Longitudinal Elastic Waves Research Articles

Using Poisson’s ratio and acoustic anisotropy parameter to assess damage and accumulated plastic strain during fatigue loading of austenitic steel

The work investigated the effect of fatigue failure on the elastic characteristics of metastable austenitic steel AISI 321: Poisson’s ratio and acoustic anisotropy parameter. The elastic characteristics were calculated using ultrasonic measurements of the propagation time of longitudinal and shear elastic waves. The volume fraction of strain-induced martensite was determined by the eddy current method. Theoretical studies have shown that the main factors influencing Poisson’s ratio are the accumulation of microdamages and changes in phase composition. The change in the acoustic anisotropy parameter is associated with the influence of cyclic deformation on the crystallographic texture of the material matrix and the formation of oriented crystals of strain-induced martensite. Based on the analysis of experimental results, expressions were obtained for calculating damage and relative accumulated plastic deformation based on acoustic measurement data, which are widely used in engineering practice to determine the fatigue life of structural materials.

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

The propagation of coherent longitudinal waves in a viscous liquid containing a random distribution of spherical elastic particles is analysed using a model based on multiple scattering theory. This model, initially developed to describe the propagation of coupled longitudinal and transverse elastic waves in isotropic solid materials, takes into account wave conversions at the particle surface as well as positional correlations between particles via the pair correlation function. By modelling a Newtonian viscous liquid through complex frequency-dependent elastic moduli (i.e. using an imaginary shear modulus), the model is adapted to the case of viscous fluids and we show that conversions of longitudinal waves into transverse waves are important to take into account. We present asymptotic results from the model for case of long wavelength for the longitudinal waves, without assumptions on the shear wavelength. For high concentrations, these wave conversions are reinforced by the contribution of position correlations between the particles. In a subsequent paper, we present numerical validation of the asymptotic approximations and compare them with experimental results for solid particles in water.

The influence of hydrocarbons on the physical properties of sea bottom sediments of the Black Sea of different stages of diagenesis under conditions of high pressures and temperatures and the degree of saturation

The influence of hydrocarbons on the physical properties of sea bottom sediments of the Black Sea of different stages of diagenesis under conditions of high pressures and temperatures and the degree of saturation

An investigation into vibration transmission patterns within metro turnout areas utilizing the structural sound intensity method

Urban rail transit turnout areas are notorious for inducing elevated environmental vibrations due to the complex interactions between wheels, rails, and supporting infrastructure. This paper establishes a comprehensive vehicle-track-tunnel-soil coupled dynamic model of a train traversing a turnout region. The intricate vibration transmission mechanisms within the turnout are explored through numerical simulation and visualization of vibration energy flow pathways. The structural sound intensity method facilitates the directional characterization of both transverse and longitudinal elastic waves emanating from the wheel-rail contact zone. Results reveal distinct propagation patterns between the switch panel and crossing panel, with more pronounced low-frequency energy backflow occurring in the switch panel. The transverse wave is found to dominate the elevated lateral vibrations observed along the tunnel walls. Frequency domain analysis maps the variation in energy flow directionality across one-third octave bands. The findings align closely with field measurement outcomes, validating the capacity of the approach to identify vibration "hot spots." Overall, this research enhances the theoretical comprehension of the complex interplay between diverse factors influencing turnout vibration transmission dynamics. The visualization technique proves instrumental in elucidating the critical mechanisms underlying the exacerbated environmental impact within these structurally intricate domains. Practical insights are distilled regarding turnout design strategies, vibration monitoring, and control methodologies to facilitate the mitigation of detrimental vibration effects.

Elastic wave speeds, Debye temperature and microhardness of YX3 (X = In, Sn, Tl and Pb) intermetallic compounds

In the present work, we reviewed and report on the theoretical prediction of the longitudinal, transverse and average elastic wave veloci-ties, and the Debye temperature for some nonmagnetic YX3 (X = In, Sn, Tl, and Pb) intermetallic compounds with stable cubic AuCu3-type structure. The lattice parameters and the elastic constants used here are taken from the work of Abraham et al [1] using the general-ized gradient approximation (PBE-GGA). Our results are analyzed and compared with the available theoretical and experimental data, and in general a good agreement is found. The deviation between our value (224.4 K) of the Debye temperature θD for YSn3 material and the experimental one (210 K) is around 6.62%, while the deviation between our result (1401 m/s) of the transverse elastic wave velocity for YTl3 intermetallic material and the calculated one (1470 m/s) is about 4.93%. In addition the Young’s Modulus and Poisson’s Ratio of YX3 intermetallic compounds for the crystallographic planes (100), (110) and (111) are predicted.

