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We introduce a novel approach that combines the scaled boundary finite element method (SBFEM) with a mortar coupling to enhance the computational modelling of elastic wave propagation and interaction with local features in the ultrasonic range. The key objective is to achieve decoupling between different regions of interest, enabling independent meshes for the zones where waves either propagate or interact with localised discontinuities in the elastic media. This decoupling allows us to exploit the benefits offered by various SBFEM formulations. Thus, we can select the most suitable solution for each specific region. An important concept we emphasise is the differentiation between the near field and far field regions. The near field encompasses zones where the precise representation of small features compared to the wavelength is crucial. At the same time, the far field comprises homogeneous regions where the waves propagate without interactions, eventually radiating towards infinity if the domain is unbounded. By separating these two zones, we can improve the computational performance by employing finer discretisation only where necessary. Furthermore, this decoupling enables the reuse of far field models in parametric analyses, making it highly valuable for scenarios focused particularly on local elastic wave interactions. This approach offers considerable potential in such cases. The modelling technique is validated, and its potential is demonstrated through practical applications.
It can be difficult to efficiently model ultrasonic waves in 3D structures, especially when the computational model needs to account for complex geometries. This contribution presents a solution based on the Scaled Boundary Finite Element Method (SBFEM). It is a numerical tool suitable for elastodynamic problems. A space-tree discretisation, namely quad-trees, is used. This technique allows the decomposition of an image into quadrilaterals or quads, which are extruded to generate the 3D plate geometry. In particular, small quads resolve regions with discontinuities, allowing them to represent fine details in the structure. Moreover, this meshing technique allows for exploiting cell similarities, making the calculation procedure more efficient. The space-tree discretisations are generated from a high-resolution image containing all the information about damaged regions or boundary conditions. The resulting SBFEM polyhedral domains employ transition elements to ensure correct coupling between cells of different sizes. The analytical solution of a cylindrical scatterer serves as a reference to validate the proposed approach. Other examples also demonstrate the validity of the methodology and its flexibility.
Wavefield measurements by a scanning laser Doppler vibrometer are generally carried out in a cartesian coordinate. As a piezoelectric transducer generates Lamb waves following radial paths, the use of a polar coordinate can be a suitable alternative to the use of a cartesian coordinate. Therefore, in the proposed method, using a single transducer placed on the center of the specimen, the measured wavefields are transformed into polar coordinates, making several identical radial line inspections from the center in a direction of incident waves. Taking advantage of the properties of the polar coordinates, a signal processing technique is proposed through a frequency-wavenumber filtering process in these coordinates. In this technique, by using proper filters, unwanted wave modes of the incident wave along with all reflected waves are filtered out. In addition, the conventional features of RMS and Euclidean distance are adapted for the polar coordinate system to image the bonded plate. The proposed signal processing and damage imaging are first introduced through a numerical simulation. Then, the performance of the proposed technique is presented by experimental measurements of two specimens including adhesively bonded carbon fiber-reinforced plastic composite plates and bonded aluminum plates.