Behavior Of Elastic Waves Research Articles

Impact of Model Knowledge on Acoustic Emission Source Localization Accuracy

Reliable and precise damage localization in mechanical structures is of high importance in the context of structural health monitoring (SHM). The acoustic emission (AE) method has already shown its excellent suitability for damage localization. However, low signal-to-noise ratios (SNRs) are often prevalent in SHM, thus an increase in localization accuracy and robustness is still in demand. The present study faces this task through the integration of various model knowledge for AE source localization. The basis of the presented algorithm is the consideration of the dispersive behavior of elastic waves in thin-walled structures. The continuous wavelet transform (CWT) is used to obtain time-frequency representations of the signals, where frequency-dependent values for time-of-arrival (TOA) are extracted. Furthermore, the algorithm incorporates the knowledge that all sensors receive signals with the same time and location of origin, as well as the slightly different sensitivity of the theoretically equal sensors. The final localization results are achieved by a two parameter grid search optimization. The algorithm is experimentally tested on a large aluminum plate with four piezoelectric wafer active sensors (PWASs) arranged in an array of 100 mm × 100 mm. The mean localization error of pencil lead breaks at ten different positions within the sensor array is used as an accuracy measure. It is shown that as more of the described model knowledge is incorporated into the localization, the accuracy increases. With the final algorithm, the mean localization error is more than halved compared to AE localization based on classical TOA estimation. Although the experiment described is conducted under laboratory conditions, the remarkable increase in accuracy suggests that AE source localization may be successful even at low SNR as typical for operational conditions.

All‐Polarized Elastic Wave Attenuation and Harvesting via Chiral Mechanical Metamaterials

AbstractManipulating elastic waves of all polarizations is highly challenging due to the complex behavior of elastic waves. To achieve simultaneous broadband vibration attenuation and energy harvesting across all polarizations of elastic waves at low‐frequency ranges, a chiral mechanical metamaterial‐based energy harvester is proposed in this study. The systematic development of a complete bandgap and defect structure is achieved through theoretical eigenfrequency analysis and numerical simulations. The defect structure is incorporated to induce defect modes for all wave polarizations within the complete bandgap region, ensuring their compatibility with the overall shape of the structure. The proposed chiral mechanical metamaterial with defect (CMMD) demonstrated significant performance improvements, achieving electrical output power enhancements that are 20.5 times for flexural waves and 511.4 times for longitudinal‐torsional waves compared to the defectless chiral mechanical metamaterial. This study accentuates the thoughtful design and multifaceted utility of chiral mechanical metamaterials, paving the way for their application not only in energy harvesting but also in wave attenuation for various polarizations.

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

The purpose of this investigation is to see the dispersion of an inhomogeneous sandwich plate with imperfect interfaces between the layers and supported by the two parameters Pasternak foundation under long-wave low-frequency conditions. The governing equation of motion has been considered from the perspective of an anti-plane shear propagation to achieve simplicity. The overall cut-off frequency and the exact dispersion relation (EDR) are computed. In the context of the structure under investigation, one material contrast setup has been considered. The shortened polynomial dispersion relation, which corresponds to the EDR under material contrast setup, has been reported and investigated further. Additionally, the variational effects of the Pasternak foundation parameters as well as the interface imperfect parameter on the lowest dispersion curve subject to the long-wave low-frequency domain have been investigated using numerical simulations and graphical representations. This study is noteworthy because it sheds light on the behavior of elastic waves in multilayered structures and may be utilized to enhance the layout of three-layered structures used in a variety of industrial fields. Furthermore, we have provided the optimum values of the involved parameters to control and confine the sandwich plate’s vibration within the long-wave low-frequency regime.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations.