Propagation characteristics of elastic longitudinal wave in a piezoelectric semiconductor metamaterial rod and its tuning

Elastic metamaterial structures have many distinct wave properties such as band gap structure and topological phase inversion. The coexistence and interaction of piezoelectricity and semiconductor behavior in piezoelectric semiconductor (PS) materials endow metamaterials with some new physical effects. We investigate the propagation characteristics of elastic longitudinal waves in a metamaterial rod made of n-type PS material and piezoelectric (PE) dielectric material. Based on one-dimensional rod model, we present the transfer matrixes for the PS and PE phases as well as the interfacial transfer matrix of unit cell. The analytical dispersion relations of the considered PS-PE metamaterial rod are obtained by utilizing Bloch's theorem. Numerical results show that band gap structures of the metamaterial rod are dependent on the initial electron concentration, length ratio of PE phase, interfacial condition, and capacitor connected with the PE phase. The selection of certain initial electron concentration, length ratio of PE phase, and capacitor can lead to the appearance of topological phase inversion, highlighting the potential for controlling and manipulating the wave propagation properties of PS metamaterial structures. This paper provides a theoretical guidance on the development of smart devices based on PS metamaterial structures. The novel combination of piezoelectricity and semiconductor behavior in these materials opens up new avenues for designing and engineering advanced devices with tailored wave properties and functionalities.

Exploring wave propagation and attenuation in a metamaterial bar using dual-action vibration absorber with multifrequency resonators

This paper introduces a method for attenuating longitudinal elastic waves in metamaterial bars through the utilization of Dual-Action (DA) vibration absorbers equipped with multifrequency resonators (MFRs). The metamaterial bar (Metabar) is composed of a linear arrangement of evenly distributed and enclosed DA vibration absorbers connected to an isotropic bar. The DA vibration absorber is constructed with multiple spring-mass resonators interconnected with each segment of the isotropic bar at two points. An analytical methodology is formulated employing Finite Element Modeling (FEM) and Bloch’s theorem to demonstrate the existence of multiple stopbands, leading to the generation of broad and configurable frequency stopbands. The article illustrates the design and modeling of the metabar’s DA vibration absorber, showcasing analytically that the vibration suppression and, consequently, wave attenuation within the metamaterial bar are grounded in the fundamental principles of basic mechanical vibration absorption. The DA absorber effectively prevents longitudinal wave propagation through the metabar by generating two internal forces to counteract any incoming wave within the stopband frequencies. Furthermore, these internal forces can be adjusted by optimizing the effective properties of the DA vibration absorber. A comprehensive parametric investigation is then conducted to analyze how the properties of the enclosed MFRs of the DA absorber, such as mass densities and stiffness coefficients, influence the locations and sizes of the frequency stopbands. The results from FEM simulations show a substantial alignment with dispersion curves across various prescribed configurations, offering strong validation for the proposed metamaterial design that integrates the DA vibration absorber with MFRs. The introduced mechanism for vibration absorption and suppression is of significance in applications involving the control and manipulation of wave propagation.

Simultaneous manipulation of longitudinal and transverse elastic waves with a sharp focusing effect and customizable energy splitting ratios

Mode coupling and conversion between longitudinal and transverse modes are ubiquitous and universal in elastic waves, presenting a challenge in realistic applications such as nondestructive evaluation and geological exploration, where independent and separate manipulation of each mode is demanded. In this article, we propose a design of elastic metalens that can realize a high-efficiency focusing for the longitudinal wave and a V-shaped converging pattern for the transverse wave at the same time. The metalens is constructed from a metagrating, where each meta-atom has a simple configuration and renders high diffraction efficiency even for large steering angles, enabled by concurrent utilization of grating diffraction theory and advanced optimization algorithms. Interestingly, an arbitrary energy splitting ratio between the reflected longitudinal and transverse waves can be obtained by precisely controlling the coupling strength and conversion efficiency between them, providing improved flexibility and adaptability to various application environments. Two illustrative examples with a sharp focusing effect and tailored conversion efficiency are explicitly demonstrated, with a 50/50 energy splitting ratio between the longitudinal and transverse waves in the first case, and a 70/30 ratio in the second one.

