Interaction Of Elastic Waves Research Articles

Low-frequency air-coupled transducer based damage detection in composite materials

In this paper results of simulations of non-contact elastic wave generation in the composite panel based on acoustic to elastic wave transformation are presented. For this purpose simulations of acoustic wave generation and processing are based on the FEM method in COMSOL. Elastic wave generation and propagation are based on the spectral element method (SEM) in the time domain. The SEM model utilises time-varying acoustic pressure distributions calculated in the FEM. The SEM allows to simulate the interactions of elastic waves with the delamination. Damage localization is based on RMS elastic wave energy maps. In this research a panel made of carbon fibre-reinforced polymer composite is investigated. Research related to low-frequency air-coupled transducer (ACT) is presented. The utilisation of low-frequency waves allows for the reduction of the effects of the wave attenuation in composite material. The proposed combination of FEM and SEM gives an efficient tool for the simulation of non-contact wave generation for non-destructive testing analysis.

Investigating acoustoelasticity of plane elastic waves and second harmonics within isotropic solid media: A novel approach

This paper presents a novel approach to investigating the acoustoelasticity of plane elastic waves and second harmonics within isotropic solid media. The new contributions of this approach consist of providing an intuitive understanding of the essence of acoustoelasticity, offering a more straightforward method to deduce the expressions for acoustic velocities and pre-strains in natural coordinates compared to conventional theory of acoustoelasticity, and introducing a novel methodology for investigating acoustoelasticity of plane elastic waves and second harmonics. The core idea of this approach can be explained as follows: by introducing an intermediate state for describing predeformation between the natural state and the final state, the predefomation can be integrated into the nonlinear wave equation, and acoustoelastic equations of plane elastic waves and second harmonics can be deduced consequently by decomposing this nonlinear wave equation under the second approximation of perturbation theory. When applying this approach to study the acoustoelasticity of P wave and S wave of plane elastic waves, the validity and practicality of this approach are confirmed by contrasting expressions for acoustic velocities and pre-strains in natural coordinates to those found in previous research [8], which exhibit perfect consistency. Furthermore, this paper focuses on the acoustoelasticity of the free second harmonics and the driven second harmonics generated by self-excitation and interaction of plane elastic waves. The results concerning acoustoelasticity can be summarized as follows: firstly, pre-strain only influences wave vectors of plane elastic waves through the speed term in their expressions without altering their amplitudes; secondly, the acoustoelasticity of free second harmonics follows similar rules above; finally, Pre-strain affects the amplitudes and wave vectors of driven second harmonics through the speed terms in their expressions without changing the form of their expressions.

Interaction of elastic waves in solids with quadratic and cubic nonlinearity.

This article investigates the interactions of two-plane waves in weakly nonlinear elastic solids containing quadratic and cubic nonlinearity. The analytical solutions for generated combined harmonic waves are derived using the Green's function approach applied to a generated system of quasi-linear equations of motion. Wave mixing solutions are obtained and include shape functions that permit closed-form solutions for a variety of interaction geometries. An explicit example is highlighted for a spherical interaction volume assuming isotropic elastic constants. Several parameters of the generated field after mixing are analyzed including resonant and nonresonant mixing, the role of interaction angle, and the frequencies of the two incident waves. Wave mixing offers the potential for sensing localized elastic nonlinearity and the present model can be used to help design experimental configurations.

Interesting effects of harmonically scattered waves from 1D functionally graded nonlinear inclusions

The interaction of monochromatic elastic waves with nonlinear inclusions shows the presence of harmonically scattered waves. Challenges in obtaining theoretical solutions and limitations of conducting experiments to understand harmonic scattering of the nonlinear waves from functionally graded materials motivate us to conduct numerical experiments. Harmonic scattering of the elastic waves from highly local functionally graded nonlinear inclusions is exploited in this study to propose a novel building block of new nonlinear metamaterials that can effectively control harmonic responses. The simple, commonly observed, unique spatial distribution of the nonlinear parameters is proposed so that the area under the distribution remains the same for a constant-sized inclusion. Despite different spatial distributions, these functionally graded distributions show the same harmonic responses of both forward and backscattered waves during the interaction of monochromatic waves and one-way two-wave mixing. The amplitudes of all possible combinations of harmonics remain the same as long as the area under the spatially distributed nonlinear parameters curve, irrespective of the distribution curves. Reducing the area under the curve of the functionally graded nonlinear inclusion simply by reducing the maximum value of the functionally distributed nonlinear parameters, a decrease in the amplitudes of the harmonics is demonstrated.