This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

A Numerical Study of Elastic Wave Arrival Behavior in a Naturally Fractured Rock Based on a Combined Displacement Discontinuity-Discrete Fracture Network Model

The arrival behavior of elastic waves in a naturally fractured rock is studied based on numerical simulations. We use the discrete fracture network method to represent the distribution of a natural fracture system and employ the displacement discontinuity method to compute the propagation of elastic waves across individual fractures. We analyze macroscopic wavefield arrival properties collectively arising from the interaction between elastic waves and numerous fractures in the system. We show that the dimensionless angular frequency ῶ = ωZ/κ exerts a fundamental control on the arrival behavior of a plane wave traveling through the fractured rock, where ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. An asynchronous arrival phenomenon of the wave energy occurs and becomes more significant with an increased ῶ. Two regimes are identified according to the two-branch dependency of the fractal dimension D of the FFAW on ῶ, where the wave arrival behavior is within a non-fractal regime for ῶ smaller than the critical frequency ῶc ≈ 1.0, and enters the fractal regime for ῶ ≥ ῶc. The self-affine properties of the FFAW, i.e., the roughness exponent α and the correlation length lc, both linearly decrease as a function of the exponent ξ (with ῶ = 10ξ) in the fractal regime. Early breakthrough of wave transport occurs in regions with relatively low fracture density, while late-time arrival happens in regions of high fracture density.

In-situ monitoring of dislocation proliferation during plastic deformation of 304L steel using ultrasound

The dislocation density as a function of applied stress is monitored in-situ, continuously, for 304L steel in a standard tension test. This is done by measuring the speed of acoustic waves, both longitudinal (L) and transverse (T). In a first experiment, both wave velocities, strain, and sample thickness are measured simultaneously and independently for a single elongation of the sample. Measurements are in agreement with theoretical predictions relating acoustic wave speed and dislocation density. The resulting data for dislocation density as a function of stress in the plastic region obeys the Taylor rule, and the simultaneous measurements of acoustic velocity and applied stress allows for the determination of the two parameters appearing in said rule. X-ray diffraction (XRD) measurements are performed using the Rietveld refinement, and a Croussard–Jaoul (CJ) analysis for the stress–strain curve is carried out. Both indicate the presence of an increasing number of twins at high strains.In a second experiment three consecutive loading–unloading cycles are performed for the same steel sample. In this case the shear wave velocity, applied force and sample strain are measured. Additionally, the stress, the strain and the sample thickness are obtained through a finite element modeling, calibrated with experimental data. The plastic behavior in the first and third cycles is similar to that of the first experiment: There is an increase in dislocation density, as determined through the change in the speed of shear waves, and said increase obeys the Taylor rule. The extent to which these results constrain the values of the parameters appearing in the Taylor rule for the third cycle is discussed. The material behavior during the second cycle is markedly different, with an increase, rather than decrease, in the speed of shear waves. Using classical theory of elastic wave behavior in polycrystals, it is found that this change is consistent with a decrease in grain size due to a proliferation of twins, as foreshadowed by the XRD measurements and C–J analysis.Our work adds ultrasound as a tool to those available for in-situ testing of steels, and paves the way for the development of devices for the evaluation of pieces in service.

Effect of interaction of adjacent unit-cells on wave propagation in coupled mass-in-mass metamaterials.

This paper aims to study the effect of the interaction of adjacent unit-cells in coupled mass-in-mass metamaterial on wave behaviors, which enables us to achieve a wavy dispersion relationship. Elastic wave propagation in a coupled mass-in-mass metamaterial is investigated to clarify the effect of the interaction of adjacent unit-cells on the dispersion relation and wave velocity. Elastic wave behavior based on an infinite system is studied in terms of the band structure and group velocity. The dynamic responses in frequency domain and time domain of the finite mass-in-mass lattice are calculated by using Laplace transform and numerical methods. The band structures and transmittances show that the coupled mass-in-mass metamaterial has a bandgap, which can be used to suppress and isolate vibration. The parameter study shows that changing the stiffness and location of the coupled springs can adjust the distribution of the bandgap. Importantly, we also calculate the ratio of group velocity to phase velocity that indicates the negative group velocity appearing in the wavy dispersion relation of coupled mass-in-mass metamaterials. These results show that the interaction of adjacent unit-cells plays a crucial role in the wave behavior of the coupled mass-in-mass metamaterial.