Formation Model for Acoustic Characteristics of Solid Media with Ordered Fracturing

Introduction. The development of new structural materials and improvement of existing technologies for the production of new products on their basis lead to the emergence of new types of medium discontinuities. Therefore, the development of new models of discontinuities that take the previously ignored parameters into account seems to be relevant for the purposes of nondestructive testing and structural measurements. This concerns, e.g., the roughness of adjacent surfaces of microcrack ordered sets.Aim. Theoretical substantiation for the processes of elastic waves propagation through an elastic medium containing an ordered lattice of microcracks with boundary conditions in the linear slip approximation, modified by taking into account the parameters of micro-convexities of microcrack rough boundaries. Database formation for experimental studies aimed at determining the physical and mechanical characteristics of structural materials.Materials and methods. The acoustic characteristics of materials were determined based on the derivation and solutions of dispersion equations describing the formation and propagation of effective longitudinal, transverse, and Rayleigh surface elastic waves in elastic media with ordered cracking. Their values were also used to determine the effective speed of Rayleigh surface waves.Results. The conducted simulation of elastic wave formation processes showed that an increase in the concentration of microcracks leads to a decrease in the phase velocities of effective longitudinal, transverse, and surface waves, as well as to an increase in the attenuation coefficients at given ultrasound frequencies and material parameters.Conclusion. The radius of the microsphere that replaces the surface micro-convexity and the roughness parameter Rz have a significant impact on the formation of physical and mechanical characteristics of materials, which are determined by the results of ultrasonic measurements. The developed model can be recommended as a basis for interpreting the results of ultrasonic measurements.

Magnetoelastic Losses in the Linear Response Region for Three- and Four-Axis Idealized Magnets

In the presented studies, a description of the losses related to relaxation processes in idealized three- and four-axis ferromagnets, as well as ferrites, is considered for the case of a linear response (small perturbations) on the basis of a macroscopic approach. The description takes into account reversible 90° displacements of domain walls (DW) of concentrations (с), ways of DW pinning by linear defects, and processes of DW displacements and rotations of the spontaneous magnetization vector I⃗s, caused by a longitudinal elastic stress wave σ. As a result, the anisotropy of amplitude-independent losses emerges due to displacement processes. Frequency dependence of losses is obtained with consideration of the magnetic symmetry of the crystal, its magnetostructural parameters, and the concentration of magnetic phases ci. The paper also describes the internal frictionn Q-1, the absorption coefficient a, the velocity of propagation of elastic vibrations v and the Δ (1/E)-effect, thus allowing to reveal the texture in the distribution of DWs by their types.
 It is shown that if the relaxation times of rotation processes τ = β / 2K1 and displacement processes τc = βс / mω20 are the same, then the maxima of the dependence of internal friction on frequency Qc-1(ω) and QB-1(ω) superimpose on each other.
 The revealed features of magneto-elastic energy dissipation are of interest for laboratory studies and have promising applications in practice for determining the orientation of crystals, describing the texture, and calculating the differential ΔЕ-effect in magnets. The features of the ΔЕ-effect for the considered cases are also revealed.

High frequency multi-field continualization scheme for layered magneto-electro-elastic materials

Magneto-electro-elastic (MEE) heterogeneous materials with periodic microstructure are investigated, with special focus on the particular case of a layered MEE material. By exploiting the transfer matrix method in combination with the Floquet–Bloch boundary conditions, the frequency dispersion spectrum can be derived by solving an eigenproblem, involving a 12 × 12 transfer matrix with palindromic characteristic polynomial. In particular, by assuming the cubic symmetry of layers, the problems involving longitudinal and transverse elastic waves are uncoupled. This circumstance has the advantage of simplifying the treatment and the size of the subproblems to be solved, corresponding to a 4 × 4 transfer matrix for the longitudinal case, and a 8 × 8 transfer matrix of the transverse problem, both characterized by palindromic characteristic polynomials. Afterward, a dynamic multi-field continualization approach is proposed to investigate wave propagation in MEE layered periodic material by matching the Z-transform of the vector collecting the nodal fields to the two-sided Laplace transform of the same vector at the macroscale. The continualization technique allows identifying multi-field integral-type non-local continua as well as multi-field generalized gradient-type (higher-order) non-local continua. Finally, to verify the accuracy of the proposed approach, the dispersion curves derived from the continualization technique are compared with the curves provided by the Floquet–Bloch theory.