Domain decoupling implementation for efficient ultrasonic wave simulations using scaled boundary finite elements and the mortar method

We introduce a novel approach that combines the scaled boundary finite element method (SBFEM) with a mortar coupling to enhance the computational modelling of elastic wave propagation and interaction with local features in the ultrasonic range. The key objective is to achieve decoupling between different regions of interest, enabling independent meshes for the zones where waves either propagate or interact with localised discontinuities in the elastic media. This decoupling allows us to exploit the benefits offered by various SBFEM formulations. Thus, we can select the most suitable solution for each specific region. An important concept we emphasise is the differentiation between the near field and far field regions. The near field encompasses zones where the precise representation of small features compared to the wavelength is crucial. At the same time, the far field comprises homogeneous regions where the waves propagate without interactions, eventually radiating towards infinity if the domain is unbounded. By separating these two zones, we can improve the computational performance by employing finer discretisation only where necessary. Furthermore, this decoupling enables the reuse of far field models in parametric analyses, making it highly valuable for scenarios focused particularly on local elastic wave interactions. This approach offers considerable potential in such cases. The modelling technique is validated, and its potential is demonstrated through practical applications.

Enhanced multi-band acoustic energy harvesting using double defect modes of Helmholtz resonant metamaterial

Acoustic metamaterials (AMs) based on phononic crystals have been widely employed for acoustic energy harvesting, for their capacity to amplify incident sound waves and transfer them to piezoelectric devices. By substituting a resonator unit with a piezoelectric material having distinct characteristics, the periodicity of the AM is locally disrupted, resulting in the generation of defect bands within the band gap. At the frequencies corresponding to these defect bands, the AM exhibits the phenomenon of local resonance, which concentrates the incident acoustic energy at the defect sites and significantly enhances the output power of the piezoelectric devices. Conventional AMs primarily consist of elastic resonators, which can be regarded as spring-mass systems. The elastic resonances of these resonators lead to local resonance in the AM and are utilized for single-band acoustoelectric conversion. In contrast, Helmholtz resonators (HRs), in addition to demonstrating mechanical resonance, generate acoustic resonance at specific frequencies. By combining AM with HRs, the resulting Helmholtz AM (HAM) achieves energy localization effects within two defect bands, thereby increasing the output power and broadening the operational frequency range of the AM. This study aims to investigate the energy localization in HAM with multiple point defects within the two defect bands through numerical simulations and experimental analysis. Multiple HRs are intentionally removed from the HAM to introduce these multi-point defects. The interaction of elastic waves localized within these defects further enhances the energy harvesting efficiency of the HAM. Comparing the voltage frequency response functions, it is observed that, in both the first and second band gaps, the output voltage of the three double-defect HAM structures surpasses that of the single-defect HAM. As the distance between the two defects decreases, the energy harvesting at the defect modes intensifies due to a stronger coupling effect.

Acoustical characteristics of solid elastic mediums with oriented microfructures

Model for interaction of plane elastic longitudinal waves with contains oriented microfractures with specific boundary conditions for “linear slip@ approximation is developed. The form of dispersion equation is defined in approximation of Bloch and Floque waves theory. Results of its solution which define character of functions for propagation phase velocity and attenuation coefficient of effective longitudinal wave in dependence on crack faces microfracture parameters and other model parameters.

Time-frequency simulation of ultrasonic longitudinal wave propagation in rocks

Ultrasound numerical simulation can be used as a powerful tool to investigate the generation, propagation, and interaction of elastic waves in solid materials for non-destructive evaluation (NDE). It has been widely applied in several domains such as medical, mechanical, construction, and geotechnical engineering, especially for the detection of cracks and defects in structures and for the identification of the characteristics of rock materials. The comprehension of the propagation of the ultrasonic wave in homogeneous and isotropic elastic materials is very important. This paper presents a method for simulating normal incidence ultrasonic waves (Longitudinal waves) propagating in rock structures. A mathematical model of the response of an ultrasonic wave in a submerged rock structure is introduced analytically based on the transfer matrix method (TMM), in which the layer is established in a quadrupole formalism. The simulation results of the ultrasonic response of rock structures are represented in a time–frequency representation. The results have been compared with the experimental data available in the literature and show good agreement. The numerical simulation method established in this work can be proposed as an effective complement to experiments and used for rock characterization by performing the simulation of ultrasonic responses for different thicknesses of rock structures.

