Search Results (25)

The increasing use of layered materials in various modern industries demands effective non-destructive testing methods. Guided wave testing is a promising solution, but accurate dispersion curves are essential for its reliable implementation. These curves are crucial for the appropriate selection of testing parameters and for the reliable interpretation of inspection results. This study, therefore, aims to develop and verify a computationally efficient and versatile tool for calculating dispersion curves in multilayered media. We propose an approach based on the semi-analytical finite element (SAFE) method implemented in COMSOL Multiphysics 6.2. This approach employs commercial finite element software capabilities, including optimized solvers and the ability to handle complex material properties (e.g., layer anisotropy) and geometries, thus avoiding the need for specialized code. We present the theoretical background and implementation details of the proposed approach in COMSOL Multiphysics. The calculated dispersion curves show excellent agreement with those obtained from the established software Dispersion Calculator 3.1, with a relative error of no more than 0.001%. These results confirm the applicability of the developed SAFE implementation for calculating dispersion characteristics of multilayered structures and support its use in developing novel guided wave ultrasonic testing techniques for multilayered composite materials. Full article

Ultrasonic guided wave sensors are widely employed for structural health monitoring; yet, their signal interpretation reliability is frequently compromised in extreme environments where coupled temperature and stress induce significant nonlinear drifts in dispersion characteristics. To overcome the computational bottleneck of conventional numerical methods that hinders real-time sensor calibration, this paper proposes a Dispersion Multi-Head Attention Network (D-MHAN) that directly maps eleven raw physical parameters to full-band dispersion responses. By adopting a non-normalized input strategy to internalize underlying physical laws, the model enables robust out-of-distribution extrapolation even when material properties exceed the training manifold. It was validated against a high-fidelity dataset spanning temperatures from −250 °C to 100 °C and stresses from 0 to 150 MPa generated by the Semi-Analytical Finite Element (SAFE) method. The proposed D-MHAN achieves a Pearson correlation coefficient of 0.9999 and provides computational speeds approximately 30 and 168 times faster than SAFE and the Wave Finite Element Method (WFEM). The model’s practical utility is further corroborated by cryogenic experiments on an aerospace storage tank. This work establishes a critical foundation for real-time parameter sensitivity analysis and environmental effect compensation in practical ultrasonic sensing applications. Full article

This study aims to evaluate the effectiveness of five analytical and semi-analytical methods for estimating Lamb wave dispersion in viscoelastic plates—the Rayleigh–Lamb solution, the Global Matrix Method (GMM), the Semi-Analytical Finite Element (SAFE) method, the Scaled Boundary Finite Element Method (SBFEM), and the Legendre Polynomial Method (LPM). The Rayleigh–Lamb equations are solved using an optimized Newton–Raphson algorithm, enhancing computational efficiency while maintaining comparable accuracy. The SAFE method exhibited a remarkable balance between computational efficiency and physical accuracy, outperforming SBFEM at high frequencies. For epoxy and high-performance polyethylene (HPPE) plates, the SAFE method and the LPM significantly outperform the GMM in relation to computational efficiency, with errors below $1\%$ for fundamental symmetric and antisymmetric modes across the tested frequency range of 0 to 100 kHz. In addition, the ability of the SAFE method to accurately predict both phase velocity and attenuation in viscous media supports their use in guided-wave-based structural health monitoring applications. Among the investigated approaches, the SAFE method emerges as the most robust and accurate for viscoelastic plates, while the SBFEM and LPM show limitations at higher frequencies. This study provides a quantitative and methodological foundation for selecting and implementing numerical methods for guided wave analysis, emphasizing the dual necessity of physical fidelity and numerical stability. Full article

