrow-band guided waves with circular and rectangular holesalbeit with a simplified mathematical model based on use of scalar waves on a two-dimensional domain.…”

“…In the present section we revisit this problem, but we tackle the numerical simulation problem by means of our full three-dimensional elastic wave solver. The incident waves in these laboratory experiments were generated by means of the wedge method described in [25]: the longitudinal wave emitted by a piezoelectric transducer was coupled to the surface of a thin plate through a prismatic coupling block. In the experiments under consideration the piezoelectric source was excited in such a way that the guided wave trains had a frequency of f = 1 MHz and were quasi-monochromatic with wavelength λ = 2.96mm, yielding a Rayleigh phase velocity c = λf = 2960 m/s.…”

“…In the experiments under consideration the piezoelectric source was excited in such a way that the guided wave trains had a frequency of f = 1 MHz and were quasi-monochromatic with wavelength λ = 2.96mm, yielding a Rayleigh phase velocity c = λf = 2960 m/s. The instantaneous out-of-plane displacement field u 2 (x, t) due to the propagation of the guided wavetrain were obtained by means of a novel double-pulsed TV holography system-details can be found in [18,25,30]. For our numerical experiments we use analytical representations provided by our collaborators for the experimentally observed Dirichlet boundary condition on the left edge of the computational domain, representing small wave-trains incident on a circular hole of diameter 12mm centered in a plate of thickness 10mm.…”

Transient elastic wave propagation and scattering in plates: comparison between pulsed TV-holography measurements and finite element method predictions

“…CCD ca me ra Fre quency doubler To specify the stress-free boundary conditions at the hole border it would be neccessary, in general, to consider SH and Lamb evanescent modes and associated conversion effects. Nevertheless, for the particular case of quasi-Rayleigh waves we follow the same approach that in our previous works 11,12 assuming, as a first approximation, that stress-free condition at the hole boundary can be described by the homogeneous Neumann boundary condition ∂û…”

“…9,10 Exploring this last possibility, we have succeeded in obtaining a quantitative description of the scattering of Rayleigh-Lamb waves produced by holes and slots in harmonic regime using the scalar Helmholtz equation. 11,12 In this work, a similar modelling approach is employed to characterize equivalent scattering phenomena but in transient regime. We first establish the framework for the scalar model and the nomenclature.…”