Search Results (18)

This paper describes, for the first time, the application of an Elastodynamic Boundary Element Method (BEM) in Laplace Domain for the Structural Health Monitoring (SHM) of poly-crystalline materials. The study focuses on Ultrasonic Guided Wave (UGW) propagation and investigates the wave–material interactions at micro-scale. The study aims to investigate the interaction of UGWs with assessing micro-structural features such as grain size, morphology, degradation, and flaws. Numerical simulations of the most common micro-structural features demonstrate the accuracy and validity of the proposed method. Particular attention is paid to the study of porosity and its influence on material macro-properties. Different crystal morphologies such as cubic, rhombic, and truncated octahedral are considered. The detection of voids based on the changes in the amplitude and Time of Arrival (ToA) of the backscattered signal is investigated. The study also considers inter-granular cracks, which cause laceration, and examines flaw position/orientation, length, and distance from a specific reference. Furthermore, a framework is proposed for generating Probability of Detection (PoD) curves using numerical simulations. Experimental tests in pristine conditions are shown to be in good agreement with the numerical simulations in terms of ToA, signal amplitude, and wave velocity. The numerical simulations provide insights into wave propagation and wave–material interactions, including different types of defects at the micro-scale. Overall, the BEM and UGW methods are shown to be effective tools for better understanding micro-structural features and their influence on the macro-structural properties of poly-crystalline materials. Full article

In recent years, there has been increasing attention on the development of non-destructive evaluation (NDE) methods using guided waves for long-length materials such as thin plates and pipes. The guided waves are capable of long-distance propagation in thin plates and pipes, and they exhibit properties such as multimodality and dispersion. These characteristics of the guided waves make inspection using guided waves challenging. In this study, we apply a 2-D elastodynamic time-reversal method to detect surface breaking cracks of a thin plate where guided waves are present. The finite element method (FEM) is used to calculate the scattered waves from surface breaking cracks and their corresponding time-reversal waves. We also employ topological sensitivity as an assessment index for detecting surface breaking cracks using the time-reversal method. As numerical examples, we demonstrate guided wave propagation, scattering, and the time-reversal wave propagation obtained by using the FEM. Finally, we present the results of surface breaking crack detection in a thin plate and discuss the validity and effectiveness of the proposed method. Full article

This paper presents the numerical simulation of the ultrasonic wave transmittance utilizing the elastodynamic finite integration technique (EFIT). With this methodology, it is possible to simulate the propagation of the ultrasound in a medium with a relatively low computational cost. The capability of this technique for determining the elastic properties of fluorophosphate and the aluminosilicate glasses is described in detail. The elastic constants of the glasses were calculated from the theoretically predicted longitudinal and transversal sound velocities and compared with the corresponding experimental data. Furthermore, the calculated and experimental elastic properties of the fluorophosphate and aluminosilicate glasses were correlated with the structural peculiarities of these glasses. This simulation technique is also suitable for unveiling the existence of possible defects in the glasses by comparing the experimental and simulation data. The EFIT technique is shown to be a very useful tool in order to provide fast and easy-to-acquire data regarding also the structural characteristics of various glassy systems. This can be used in conjunction with other spectroscopic techniques which can prove to be extremely useful for the non-destructive testing of vitreous materials. The latter can prove very important when vitreous materials used in optical or optoelectronic applications need continuous monitoring in order to ensure their optimum operation and functionality with limited intervention. The main contribution of this paper is the treatment of numerical time-domain modeling of 2D acoustic wave propagation in a viscoelastic medium by implementing the elastodynamic finite integration technique (EFIT). Full article

Structural health monitoring (SHM) strategies based on ultrasonic guided waves are very promising regarding thin-walled lightweight structures. To study the performance of such systems, validated numerical analysis tools have to be used. For that procedure, a benchmark between two numerical methods will be presented. The first promising approach is the elastodynamic finite integration technique (EFIT). Miscellaneous research shows that its capability of capturing wave characteristics and interactions is advanced in various media and structures, including thin-walled composites. The second approach employs conventional shell-type finite elements following the Reissner–Mindlin theory for modelling layered composite structures. The advantage of using such finite element methods (FEM) is their high availability in general purpose simulation tools. As a reference model, the measurement data coming from the Open Guided Waves Project (OGW) was taken into account. The OGW dataset provides the experimental data of ultrasonic guided wave propagation in carbon fiber composite plates with an additional omega stringer. By using this contribution, this experiment was reproduced by simulation. The paper presents the results of a validation and motivates further research, such as in research related to the probability of detection analysis and numerical performance. Full article

The geological structure, such as inclusions, may strongly affect the wave propagation and underground motions during earthquakes. Previous studies mainly focus on geological inclusion with the homogeneous medium. In this paper, the propagation and scattering of incident plane SH waves in and around an inhomogeneous cylindrical inclusion with a radially-varying modulus is studied. In terms of a radial wave function expansion, a rigorous analytical approach is formulated for general computation for the elastodynamic problem. A comprehensive set of numerical examples are presented to illustrate the sensitivity of the underground motion to the rigidity profile of the geological inclusion. Full article