This study investigates the propagation of shear horizontal transverse waves in a functionally graded piezoelectric half-space (FGPHS), where the material properties vary linearly and quadratically. The analysis focuses on deriving and understanding the dispersion characteristics of such waves in in-homogeneous media. The WKB approximation method is employed to obtain the dispersion relation analytically, considering the smooth variation of material properties. To validate and study the wave behavior numerically, two advanced techniques were utilized: the Semi-Analytical Finite Element with Perfectly Matched Layer (SAFE-PML) and the Semi-Analytical Infinite Element (SAIFE) method incorporating a (1/r) decay model to simulate infinite media. The numerical implementation uses the Rayleigh–Ritz method to discretize the wave equation, and Gauss 3-point quadrature is applied for efficient numerical integration. The dispersion curves are plotted to illustrate the wave behavior in the graded piezoelectric medium. The results from SAFE-PML and SAIFE are in excellent agreement, indicating that these techniques effectively model the shear horizontal transverse wave propagation in such structures. This study also demonstrates that combining finite and infinite element approaches provides accurate and reliable simulation of wave phenomena in functionally graded piezoelectric materials, which has applications in sensors, actuators, and non-destructive testing. Full article

At present, researchers in the field of pipeline inspection focus on pipe wall defects while neglecting pipeline defects in special situations such as welds. This poses a threat to the safe operation of projects. In this paper, a multi-node fusion and modal projection algorithm of steel pipes based on guided wave technology is proposed. Through an ANSYS numerical simulation, research is conducted to achieve the identification, localization, and quantification of axial cracks on the surface of straight pipelines and internal cracks in circumferential welds. The propagation characteristics and vibration law of ultrasonic guided waves are theoretically solved by the semi-analytical finite element method in the pipeline. The model section is discretized in one-dimensional polar coordinates to obtain the dispersion curve of the steel pipe. The T(0,1) mode, which is modulated by the Hanning window, is selected to simulate the axial crack of the pipeline and the L(0,2) mode to simulate the crack in the weld, and the correctness of the dispersion curve is verified. The results show that the T(0,1) and L(0,2) modes are successfully excited, and they are sensitive to axial and circumferential cracks. The time–frequency diagram of wavelet transform and the time domain diagram of the crack signal of Hilbert transform are used to identify the echo signal. The first wave packet peak point and group velocity are used to locate the crack. The pure signal of the crack is extracted from the simulation data, and the variation law between the reflection coefficient and the circumferential and radial dimensions of the defect is calculated to evaluate the size of the defect. This provides a new and feasible method for steel pipe defect detection. Full article

High-density polyethylene (HDPE) pipes are becoming increasingly popular, being used in various fields, such as construction, marine, petroleum, water transfer, process water, methane gas collection, oil and gas gathering, gas distribution systems, mining, acid and wet gas lines, offshore oil and gas and in nuclear power plants. Higher-order guided Lamb wave (UGW) modes can be used to detect various defects in complex structures. We will apply this methodology to one of the types of plastic—the structure of high-density polyethylene (HDPE). However, the excitation of UGW modes faces numerous challenges, especially when there is a need to identify which mode is excited. It is essential to note that, in the higher frequency range, multiple different higher-order modes can usually be excited. This can make it difficult to determine which modes have actually been excited. The objective of this research was to successfully excite and receive various higher-order UGW modes in high-density polyethylene structures using both ultrasonic single-element transducers and a phased array. Theoretical calculations were performed using a variety of methods: semi-analytical finite element (SAFE) method, 2D spatial–temporal spectrum analysis and finite element modeling (FEM). The results obtained from both measurements and simulations clearly demonstrate the possibility of efficiently exciting and receiving different Lamb wave modes possessing different phase velocities. Full article

Nonlinear ultrasonic guided waves have attracted increasing attention in the field of structural health monitoring due to their high sensitivity and long detection distance. In practical applications, the temperature of the tested structure will inevitably change, so it is essential to evaluate the effects of temperature on nonlinear ultrasonic guided waves. In this paper, an analytical approach is proposed to obtain the response law of nonlinear guided waves to temperature based on the semi-analytical finite element (SAFE) method. The plate structure is investigated as a demonstration example, and the corresponding simulation analysis and experimental verification are carried out. The results show that the variation trends of different cumulative second harmonic modes with temperature are distinct, and their amplitudes monotonically increase or decrease with the continuously rising temperature. Therefore, in the applications with nonlinear ultrasonic guided waves, it is necessary to predict the changing trend of selected cumulative second harmonics under the action of temperature and compensate the result for the influence of temperature. The methods and conclusions presented in this paper are also applicable to other types of structures and have general practicality. Full article

