Modal Decomposition of Acoustic Emissions from Pencil-Lead Breaks in an Isotropic Thin Plate.

Acoustic emission (AE) testing and Lamb wave inspection techniques have been widely used in non-destructive testing and structural health monitoring. For thin plates, the AEs arising from structural defect development (e.g., fatigue crack propagation) propagate as Lamb waves, and Lamb wave modes can be used to provide important information about the growth and localisation of defects. However, few sensors can be used to achieve the in situ wavenumber-frequency modal decomposition of AEs. This study explores the ability of a new multi-element piezoelectric sensor array to decompose AEs excited by pencil lead breaks (PLBs) on a thin isotropic plate. In this study, AEs were generated by out-of-plane (transverse) and in-plane (longitudinal) PLBs applied at the edge of the plate, and waveforms were recorded by both the new sensor array and a commercial AE sensor. Finite element analysis (FEA) simulations of PLBs were also conducted and the results were compared with the experimental results. To identify the wave modes present, the longitudinal and transverse PLB test results recorded by the new sensor array at five different plate locations were compared with FEA simulations using the same arrangement. Two-dimensional fast Fourier Transforms were then applied to the AE wavefields. It was found that the AE modal composition was dependent on the orientation of the PLB direction. The results suggest that this new sensor array can be used to identify the AE wave modes excited by PLBs in both in-plane and out-of-plane directions.

Using reciprocity to derive the far field displacements due to buried sources and scatterers.

It is shown that elastodynamic reciprocity provides a simpler approach for deriving the far-field displacements due to buried (sub-surface) sources in a half-space, compared with integral transform techniques. The auxiliary fields employed in this approach are the fields associated with the reflection of plane waves of the three possible polarisations, and the required far field can be expressed in terms of these well-known auxiliary fields. The crucial step in this approach is to evaluate a surface integral involving cross-work terms between an outgoing spherical wavefront and the auxiliary fields consisting of incident and reflected plane waves. This integral can be evaluated by the stationary phase approximation for the two-dimensional case, or by a generalisation of this approximation for the three-dimensional case. Although this evaluation involves several distinct contributions, the final result is shown to be very simple, and it can be interpreted as a generalisation of a known result for the one-dimensional case, whereby the net contribution arises only from counter-propagating waves of the same mode. The results derived for a buried force are extended to the case of buried cracks by exploiting the body force equivalents for displacement discontinuities across a surface.

An extended diffraction tomography method for quantifying structural damage using numerical Green's functions.

Existing damage imaging algorithms for detecting and quantifying structural defects, particularly those based on diffraction tomography, assume far-field conditions for the scattered field data. This paper presents a major extension of diffraction tomography that can overcome this limitation and utilises a near-field multi-static data matrix as the input data. This new algorithm, which employs numerical solutions of the dynamic Green's functions, makes it possible to quantitatively image laminar damage even in complex structures for which the dynamic Green's functions are not available analytically. To validate this new method, the numerical Green's functions and the multi-static data matrix for laminar damage in flat and stiffened isotropic plates are first determined using finite element models. Next, these results are time-gated to remove boundary reflections, followed by discrete Fourier transform to obtain the amplitude and phase information for both the baseline (damage-free) and the scattered wave fields. Using these computationally generated results and experimental verification, it is shown that the new imaging algorithm is capable of accurately determining the damage geometry, size and severity for a variety of damage sizes and shapes, including multi-site damage. Some aspects of minimal sensors requirement pertinent to image quality and practical implementation are also briefly discussed.

Mindlin plate theory for damage detection: imaging of flexural inhomogeneities.

The scattering of plate waves by localized damage or defects that can be modeled as flexural inhomogeneities is examined within the framework of Mindlin plate theory. These inhomogeneities are characterized by variations in one or more of the four plate-theory parameters: the bending stiffness, shear stiffness, rotary inertia, and transverse inertia. It is shown that the Born approximation for the scattered field leads to a plate-theory analog of the Fourier diffraction theorem, which relates the far-field scattering amplitude to the spatial Fourier transform of the inhomogeneity variations. The application of this result is illustrated by using synthetic data derived for an idealized model of a delamination as a flexural inhomogeneity, ignoring mode coupling effects. A computationally efficient implementation of the filtered back-propagation algorithm, based on the eigensystem of the scattering operator, is employed for image reconstruction. The implications for in-situ imaging of structural damage in plate-like structures are briefly discussed, and some directions for further work are indicated.