Asymmetric Behaviour of Elastic Waves in Anisotropic Plate having Graded Properties: A Fast Fourier Transform-based Spectral Analysis

Asymmetric Behaviour of Elastic Waves in Anisotropic Plate having Graded Properties: A Fast Fourier Transform-based Spectral Analysis

Monochannel Demultiplexer Phononic Crystal Slab Based on Hollow Pillars

A mono-channel waveguide with alternate hollow pillars of different radius to passively select and reject particular frequencies for filtering applications are numerically simulated based on the Finite Element Method (FEM). The waves are guided while the frequencies can be filtered according to pillar inner radius as its waveguiding mechanism. The computations of dispersion relation, transmission coefficient and stress displacement profile of the waveguides were carried out to understand the propagation behaviour of elastic waves on the waveguide structure. The proposed model shows a complete bandgap around 700 kHz, while its respective blocking phenomenon is demonstrated using square-ring shapes. The introduction of defect lines in linear and L-Shaped form enables a tailorable frequency shift within the bandgap region with optimized inner radius of hollow pillar. The proposed model eliminates the need for a multi-channel filtering system with conventional several separated lines thus reduces the dimension of filtering device.

Calculation of reflection and transmission coefficients for waves in multilayered piezoelectric structures using the mixed variable method.

The reflection and transmission (R/T) behavior of elastic waves in an anisotropic multilayered piezoelectric structure bounded by two homogeneous half-spaces is studied using the mixed variable method. The mixed variable method, which is based on the mixed energy matrix, takes the displacement vector at one end of the structure and the stress vector at other end of the structure as the basic variables. The wave equation for a homogeneous piezoelectric layer is transformed into a first-order state equation in the Hamiltonian system by introducing a dual vector. The general solution of the state equation can be expressed in terms of the eigenvalues and eigenvectors of the complex Hamiltonian matrix. A mixed energy matrix is applied to establish the relationship between the generalized displacement and stress vectors on the upper and lower interfaces of a layer. By an efficient recursive algorithm, the global mixed energy matrix is formed for an arbitrarily anisotropic multilayered piezoelectric structure. The R/T coefficients of the waves in an anisotropic multilayered piezoelectric structure are derived by the global mixed energy matrix. Numerical examples are provided to show the robustness of the mixed variable method. The effects of the incident angles, wavenumbers, and critical angles on the R/T coefficients are discussed.

QED treatment of linear elastic waves in asymmetric environments

Considering the importance of correctly understanding the dynamics of microstructure materials for their applications in related technologies, by eliminating the shortcomings and some overlooked physical concepts in the existing asymmetric elastic theories, we have presented an asymmetric elastodynamic model based on a U ( 1 ) gauge theory with quantum electrodynamics (QED) structure. Accordingly, we have shown that there is a correspondence between an elastic theory, which can explain the behavior of elastic waves within an asymmetric elastic medium and QED. More specific, we have indicated that the corresponding elastic wave equations are somehow analogous to QED ones. In this regard, by adding vibrational degrees of freedom and introducing a gauge property of the waves of displacement for the waves of rotation, we have generalized and modified the related Cosserat theory (CT) for an elastic environment. Thus on macro scales, the elastic waves can possess the QED treatment. This analogy provides a new paradigm of fermions and bosons. Also, from experimental point of view, we have shown that the behavior of elastic waves in a granular medium is equivalent to behavior of light in dispersive media, which can be explained using QED. Hence, contrary to the Cosserat and discrete models, this amended CT has qualitatively been indicated to be consistent with the corresponding empirical observations.

Three-dimensional similarity law for elastic wave propagation in CFRP with concentrically curved fibers

The wave front of an elastic wave in carbon fiber reinforced plastic (CFRP) with curved fibers is distorted owing to the fiber curvature effect. The similarity law to estimate the two-dimensional (2D) elastic bulk wave behavior in CFRP with concentrically curved fibers was presented in our previous study. In this research, the three-dimensional (3D) propagation of bulk waves in CFRPs with concentrically curved fibers was examined. Using 3D-printed CFRP specimens, the 3D propagation behavior of the quasi-longitudinal wave emitted from the point source was visualized virtually. Considering these results, the similarity law was expanded to the case of the 3D propagation behaviors of the bulk waves. Mathematical discussion based on the governing equations shows that the expansion parameters need to be equal in both the thickness and the radial directions to satisfy the similarity law in the 3D case, in addition to the conditions required to satisfy the 2D similarity law. By conducting the experimental visualization, it was demonstrated that the shape changes of quasi-longitudinal waves follow the similarity law, which was eventually verified for 3D propagation.