The Semi-Analytical Finite-Element (SAFE) method represents one of the most established numerical approaches for predicting the propagation of elastic waves in one-dimensional structures of arbitrary cross-sections. Its implementation in the commercial finite-element software COMSOL Multiphysics has been proposed in recent years; however, it is limited to only the free wave propagation for computing dispersion curves. To overcome this limitation, this paper proposes an extension of this approach that combines COMSOL and its Livelink for Matlab tool. This enables the extraction from COMSOL of the assembled mass and stiffness SAFE matrices to solve problems of both free and forced wave propagation in the Matlab environment. The resulting customised software takes advantage of both the potential of commercial FE software and the power of Matlab without worrying about compatibility issues. A model of a simply supported plate strip and that of a more complex geometry are implemented to validate, respectively, the SAFE matrix extraction procedure and the implemented forced response formulation. The results agree well with corresponding analytical and numerical results validating the proposed implementation of the SAFE method. Full article

Square steel tube, which is widely used in civil engineering, can suffer from a wide variety of damages and aging defects, thus its nondestructive testing (NDT) has attracted wide attention. This work proposes an ultrasonic guided wave (UGW)-based damage detection method for square steel tubes using structure symmetry. Firstly, the dispersion characteristics of square steel tubes are obtained using the semi-analytical finite element (SAFE) method, after which the optimal guided wave modes for damage located on the long and short edges of the steel tube are selected by modal analysis. Then, using the symmetry of the square steel tube’s section, the symmetric layout scheme of the transmitters and the receivers is designed; on this basis, a signal processing strategy for damage detection is proposed by subtracting the receiving signals obtained from symmetric positions. Finally, the effectiveness of the proposed damage detection method is verified by numerical simulations and laboratory experiments. The results show that the proposed method has good inspection accuracy for crack and hole damages on both the long and short edges of square steel tube because the dispersion effect and clutters can be reduced utilizing structure symmetry. It is worth mentioning that the inspection effect for corner holes can be enhanced by modifying the position of the receivers. Full article

Early detection of defects inside a rail is of great significance to ensure the safety of rail transit. This work investigated the ability of ultrasonic guided waves (UGWs) to detect internal defects in a rail head. First, the model of UGW propagation in rail, which has an irregular cross-section, was constructed based on the semi-analytical finite element (SAFE) method. Fundamental characteristics, such as wavenumber, phase or group velocity, and wave structure inside the rail, were then calculated. Following modal and vibration energy distribution analysis, a guided wave mode that is sensitive to transverse fissure (TF) defects was selected, and its excitation method was proposed. The effectiveness of the excitation method was confirmed by simulations performed in the ABAQUS software. According to the simulation data, the dispersion curve calculated by using the two-dimensional Fourier fast transform (2D-FFT) coincided well with that of the SAFE method. After that, the sensitivity of the selected mode to internal rail defects was validated and its ability to locate defects was also demonstrated. Finally, the effects of excitation frequency, defect size, and vertical and horizontal defect depth on the reflection waveforms were investigated. Full article

In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the finite element method), Lagrange polynomials defined over non-equidistant nodes (spectral element method), and non-uniform rational B-splines (isogeometric analysis) are implemented in an in-house SAFE code, along with different refinement strategies such as h-, p-, and k-refinement. Since the numerical analysis of wave propagation is computationally quite challenging, high-order shape functions and local mesh refinement techniques are required to increase the accuracy of the solution, while at the same time decreasing the computational costs. The obtained results reveal that employing a suitable high-order basis in combination with one of the mentioned mesh refinement techniques has a notable effect on the performance of the SAFE method. This point becomes especially beneficial when dealing with applications in the areas of structural health monitoring or material property identification, where a model problem has to be solved repeatedly. Full article