An experimental investigation on the combined effect of plastic deformation and grain size variation on the acoustic nonlinearity parameter.

The combined effect of grain size variation and plastic deformation on the acoustic nonlinearity parameter has been investigated in an austenitic stainless-steel material of grade 304. The nonlinear behavior of this parameter with grain growth has deviated to linear fit with deformation. This is due to the interaction of elastic waves with the strain-induced dislocation substructure in the grains. The normalized mean square strain of the deformed specimens has been estimated through angle dispersive x-ray diffraction studies using a synchrotron source, and this has been correlated with the change in the acoustic non-linearity parameter with deformation. The nonlinearity parameter is found to be very sensitive to the plastic deformation even in the presence of grain size variations. The results infer that the variations in the nonlinearity parameter can be used to have an estimate of the extent of localized deformations often occurring during the fabrication of metallic components.

Relaminarization of elastic turbulence

We report frictional drag reduction and a complete flow re-laminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that intensity of observed elastic waves and wall-normal vorticity correlate well with the measured drag above the ET onset. Moreover, we find that the elastic wave frequency grows with Weissenberg number, and at sufficiently high frequency it causes decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and re-laminarization phenomena at low Reynolds number.

System of cracks under the impact of plane elastic waves

The problem of determining the two-dimensional diffraction field and the stress state arising from the interaction of elastic waves with a system of arbitrarily located cracks is solved. Cracks are located in an unbounded elastic medium which is in a plane deformation state. The method of solution is based on the use of discontinuous solutions of the equations of motion of elastic media and the reduction of the original problem to a system of singular integro-differential equations. The obtained systems are solved numerically the mechanical quadrature method.

Nonlinear interaction of Rayleigh waves in isotropic materials: Numerical and experimental investigation

Surface treatment intensity monitoring is still an open and challenging nondestructive testing problem. For the estimation of residual stress with ultrasonic measurements, local linear and nonlinear elastic constants are needed as input. In this paper, nonlinear elastic-wave interactions (also called wave mixing or scattering) — namely, the generation of secondary ultrasonic waves in a nonlinear medium — are considered as a prospective means for near-surface nonlinear elastic parameter evaluation. The allowed interactions between bulk and surface waves, as well as the dependence of the scattering efficiency on the frequency and angle between source waves, were investigated through an analytical model, then compared with FEM simulations and experimental results. Finally, possible future steps for the development of the applied methods for the determination of near-surface higher-order elastic constants are discussed. In addition, several problem-relevant data processing procedures are presented.

A 3D HIGHER-ORDER GRADIENT MODEL FOR A HALF-SPACE GEOMEDIUM

In this paper, a structural model of a geomedium (a soil) is proposed in the form of a simple cubic lattice of spherical particles (blocks) possessing three translational and three rotational degrees of freedom. The force and couple interactions between the particles are modeled by elastic springs of five types. A long-wavelength continuum mathematical model of the soil has been elaborated by the method of structural modeling. An analytical relationship between its macroconstants and microstructure parameters has been found. It is shown that the obtained model differs from the model of the reduced Cosserat medium, which is often employed to describe granular media. In the low-frequency approximation, it can be reduced to the equations of the higher-order gradient theory of elasticity, which are similar to the Cosserat continuum equations with constrained rotation of particles. These equations contain both terms with mixed derivatives with respect to time and coordinate that take into account the inertia of particles rotation in the medium and lead to the wave dispersion, and terms proportional to the spatial derivatives of the fourth order, which describe the contribution of stresses caused by bending of the medium to the potential energy. In the framework of the higher-order gradient model, expressions for the classical and couple stresses in the considered geomedium are found. Boundary conditions are set that consist in the absence of normal and shear stresses on the upper platform of a half-space medium. A condition for the microstructure parameters has been revealed, under which the couple stresses can be neglected. The proposed here higher-order gradient model with given boundary conditions can be used to investigate the propagation and interaction of elastic waves in a semi-infinite geomedium, which are generated by the high-speed movement of trains, as well as to identify and study potentially dangerous effects caused by such movement.