Topological interface states in translational metamaterials for sub-wavelength in-plane waves

In this work, we numerically investigate topological interface states for subwavelength in-plane waves in elastic metamaterials composed mainly of translational resonators. The relationships among bandgap, effective mass and effective stiffness are analyzed for the mass-spring and continuum models. Besides, the locations of stop-bands and negative effective parameters are manipulated by tuning the parameters of translational resonances. It is observed that the topological phase transition occurs to the single mass-negative region from the single stiffness-negative region while the Zak phase varies following a shift in parameter changing. It also implies that the characteristic behavior of topological interface elastic waves can exist in the sub-wavelength region. Furthermore, the frequency response is analytically and computationally investigated in one heterostructure composed of two lattices with different negative effective properties, which show the existence of the sub-wavelength topological interface mode. Finally, we have further verified the dynamic behavior of the interface state by employing the transient response analysis computed by the finite element numerical approach.

Deriving Peridynamic Influence Functions for One-dimensional Elastic Materials with Periodic Microstructure

The influence function in peridynamic material models has a large effect on the dynamic behavior of elastic waves and in turn can greatly effect dynamic simulations of fracture propagation and material failure. Typically, the influence functions that are used in peridynamic models are selected for their numerical properties without regard to physical considerations. In this work, we present a method of deriving the peridynamic influence function for a one-dimensional initial/boundary-value problem in a material with periodic microstructure. Starting with the linear local elastodynamic equation of motion in the microscale, we first use polynomial anzatzes to approximate microstructural displacements and then derive the homogenized nonlocal dynamic equation of motion for the macroscopic displacements, which is easily reformulated as linear peridyamic equation with a discrete influence function. The shape and localization of the discrete influence function are completely determined by microstructural mechanical properties and length scales. By comparison with a highly resolved microstructural finite element model and the standard linear peridynamic model with a linearly decaying influence function, we demonstrate that the influence function derived from microstructural considerations is more accurate in predicting time-dependent displacements and wave dynamics.

A far-field scattering model in textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry

Modeling the scattering-induced attenuation of elastic waves in heterogeneous polycrystals has practical applications in seismology and non-destructive evaluation. However, attenuation modeling for polycrystals with preferred crystallographic orientation (statistically anisotropic or textured polycrystals) has not been well studied. The far-field approximation (FFA) model, which is applicable for arbitrary crystal (triclinic) symmetry and valid for the whole frequency range (Rayleigh region, stochastic regime, and geometric region), has been reported for texture-free polycrystalline materials. This paper extends the FFA model to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. This FFA model for textured polycrystals encompasses two advantages: a simple form of dispersion equation and high computational efficiency. Furthermore, this FFA model can predict both the attenuation and phase velocity of elastic waves in textured polycrystals. The FFA model in this study has also been validated by comparison with the full-wave second-order attenuation model on textured polycrystals of triclinic grains. This work provides a simple and efficient tool to predict the elastic wave behavior in heterogeneous polycrystalline materials.

Reflection behavior of elastic waves in the functionally graded piezoelectric microstructures

The reflection behaviors of elastic waves in the functionally graded piezoelectric (FGP) microstructures are studied based on the modified couple stress theory. The extended Legendre orthogonal polynomial method (LOPM) is employed to obtain the analytical solutions of governing equations. The LOPM does not require delamination and calculation of the displacements of each partial wave. It is more suitable for solving FGP microstructure. The solutions of the incident P wave and SH wave with the consideration of open-circuit surface and short-circuit surface electrical boundaries are illustrated, respectively. The convergence of the polynomial series method is analyzed through numerical examples. The influences of the length scale parameters, gradient shapes and different electrical boundaries on the reflection behaviors are discussed. It is found that the couple stress can increase the propagation velocity of SH waves in the microstructures, and then reduce the critical angle of the total reflection of the incident SH wave.

