Two analytical modifications of the original viscoelastic time-harmonic Lamb’s problem
expressions are presented with the aim of improving their numerical integration efficiency.
Firstly, a new change of variable in the Lamb’s problem integrands is proposed, which
allows a standardization of the integration sampling vector and a complete spatialfrequency
field solution after performing only one numerical integration/transformation.
Secondly, the Lamb’s problem static integrands are modified and introduced into the
original integrands to reduce their spectral content at high wavenumbers and, therefore,
the sampling vector lengths needed to avoid aliasing.
A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious reflections of non-decaying Rayleigh waves introduced by the truncation of the boundary. The proposed method exploits the knowledge of the far-field asymptotic behavior of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution exclusively in terms of the boundary integrals of the original BEM system. The method is applied to the study of the acoustic emission from nucleating and propagating surface-breaking and buried cracks in a two-dimensional elastic half-space. It is shown to be particularly advantageous since it allows for an accurate calculation of the generated signal even when the observation point is located far from the acoustic emission source.
A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection of small surface-breaking cracks. The generated ultrasonic signal is monitored as a line-focused laser is scanned over the defect. Characteristic changes in the amplitude and the frequency content are observed. The modeling approach is based on the decomposition of the field generated by the laser in a cracked two-dimensional half-space, by virtue of linear superposition, into the incident and the scattered fields. The incident field is that generated by laser illumination of a defect-free half-space. A thermoelastic model has been used which takes account of the effect of thermal diffusion, as well as the finite width and duration of the laser source. The scattered field incorporates the interactions of the incident field with the surface-breaking crack. It has been analyzed numerically by a direct frequency domain boundary element method. A comparison with an experiment for a large defect shows that the model captures the observed phenomena. A simulation for a small crack illustrates the ability of the SLS technique to detect defects smaller than the wavelength of the generated Rayleigh wave.