Inspired by recent developments in wave propagation and scattering experiments with parity-time ($\mathcal{PT}$) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous $\mathcal{PT}$-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with $\mathcal{PT}$-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in $\mathcal{PT}$-symmetric materials. Full article

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level were known a priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green’s function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation. Full article

The in-plane elastic waves in periodically multilayered isotropic structures, which are decoupled from the out-of-plane waves, are represented mainly by the frequency–wavenumber spectra and occasionally by the frequency–phase velocity spectra as well as being studied predominantly for periodic bi-layered media along and perpendicular to the thickness direction in the existing research. This paper investigates their comprehensive dispersion characteristics along arbitrary in-plane directions and in entire (low and high) frequency ranges, including the frequency–wavelength, wavenumber–phase velocity, wavelength–phase velocity spectra, the dispersion surfaces and the slowness curves with fixed frequencies, as well as the frequency–wavenumber and frequency–phase velocity spectra. Specially, the dispersion surfaces and the slowness curves completely reflect the propagation characteristics of in-plane waves along all directions. First, the method of reverberation-ray matrix (MRRM) combined with the Floquet theorem is extended to derive the dispersion equation of in-plane elastic waves in general periodic multilayered isotropic structures by means of the elastodynamic theory of isotropic materials and the state space formalism of layers. The correctness of the derivation and the numerical stability of the method in both low and high frequency ranges, particularly its superiority over the method of the transfer matrix (MTM) within the ranges near the cutoff frequencies, are verified by several numerical examples. From these demonstrations for periodic octal- and bi-layered media, the comprehensive dispersion curves are provided and their general characteristics are summarized. It is found that although the frequencies associated with the dimensionless wavenumber along thickness $ql=n\pi$ ($n$ is an integer) are always the demarcation between pass and stop bands in the case of perpendicular incident wave, but this is not always exist in the case of the oblique incident wave due to the coupling between the two modes of in-plane elastic waves. The slowness curves with fixed frequencies of Floquet waves in periodically multilayered isotropic structures, as compared to their counterpart of body waves in infinite isotropic media obtained from the Christoffel equation now have periodicity along the thickness direction, which is consistent to the configuration of the structures. The slowness curves associated with higher frequencies have a smaller minimum positive period and have more propagation modes due to the cutoff properties of these additional modes. Full article

The present work investigates the technical feasibility of a condition monitoring setup aiming at the detection of gauge corner cracks (aka head checks) in pearlitic railway rails, using a wayside (i.e., stationary) setup with surface acoustic waves (SAW) as its detection principle. The experimental SAW setup consists of a pitch-catch setup using piezo transducers equipped with comb adaptors to excite and measure narrowband Rayleigh waves with a center frequency of 1 MHz. SAW experiments were performed on a rail subjected to cyclic loading in a 1:1 wheel–rail test rig yielding the specific rolling contact fatigue, i.e., head checks. Elastodynamic finite integration technique (EFIT) simulations were performed to analyze the surface and bulk wave propagation in the rail and to predict the signals at specific receiver positions. SAW transmission and reflection scenarios at cracks were analyzed numerically via modelled variations of gauge corner crack configurations according to number of cracks (0–3) and depth (0, 0.5 mm and 1 mm). The numerical and the experimental results each show a clear correlation between the appearance and intensity of head check damage and the wave attenuation in transmission mode. Full article

Surface acoustic waves (SAWs) are the guided waves that propagate along the top surface of a material with wave vectors orthogonal to the normal direction to the surface. Based on these waves, SAW sensors are conceptualized by employing piezoelectric crystals where the guided elastodynamic waves are generated through an electromechanical coupling. Electromechanical coupling in both active and passive modes is achieved by integrating interdigitated electrode transducers (IDT) with the piezoelectric crystals. Innovative meta-designs of the periodic IDTs define the functionality and application of SAW sensors. This review article presents the physics of guided surface acoustic waves and the piezoelectric materials used for designing SAW sensors. Then, how the piezoelectric materials and cuts could alter the functionality of the sensors is explained. The article summarizes a few key configurations of the electrodes and respective guidelines for generating different guided wave patterns such that new applications can be foreseen. Finally, the article explores the applications of SAW sensors and their progress in the fields of biomedical, microfluidics, chemical, and mechano-biological applications along with their crucial roles and potential plans for improvements in the long-term future in the field of science and technology. Full article