Numerical dispersion analysis of discontinuous Galerkin method with different basis functions for acoustic and elastic wave equations

The discontinuous Galerkin method (DGM) has been applied to investigate seismic wave propagation recently. However, few studies have examined the dispersion property of DGM with different basis functions. Therefore, three common basis functions, Legendre polynomial, Lagrange polynomial with equidistant nodes, and Lagrange polynomial with Gauss-Lobatto-Legendre (GLL) nodes, are used for numerical approximation. The numerical dispersion and anisotropy numerical behavior of acoustic and elastic waves are compared, and the numerical errors of different order methods are analyzed. The result shows that the dispersion errors for all basis functions reduce generally with increasing interpolation orders, but with large differences in different directions. Specifically, the Legendre basis function and Lagrange basis function with GLL nodes have attractive advantages over the Lagrange polynomial with equidistant nodes for numerical computation. We verified the dispersion properties by theoretical and numerical analyses.

Study on the Single Scattering of Elastic Waves by a Cylindrical Fiber with a Partially Imperfect Bonding Using the Collocation Point Method

The single scattering of P‐ and SV‐waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP) method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P‐ and SV‐waves is studied. Results indicate that (i) the total scattering cross section (SCS) is almost symmetric about the axis α = π/2 with respect to the location (α) of the imperfect interface, (ii) imperfect interfaces located at α = 0 and α = π highly reduce the total SCS under a P‐wave incidence and imperfect interfaces located at α = π/2 reduce the total SCS most significantly under SV‐incidence, and (iii) under a P‐wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV‐wave incidence.

Inspection of the lids of shallowly buried concrete structures based on the propagation of surface waves- PART II

The possibility of performing the inspection of an underground structure directly from the surface of the soil would be advantageous for the inspection of various type of underground utility structures present in modern cities. In part I, the behavior of elastic waves propagating in a soil profile containing a shallowly buried underground concrete utility structure was studied and it was found that it is possible to evaluate the condition of the surface of the lid of such structures based on the propagation velocity of elastic waves. The part II follows from the work that was previously performed to develop a nondestructive technique for the inspection of shallowly buried utility structures based on the propagation of elastic waves. First, the three-dimensional finite difference method implemented in the software Fast Lagrangian Analysis of Continuum was used to model an underground concrete structure to show how the presence of a manhole and of a pavement at the surface of the soil affect the propagation of elastic waves. Second, a receiver configuration typically used in three-dimensional seismic surveys is presented and its effectiveness is tested on three different existing underground structures. The signals collected during the field tests are analyzed independently in the velocity-frequency plane using an adaptive signal processing technique. The velocity-frequency representation of each signal is then used to identify the different elastic waves and to calculate their group velocities. Third, the variation of the group velocity at the surface of the three concrete structures is presented in the form of two-dimensional contour maps that enabled the detection of anomalies on the surface of two of these structures. Finally, it is shown how the collected data can be used to obtain a three-dimensional tomography representative of the condition of the surface of an underground structure.

Analysis of in-plane wave propagation in periodic structures with Sierpinski-carpet unit cells

In this study, the dispersion relationships and characteristics of directional periodic structure waveguides with Sierpinski carpet unit cells were investigated. Finite element method was used to analyze the Sierpinski-carpet periodic structures with square Pb cylinders inserted in the rubber background. The dispersion curves of unit cells with different stages were investigated first, then group velocities of periodic structures at given frequencies were calculated and used to analyze the directional waveguide characteristics in the Sierpinski-carpet periodic structures. The dynamic responses of finite periodic structures were investigated to observe the directional features, and the results were used to support the fact that Sierpinski carpet unit cells with different stages can control the propagation behavior of elastic waves in specific ways; the dispersion curves grew compressed as the stage increased. Multiple band characteristics were observed in the case of the second-stage fractal configuration. The directional propagation characteristics in Sierpinski carpet periodic structures can be utilized to further extend the range of vibration reduction zones. The results of this study have significant potential in terms of the application of Sierpinski-carpet periodic structures for vibration isolation.