Efficient simulation of elastic guided waves interacting with notches, adhesive joints, delaminations and inclined edges in plate structures

Experimental validation of an inverse method for defect reconstruction in a two-dimensional waveguide model

Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible.

Nondestructive corrosion degradation assessment based on asymmetry of guided wave propagation field

The article presents the results of numerical and experimental investigation of guided wave propagation in steel plates subjected to corrosion degradation. The development of novel procedures allowing for the assessment of the corrosion degradation level is crucial in the effective diagnostics of offshore and ship structures that are especially subjected to aggressive environments. The study's main aim is to investigate the influence of surface irregularities on wave propagation characteristics. The paper investigates wavefront asymmetry caused by the non-uniform thickness of damaged specimens. In the first step, the influence of thickness variability on the symmetry of the wave field has been investigated numerically. The corroded plates with variable degrees of degradation have been modeled using the random fields approach. The degree of degradation (DoD) varied from 0% to 40%. In the next step, the developed method was examined during experimental tests performed on specimens subjected to accelerated corrosion degradation. The experimental tests were conducted for intact and for corroded plates characterized by a DoD of 10%. It is demonstrated that the new approach based on wave field analysis can be used in structural state assessment.

Three-dimensional scaled boundary finite element method to simulate Lamb wave health monitoring of homogeneous structures: Experiment and modelling

Exploiting scattering and reflection related data of ultrasonic Lamb wave interactions with damage is a common approach to health monitoring of thin-walled structures. Using thin PZT sensors, the method can be implemented in real-time. Simulation of Lamb wave propagation and its interaction with damage plays an important role in damage diagnosis and prognosis. It is, however, a time-consuming task due to the high-frequency waves that are commonly used to detect tiny damage. The current study employs the Scaled Boundary Finite Element Method (SBFEM) for effective modeling of Lamb wave health monitoring of homogenous thin plates. The electromechanical effects of piezoelectric sensors are included in the model to improve accuracy and make the results comparable to those of laboratory experiments. Simple meshing of complex topologies is possible by converting standard finite elements to scaled boundary elements. The 3D SBFEM wave motion equations are solved in the time domain to capture the sensor's PZT response to a high-frequency tone-burst actuation. The results are validated by pitch-catch and pulse-echo laboratory tests carried out on thin plates. SBFEM is used to study wave propagation in complex configurations, such as a stiffened plate, and the results are compared to their FEM counterparts. According to the findings, SBFEM significantly reduces the computational costs associated with simulation of Lamb wave health monitoring while also providing significant accuracy in comparison to the experimental results.

Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods

Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in GEW ZGV computation (doi: 10.5281/zenodo.7537442).

Defect reconstruction in a two-dimensional semi-analytical waveguide model via derivative-based optimization

This paper considers an indirect measurement approach to reconstruct a defect in a two-dimensional waveguide model for a non-destructive ultrasonic inspection via derivative-based optimization. The propagation of the mechanical waves is simulated by the scaled boundary finite element method that builds on a semi-analytical approach. The simulated data are then fitted to given data associated with the reflected waves from a defect which is to be reconstructed. For this purpose, we apply an iteratively regularized Gauss-Newton method in combination with algorithmic differentiation to provide the required derivative information accurately and efficiently. We present numerical results for three kinds of defects, namely, a crack, delamination, and corrosion. The objective function and the properties of the reconstruction method are investigated. The examples show that the parameterization of the defect can be reconstructed efficiently as well as robustly in the presence of noise.

Application of the reciprocity principle to evaluation of mode-converted scattered shear horizontal (SH) wavefields in tapered thinning plates

The interaction of guided waves with wall thinning can be complex, depending on the thinning geometry and the frequency. At a high frequency-thickness, when a shear-horizontal (SH) guided wave mode impinges upon a tapered wall thinning region, there is mode conversion to other propagating SH modes, either in reflection or transmission, which heavily depends on the shape of the taper. In this paper, we have combined the reciprocity theorem of elastodynamics and the theory of multiple reflections, in order to analytically calculate the scattered SH wavefield in plates, due to the interaction with an arbitrary tapered thinning. The taper is discretized into several sections and the formulation is addressed in matrix notation, in order to tackle several modes which arise due to mode interconversion distributed within the taper. The method was validated with experimental and numerical data at linear tapered thinning, in the high-frequency-thickness regime. It was also applied to provide understanding of the reflection behaviour within smoother taper profiles, namely, raised-cosine and Blackman window tapers, and to visualize the propagating field of each mode. It is shown that for a linear taper profile, the reflection within the taper is virtually constant, which produces an interference pattern in the overall reflection from the whole taper. Such a mechanism is broken with smoother tapers, since they impose lower reflection close to the taper ends. The method proves itself useful for analytically investigating the scattering from arbitrary wall thinning when mode-conversion arises.

Efficient semi-analytical simulation of elastic guided waves in cylinders subject to arbitrary non-symmetric loads

In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads f(r,θ) on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

Wave propagation in immersed waveguide with radial inhomogeneity

In this paper, we investigate wave propagation in an inhomogeneous cylindrical waveguide immersed in a medium. To model external medium influence, we use the impedance boundary conditions on the waveguide outer wall. Some structural properties of the dispersion set are studied. To treat the problem of the waveguide forced oscillations, we solve boundary value problems for the first order vector differential equation sequentially in the Fourier transform space and then build the actual space on the basis of the residue theory. The residues for the numerically given function with the first order poles were found by considering auxiliary boundary value problems. The wave fields on the waveguide internal wall are obtained for different inhomogeneity laws and boundary conditions.

Analysis of Guided Wave Propagation in a Multi-Layered Structure in View of Structural Health Monitoring

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.