Scanning laser Doppler vibrometry is a widely adopted method to measure the full-field out-of-plane vibrational response of materials in view of detecting defects or estimating stiffness parameters. Recent technological developments have led to performant 3D scanning laser Doppler vibrometers, which give access to both out-of-plane and in-plane vibrational velocity components. In the present study, the effect of using (i) the in-plane component; (ii) the out-of-plane component; and (iii) both the in-plane and out-of-plane components of the recorded vibration velocity on the inverse determination of the stiffness parameters is studied. Input data were gathered from a series of numerical simulations using a finite element model (COMSOL), as well as from broadband experimental measurements by means of a 3D infrared scanning laser Doppler vibrometer. Various materials were studied, including carbon epoxy composite and wood materials. The full-field vibrational velocity response is converted to the frequency-wavenumber domain by means of Fourier transform, from which complex wavenumbers are extracted using the matrix pencil decomposition method. To infer the orthotropic elastic stiffness tensor, an inversion procedure is developed by coupling the semi-analytical finite element (SAFE) as a forward method to the particle swarm optimizer. It is shown that accounting for the in-plane velocity component leads to a more accurate and robust determination of the orthotropic elastic stiffness parameters. Full article

Multilayered carbon fiber-reinforced polymers (CFRP) are increasingly used in aircraft components because of their superior mechanical properties. However, composite materials are vulnerable to impact loads, resulting in delamination-type damage which, if unnoticed, could lead to catastrophic structural failure. The objective of this research was to investigate possibilities to improve damage detection and the localization using signal processing methods. Numerical modeling using the semi-analytical finite element (SAFE) method was performed to obtain guided wave dispersion curves and to perform modal analysis. From the modal analysis, ${\mathrm{A}}_0$ mode for inspection of the composite with delamination type defects was selected. From the numerical simulation, ${\mathrm{A}}_0$ mode interaction with delamination along the longitudinal direction was analyzed and the location of the defect was estimated by measuring the time of flight (ToF) of the signal using Hilbert transform (HT) and continuous wavelet transform (CWT). The CWT has shown better results in estimating the delamination location compared with HT. The depth of delamination was characterized in the frequency domain by comparing the amplitude of the ${\mathrm{A}}_0$ mode. Inverse fast Fourier transform (IFFT) is recommended to reconstruct the reflected and transmitted modes for better damage detection and to reduce the complexity of signal interpretation. Full article

Bars are significant load-carrying components in engineering structures. In particular, L-bars are typical structural components commonly used in truss structures and have typical irregular asymmetric cross-sections. To ensure the safety of load-carrying bars, much research has been done for non-destructive testing (NDT). Ultrasonic guided waves have been widely applied in various NDT techniques for bars as a result of the long-range propagation, low attenuation, and high sensitivity to damages. Though good for inspection of ultrasonic guided waves in symmetric cross-section bar-like structures, the application in asymmetric ones lacks further research. Moreover, traditional damage detection in bars using ultrasonic guided waves usually depends on a single-mode at a lower frequency with lower sensitivity and accuracy. To make full use of all frequencies and modes, a multi-mode characteristic-based damage detection method is presented with the sum of multiple signals (SoM) strategy for L-bars with asymmetric cross-section. To control the desired mode in multi-mode ultrasonic guided waves, excitation optimization and weighted gathering are carried out by the analysis of the semi-analytical finite element (SAFE) method and the normal mode expansion (NME) method. An L-bar example with the asymmetric cross-section of 35 mm × 20 mm × 3 mm is used to specialize the proposed method, and some finite element (FE) models have been simulated to validate the mode control. In addition, one PZT is applied as a contrast in order to validate the multielement mode control. Then, more FE simulations experiments for damage detection have been performed to validate the damage detection method and verify the improvement in detection accuracy and damage sensitivity. Full article

This work presents a non-destructive method for quantitative essessment of fatigue damage of materials with linear elastic properties using nonlinear ultrasonic techniques. A nonlinear study was conducted on these materials with fatigue and shot peening processing using a nonlinear ultrasonic technique. A numerical method based on the semi-analytical finite element (SAFE) technique, was used to obtain the phase-matching modes of the specimens. Experiments confirm that the nonlinearity for shot peening and samples with a certain level of fatigue shows a tendency to increase with levels of fatigue. Full article