Взаємодія плоских пружних хвиль. Врахування квадратичної та кубічної нелінійності

The interaction of elastic plane harmonic waves in the material, the nonlinear properties of which are described by the elastic potential of Murnaghan, is investigated theoretically. The displacement vector is depended of only one spatial variable and time, a record of the complete system of equations for plane waves moves along the abscissa axis is recorded and used. The interaction of longitudinal waves with a separate considering cubic nonlinearity is investigated. On the basis of the cubic equation of motion, the interaction of four harmonic waves is studied. The method of slowly variable amplitudes is used. Firstly the two-wave interaction is investigated, then the interaction of four waves is described. Shorten and evolutionary equations are obtained, the first integrals of these equations and the record of the law of conservation for a set of four interacting waves are obtained. An analogy is made between the triplets studied when taking into account the interaction of three waves and the triplets investigated in the case under consideration, taking into account the four-wave interaction, quadruplets.

Generalized model of Kapitza conductance across rough interfaces

This paper is devoted to the theoretical prediction of the interfacial heat transfer in nanostructured materials. The main task of this work is the analysis of interaction of elastic waves with the rough interface between two different solids. The presence of toughness leads to a significant increase in the resistance to heat transfer in nanostructures. This fundamental problem is discussed in relation to the commonly used method of wave scattering at rough surface: the Kirchhoff tangent plane method. The method assumes that at the point of the rough surface profile, the surface is regarded as locally smooth, and the reflection and transmission of the incident wave can be described by the scattering at the tangent plane of this point. Based on the elastic wave theory, we use the frequency-dependent continuity conditions to calculate the energy transmission coefficient at the interface. And then its effective value at the rough interface is estimated by using the Kirchhoff method. By substituting this effective value into the formula of Kapitza conductance, we can calculate the Kapitza conductance at the rough interface and analyze the effect of roughness on the interfacial heat transfer.

Application of PZT Ceramic Sensors for Composite Structure Monitoring Using Harmonic Excitation Signals and Bayesian Classification Approach.

The capabilities of ceramic PZT transducers, allowing for elastic wave excitation in a broad frequency spectrum, made them particularly suitable for the Structural Health Monitoring field. In this paper, the approach to detecting impact damage in composite structures based on harmonic excitation of PZT sensor in the so-called pitch–catch PZT network setup is studied. In particular, the repeatability of damage indication for similar configuration of two independent PZT networks is analyzed, and the possibility of damage indication for different localization of sensing paths between pairs of PZT sensors with respect to damage locations is investigated. The approach allowed for differentiation between paths sensitive to the transmission mode of elastic wave interaction and sensitive reflection mode. In addition, a new universal Bayesian approach to SHM data classification is provided in the paper. The defined Bayesian classifier is based on asymptotic properties of Maximum Likelihood estimators and Principal Component Analysis for orthogonal data transformation. Properties of the defined algorithm are compared to the standard nearest-neighbor classifier based on the acquired experimental data. It was shown in the paper that the proposed approach is characterized by lower false-positive indications in comparison with the nearest-neighbor algorithm.

Elastically driven Kelvin–Helmholtz-like instability in straight channel flow

Originally, Kelvin-Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn's bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.

Revisiting imperfect interface laws for two-dimensional elastodynamics.

We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

Multiresolution Dynamic Mode Decomposition (mrDMD) of Elastic Waves for Damage Localisation in Piezoelectric Ceramic

The performance of piezoelectric sensors deteriorated due to the presence of defect, delamination, and corrosion that needed to be diagnosed for the effective implementation of the structural health monitoring (SHM) framework. A novel experimental approach based on Coulomb coupling is devised to visualise the interaction of ultrasonic waves with microscale defects in the Lead Zirconate Titanate (PZT). Multiresolution dynamic mode decomposition (mrDMD) technique in conjunction with image registration, and Kullback Leibler (KL) divergence is utilised to diagnose and localise the surface defect in the PZT. The mrDMD technique extracts the spatiotemporal coherent mode and provides an equation-free architecture to reconstruct underlying system dynamics. Additionally, due to the strong connection between mrDMD and Koopman operator theory, the proposed technique is well suited to resolve the nonlinear and dispersive interaction of elastic waves with boundaries and defects. The mrDMD sequentially decomposes the three-dimensional spatiotemporal data into low and high frequency modes. The spectral modes are sensitive to defects based on the scaling of wavelength with the size of the defect. The error due to offset and distortion was minimised with ad hoc image registration technique. Further, localisation and quantification of defect are performed by evaluating the distance metric of the probability distribution of coherent data of mrDMD acquired from healthy and defected samples. In the arena of big-data that is ubiquitous in SHM, the paper demonstrates an efficient damage localisation algorithm that explores the nonlinear system dynamics using spectral multi-mode resolution techniques by sensitising the damage features.

The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations.

A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.