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In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.
Automated Wall Thickness Evaluation for Turbine Blades Using Robot-Guided Ultrasonic Array Imaging
(2024)
Nondestructive testing has become an essential part of the maintenance of modern gas turbine blades and vanes since it provides an increase in both safety against critical failure and efficiency of operation. Targeted repairs of the blade’s airfoil require localized wall thickness information. This information, however, is hard to obtain by nondestructive testing due to the complex shapes of surfaces, cavities, and material characteristics. To address this problem, we introduce an automated nondestructive testing system that scans the part using an immersed ultrasonic array probe guided by a robot arm. For imaging, we adopt a two-step, surface-adaptive Total Focusing Method (TFM) approach.
For each test position, the TFM allows us to identify the outer surface, followed by calculating an adaptive image of the interior of the part, where the inner surface’s position and shape are obtained. To handle the large volumes of data, the surface features are automatically extracted from the TFM images using specialized image processing algorithms. Subsequently, the collection of 2D extracted surface data is merged and smoothed in 3D space to form the outer and inner surfaces, facilitating wall thickness evaluation. With this approach, representative zones on two gas turbine vanes were tested, and the reconstructed wall thickness values were evaluated via comparison with reference data from an optical scan. For the test zones on two turbine vanes, average errors ranging from 0.05 mm to 0.1 mm were identified, with a standard deviation of 0.06–0.16 mm.
The Synthetic Aperture Focusing Technique (SAFT) is an algorithm applied in non-destructive ultrasonic testing which provides an image of flaws within a specimen. The image is reconstructed from A-scans measured at different positions. Reliable evaluation of the images obtained by the SAFT-algorithm, however, depends on the representation of the reconstructed data, which is initially given in terms of positive and negative local values only. A suitable way of processing this data for evaluation is to calculate the envelope, which can be achieved by means of the analytic signal. The extension of this concept to the multidimensional case is neither trivial nor unique and although extensive work on this subject has been carried out in the past, a correct envelope calculation in multidimensional data remains difficult since it depends on an additional condition, namely the separability of the signal. In this paper, the concept of analytic signals with single-quadrant spectra is applied to process 2-dimensional data obtained by the SAFT-algorithm. Furthermore, we present a procedure to overcome the limitations of that approach by selecting local magnitude values from a number of rotated frames after evaluating the signals separability in each frame, which is briefly validated against synthetic and experimental data.
Guided waves (GW) are of great interest for non-destructive testing (NDT) and structural health monitoring (SHM) of engineering structures such as for oil and gas pipelines, rails, aircraft components, adhesive bonds and possibly much more. Development of a technique based on GWs requires careful understanding obtained through modelling and analysis of wave propagation and mode-damage interaction due to the dispersion and multimodal character of GWs. The Scaled Boundary Finite Element Method (SBFEM) is a suitable numerical approach for this purpose allowing calculation of dispersion curves, mode shapes and GW propagation analysis. In this article, the SBFEM is used to analyse wave propagation in a plate consisting of an isotropic aluminium layer bonded as a hybrid to an anisotropic carbon fibre reinforced plastics layer. This hybrid Composite corresponds to one of those considered in a Type III composite pressure vessel used for storing gases, e.g., hydrogen in automotive and aerospace applications. The results show that most of the wave energy can be concentrated in a certain layer depending on the mode used, and by that damage present in this layer can be detected. The results obtained help to understand the wave propagation in multi-layered structures and are important for further development of NDT and SHM for Engineering structures consisting of multiple layers.
An approach to adhesive bond characterisation using guided acoustic waves in multi-layered plates
(2021)
An approach for the non-destructive characterisation of adhesive bonds using guided ultrasonic waves is presented. Pulsed laser radiation is used to thermoacoustically excite broadband ultrasonic waves in a multi-layered sample, consisting of a metal plate adhesively joined to a polymeric layer using synthetic resin. The resulting signals are received by a purpose-built piezoelectric transducer. Varying the distance between excitation and detection yields spatio-temporal measurement data, from which the dispersive properties of the propagating waves can be inferred using a two-dimensional Fourier transform, assuming the plates to act as coupled waveguides. Coupled multi-layered waveguides show an effect referred to as mode repulsion, where the distance between certain modes in the frequency-wavenumber domain is assumed to be a measure of coupling strength. Measurements at different stages of curing of the adhesive layer are performed and evaluated. A comparison of the results shows changes in the dispersive properties, namely an increased modal bandwidth for the fully cured sample as well as an increased modal distance.
In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.