Local gradient theory of dielectrics incorporating polarization inertia and flexodynamic effect

A higher-grade theory of non-ferromagnetic thermo-elastic dielectrics which incorporates the local mass displacement, the heat flux gradient, polarization inertia, and flexodynamic effects is developed. The process of local mass displacement is associated with changes in material microstructure. Using the fundamental principles of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics, the gradient-type constitutive equations are derived. Due to accounting for the polarization inertia, the rheological constitutive equation for the polarization vector is obtained. In the balance equation of linear momentum, an additional term with the second time derivative of the polarization vector appears in comparison with the classical theory. This term controls the influence of the dynamic flexoelectric effect on the mechanical motion of dielectric solids. The propagation of a plane harmonic wave is analyzed within the context of the developed theory. It is shown that the theory allows for capturing the experimentally observed phenomenon of high-frequency dispersion of a longitudinal elastic wave. The theory may be useful for modeling coupled processes in nanodielectrics and heterogeneous polarized systems.

АНАЛІЗ ПРУЖНИХ ХВИЛЕУТВОРЕНЬ У КАНАТАХ ВАНТАЖОПІДЙОМНИХ КРАНІВ

In the article the boundary value problem on the elastic longitudinal waves motion in the load lifting cranes and mine mechanisms variable length ropes is considered. Solutions of the Cauchy problem, which describe longitudinal oscillations propagation in the ropes (flexible suspensions) as in areas with moving boarders, are found. Displacements and stresses dynamic fields in variable length steel ropes of the specified load lifting mechanisms are investigated. Usually the ropes are balanced, and the main rope carries concentrated stress which before the systems movement was at the main ropes lower end. Dynamic forces in perfectly elastic variable length steel ropes estimation is shown, that only when lifting ropes without end loads under non-integrated boundary conditions, their efforts do not increase. However, practical experience shows that this phenomenon is not observed at moderate lifting speeds due to the fact that along with the dynamic forces amplitudes increase. Due to the decrease in length there is a simultaneous decrease in the amplitudes of their oscillations. The object of analysis refers to a wide range of variable length oscillations one-dimensional objects. A classical mathematical model to describe oscillations and waveforms is used. When studying wave fields in areas with moving boundaries the reflection of pulses from such boundaries is established. Elastic type waveforms in variable length rods (rope models) taking into account the fact that these rods have circular cross section of variable (length of rope/rod) area (rods are cylindrical, rotational paraboloids form, conical rods) is considered. Method based on the possibility of constructing wave equation from waves reflected from fixed and moving given boundaries of a semi-infinite domain solutions is applied.

NONLINEAR EFFECTS IN CRYSTALLINE SOLIDS WITH SATURATION OF AMPLITUDE-DEPENDENT INTERNAL FRICTION, DECREASING WITH IN-CREASING FREQUENCY

As a result of modification of quasi-static elastic and inelastic hysteresis, dynamic hysteresis equations of state of crystalline solids with frequency-dependent saturation of amplitude-dependent internal friction decreasing with increasing frequency are proposed. The nonlinear propagation of initially harmonic longitudinal elastic waves in rods made of such materials is investigated by the perturbation method. Numerical, graphical and comparative analysis of the obtained solutions is carried out and characteristic amplitude-frequency dependenc-es of nonlinear wave effects are revealed. A method for determining the type of dynamic hysteresis for crystal-line solids with frequency-dependent saturation of amplitude-dependent internal friction is proposed.

Effects of CO 2 phase state on the seismological properties of porous materials: implications for seismic monitoring of volcanic hazards and sequestered carbon

Abstract Time-lapse seismic monitoring is a key component in the geological sequestration of greenhouse gases. Currently, a lack of understanding of the influence of injected CO 2 on rocks’ geophysical signatures is reported. Using a novel ultrasonic experimental system, we measured the variations in the longitudinal (P) and transverse (S) elastic wave speeds of a CO 2 -saturated porous medium at different pressure and temperature conditions around the CO 2 critical point. The results show that both P- and S-wave speeds, corrected to seismic frequencies, decreased by more than 4.5% across the CO 2 gas to liquid and gas to supercritical states, primarily as a consequence of CO 2 density increase. This study provides a-20 firm basis for the use of seismological methods in monitoring sequestered CO 2 ; although the abruptness, and hence remote seismic detectability, depends on which phase boundary is crossed. Further, these measurements also allow us to compare observations to frequency-dependent wave propagation theory. The observed wave speeds mostly align with those calculated at 1 MHz using the Biot theory for both CO 2 and H 2 O saturated states. However, the observed and calculated wave speeds diverge above the phase transition in some of the tests, possibly due to the kinetics of the phase transition within a porous medium. As such, aside from the direct utility in providing information on the expected seismic responses, the CO 2 provides a highly tunable fluid that can be advantageous for experimental studies.