Under the assumptions of linear elasticity and small deformation in traditional elastodynamics, the anisotropy of the medium has a significant effect on rotations observed during earthquakes. Based on the basic theory of the first-order velocity-stress elastic wave equation, this paper simulates the seismic wave propagation of the translational and rotational motions in two-dimensional isotropic and VTI (transverse isotropic media with a vertical axis of symmetry) media under different source mechanisms with the staggered-grid finite-difference method with respect to nine different seismological models. Through comparing the similarities and differences between the translational and rotational components of the wave fields, this paper focuses on the influence of anisotropic parameters on the amplitude and phase characteristics of the rotations. We verify that the energy of S waves in the rotational components is significantly stronger than that of P waves, and the response of rotations to the anisotropic parameters is more sensitive. There is more abundant information in the high-frequency band of the rotational components. With the increase of Thomsen anisotropic parameters ε and δ, the energy of the rotations increases gradually, which means that the rotational component observation may be helpful to the study of anisotropic parameters. Full article

In this paper, a new stable finite-difference (FD) method for solving elastodynamic equations is presented and applied on the Biot and Biot/squirt (BISQ) models. This method is based on the operator splitting theory and makes use of the characteristic boundary conditions to confirm the overall stability which is demonstrated with the energy method. Through the stability analysis, it is showed that the stability conditions are more generous than that of the traditional algorithms. It allows us to use the larger time step $\tau$ in the procedures for the elastic wave field solutions. This context also provides and compares the computational results from the stable Biot and unstable BISQ models. The comparisons show that this FD method can apply a new numerical technique to detect the stability of the seismic wave propagation theories. The rigorous theoretical stability analysis with the energy method is presented and the stable/unstable performance with the numerical solutions is also revealed. The truncation errors and the detailed stability conditions of the FD methods with different characteristic boundary conditions have also been evaluated. Several applications of the constructed FD methods are presented. When the stable FD methods to the elastic wave models are applied, an initial stability test can be established. Further work is still necessary to improve the accuracy of the method. Full article

The topological derivative tool is applied here in structural health monitoring (SHM) problems to locate small defects in a material plate with complex geometry that is subject to permanent multifrequency guided waves excitation. Compared to more standard SHM methods, based in measuring the time-lag between emitted and received propagative pulses plus some postprocessing, the topological derivative somehow compares the measured and computed (solving the full elasto-dynamic equations) response of the damaged plate, instead of relying on only the time of flight of the wave. Thus, the method profits the knowledge behind the physics of the problem and can cope with scenarios in which classical methods give poor results. The authors of this paper have already used the topological derivative in rectangular plates with constant thickness, but with defects consisting simply in both through slits and inclusions of a different material, and actuators/sensors located near the boundary, which makes very difficult to use standard SHM methods. This is an extension of the method, also considering the much more difficult to analyze case of plates with variable thickness and complex (non-rectangular) planform. Full article

The partial-wave method takes advantage of the Christoffel equation’s generality to represent waves within a waveguide. More specifically, the partial-wave method is well known for its usefulness when calculating dispersion curves for multilayered and/or anisotropic plates. That is, it is a vital component of the transfer-matrix method and the global-matrix method, which are used for dispersion curve calculation. The literature suggests that the method is also exceptionally useful for conceptual interpretation, but gives very few examples or instruction on how this can be done. In this paper, we expand on this topic of conceptual interpretation by addressing Rayleigh waves, Stoneley waves, shear horizontal waves, and Lamb waves. We demonstrate that all of these guided waves can be described using the partial-wave method, which establishes a common foundation on which many elastodynamic guided waves can be compared, translated, and interpreted. For Lamb waves specifically, we identify the characteristics of guided wave modes that have not been formally discussed in the literature. Additionally, we use what is demonstrated in the body of the paper to investigate the leaky characteristics of Lamb waves, which eventually leads to finding a correlation between oblique bulk wave propagation in the waveguide and the transmission amplitude ratios found in the literature. Full article

Peridynamic based elastodynamic computation tool named Peri-elastodynamics is proposed herein to simulate the three-dimensional (3D) Lamb wave modes in materials for the first time. Peri-elastodynamics is a nonlocal meshless approach which is a scale-independent generalized technique to visualize the acoustic and ultrasonic waves in plate-like structure, micro-electro-mechanical systems (MEMS) and nanodevices for their respective characterization. In this article, the characteristics of the fundamental Lamb wave modes are simulated in a sample plate-like structure. Lamb wave modes are generated using a surface mounted piezoelectric (PZT) transducer which is actuated from the top surface. The proposed generalized Peri-elastodynamics method is not only capable of simulating two dimensional (2D) in plane wave under plane strain condition formulated previously but also capable of accurately simulating the out of plane Symmetric and Antisymmetric Lamb wave modes in plate like structures in 3D. For structural health monitoring (SHM) of plate-like structures and nondestructive evaluation (NDE) of MEMS devices, it is necessary to simulate the 3D wave-damage interaction scenarios and visualize the different wave features due to damages. Hence, in addition, to simulating the guided ultrasonic wave modes in pristine material, Lamb waves were also simulated in a damaged plate. The accuracy of the proposed technique is verified by comparing the modes generated in the plate and the mode shapes across the thickness of the plate with theoretical wave analysis. Full article