Deep-learning-based framework for inverse design of a defective phononic crystal for narrowband filtering

This paper proposes a deep-learning-based inverse design framework for a one-dimensional, defective phononic crystal (PnC) as a narrow bandpass filter under longitudinal elastic waves. The purpose of the design-optimization problem is to maximize the transmittance at the defect-band frequency, which is equal to the target frequency. The framework comprises three steps: (i) inverse design generation and filtering, (ii) forward analysis of frequencies and filtering, and (iii) forward analysis of transmittance and near-optimal design selection. Four deep-learning models are considered in the inverse model: a deep neural network, a tandem neural network, a conditional variation autoencoder, and a conditional generative adversarial network. The frameworks developed with each deep-learning model are evaluated using a test dataset and an arbitrarily defined defect-band frequency and phononic band-gap range. The results show that the frameworks proposed using the conditional variation autoencoder and the conditional generative adversarial network effectively present the best performance by solving the nonunique response-to-design mapping problem through probabilistic approaches. The deep-learning-based framework reduces the need for manual intervention and simplifies the inverse design process, making it a promising approach for finding the near-optimal design solution for the use of defective PnCs as narrow bandpass filters.

Manipulation of a Piezoelectric p–n Junction with an Elastic Longitudinal Wave

Manipulation of a Piezoelectric p–n Junction with an Elastic Longitudinal Wave

Elastic wave propagation and bandgaps mechanism of two-dimensional windmill-like elastic metamaterials

Inspired by the advantages of the grille structures, an innovative two-dimensional (2D) windmill-like elastic metamaterials (EMs) based on multiple resonators is presented for obtaining ultrawide bandgaps at a relatively low frequency. The dispersion relations and the mechanism of bandgap formation are investigated using an analytical model of windmill-like EMs. Moreover, the low-frequency bandgap between the optical and acoustic dispersion curves of windmill-like EMs with a single local resonator has been independently determined analytically. Afterward, the band structures of windmill-like EMs with different numbers of local resonators and symmetry and the same total mass are compared. By applying the finite element method, continuous symmetrical and chiral windmill-like EMs are established and analyzed based on the analytical results. The introduction of the antisymmetric chiral structure results in a 23.08% reduction in the frequency of the first bandgap compared to symmetric windmill-like EM.A further study is conducted on the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission spectra. Both the numerical analysis and experimental validation of finite periodic lattices demonstrate the effect of vibration attenuation on longitudinal elastic waves. This research provides important clues and theoretical guidance for the design of vibration isolators, beams, plates, and other renewed devices.

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.

Magnetically tunable longitudinal wave band gaps in hard-magnetic soft laminates

Hard-magnetic soft materials belong to the class of active materials that undergo finite deformation and alter their material properties when subjected to magnetic loading. Because of these characteristics, the periodic composites/phononic crystals made up of hard-magnetic soft materials can be promising candidates for filtering acoustic/elastic waves across frequency bands that can be tuned in real-time by applying external magnetic loading. In this work, the nonlinear finite deformation, and the superimposed small-amplitude longitudinal elastic wave band gap characteristics of an infinite periodic hard-magnetic soft material laminate under the applied magnetic flux density are investigated. The compressible Gent hyperelastic model in conjunction with the ideal hard-magnetic soft material model is used for characterizing the constitutive response of laminate phases. The band structure of an infinite periodic hard-magnetic soft material laminate subjected to magnetic load is extracted by developing an in-house finite element model with Bloch’s periodic boundary conditions. The influence of some factors such as material properties, volume fractions, and applied magnetic flux density on the tunability of the longitudinal wave band gaps is explored. The numerical findings demonstrate that the width and the position of band gaps can be tuned by varying the applied magnetic flux density. The volume fraction and the material properties of laminate phases also play significant roles in the generation of band gaps. The numerical results and inferences reported here should provide the guidelines for designing futuristic remotely and actively controlled wave-manipulating devices.