Propagation Characteristics Of Elastic Waves Research Articles

Peridynamic computations for thin elastic rods

AbstractPeridynamics is a nonlocal continuum mechanics formulation well suited for simulating dynamic fracture phenomena. Various peridynamic material formulations have been developed in recent years. These models have some differences, particularly regarding the correct handling of elastic deformation. This study investigates the elastic wave propagation characteristics of bond‐based, ordinary state‐based, continuum‐kinematics‐inspired peridynamics and a local continuum consistent correspondence formulation. Specifically, it examines the behavior of longitudinal pressure waves within thin rods. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. In contrast, the local continuum consistent formulation exhibits outstanding accuracy in modeling wave propagation. Moreover, the fascinating “spaghetti fracture” phenomenon, where a bent thin rod always breaks into three or more pieces, motivates additional investigations. It is shown that reproducing a different number of fragments using peridynamic simulations is possible. Although initial experiments can be replicated, the sensitivity to numerous parameters necessitates further investigations for a more comprehensive understanding and validation.

Research on damage identification of wind power tower structure based on deformation and vibration dual parameter analysis

Abstract During the operation of the wind turbine, the force on the wind turbine tower is mainly caused by the vibration source at the top. As a high-rise structure with a large span, traditional vibration mechanics is used to analyze the overall force on the tower body, but the analysis of vibration modes or modes is slightly insufficient. This article adopts the analysis method of elastic wave dynamics to identify damage to the structure of wind power towers based on deformation and vibration dual parameter analysis. This article analyzes the propagation characteristics of elastic waves in tower structures, concrete bases, and foundation parts when damaged. This article develops a remote online monitoring and early warning platform for wind power tower bodies based on the attenuation properties of elastic waves. This article monitors the vibration and inclination of the tower drums of 5 wind turbines (# 13, # 31, # 34, # 49, and # 52). The tower drums have not undergone irreversible tilting or torsional deformation. However, through vibration analysis, it is suggested to check whether there is crushing between the tower drums and the concrete base, as well as whether there are local cracks on the surface of the concrete base. There may be local damage to the foundation ring of tower #31. It is recommended to check for local cracks in the foundation ring. This ensures the safe operation of wind power towers and has certain practical application value.

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

The coupled band gap of longitudinal wave in metamaterial-based double-rod containing resonators

This study investigates the coupled band gap and vibration propagation characteristics of elastic waves in a metamaterial elastic double-rod system with attached periodic resonators. We derive the band gap structure and vibration attenuation equations of double-rod structure using the spectral element method, Bloch’s theorem, and the transfer matrix method. The validity of the coupled band gap is confirmed through forced vibration response analysis. Furthermore, we examine the effects of various parameters on the double-rod system, revealing that coupled band gaps exist with the average vibration attenuation rates of −50.23 dB for rod one and −47.87 dB for rod two, respectively. Remarkably, by adjusting the double-rod parameters, both the band gap frequency range and vibration attenuation ability of the coupled band gap can be adjusted to meet specific engineering requirements in low-frequency regions. This research contributes to developing continuous mechanical structures featuring coupled band gaps.

Influence of ice properties on wave propagation characteristics in partially frozen soils and rocks: A temperature-dependent rock-physics model

A better understanding of the temperature effects on the propagation characteristics of elastic waves in frozen soils and rocks is imperative for accurately quantifying their freezing degrees. Although the existing rock-physics models based on the three-phase Biot (TPB) theory adeptly interpret observed velocity variation with temperature (VVT) curves, they often lack a comprehensive understanding of the mechanisms underlying attenuation variation with temperature (AVT) curves. In this study, we first extend the TPB theory to incorporate the temperature-dependent properties of ice, such as changes in volumetric fraction, morphology, and viscoelasticity, by integrating the relevant thermodynamic laws. Model parameters related to ice properties and interactions, such as rigidity, shear moduli, density, and friction, are redefined. Then, using a numerical rock-physics modeling approach, we examine influential factors and modes of the wave VVT and AVT responses. Our results indicate that the P- and S-wave velocities increase with source frequency, consolidation degree, and frame-supporting ice content, whereas they decrease with temperature and pore-floating ice content. The P- and S-wave attenuation factors increase with the frame-supporting ice content and decrease with the consolidation degree. Rising temperatures tend to amplify the peak magnitude of the P-wave attenuation factors and shift the central frequency of the S-wave attenuation factors. Finally, within a temperature-controlled laboratory environment, we conduct ultrasonic wave transmission testing on brine-saturated sediment and rock specimens. The results demonstrate that as the temperature increases from −15°C to −3°C, the P- and S-wave velocities decrease, whereas the P-wave attenuation factors decrease and the S-wave attenuation factors initially rise before declining. Our viscoelastic TPB theory outperforms the existing ones in interpreting the S-wave AVT observations. This temperature-dependent rock-physics model holds promise for interpreting the sonic logging data in the time-lapse monitoring of permafrost, glaciers, and Antarctica.

Peridynamic computations of wave propagation and reflection at material interfaces

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy.

Nonlinear elastic waves generated by surface wave interaction with local plasticity in thick-walled structures

Thick-walled structures (TWSs) are frequently utilized as primary load-bearing structures across diverse industrial sectors, illustrated by train axles. Proper health monitoring, particularly for early damage detection, is required to ensure the operational safety and structural integrity of such structures. Nonlinear elastic-wave-based structural health monitoring techniques present a potentially efficacious methodology, which relies heavily upon the understanding of nonlinear wave generation and propagation characteristics. Unfortunately, due to the complexity introduced by various wave modes in TWSs, a comprehensive understanding of nonlinear elastic waves is still lacking. Considering practical local plasticity on the surface of a TWS, this study investigates the characteristics of nonlinear elastic wave generation and propagation resulting from the fundamental surface wave-local plasticity interaction. Theoretical analyses were carried out to examine the scattering features of the generated nonlinear bulk waves based on Snell’s law. Finite element simulations were then performed to confirm the predicted scattering characteristics of the nonlinear bulk waves, with the introduction of a local material nonlinearity to replicate the plasticity in a TWS. Using the extrusion method, a local plastic zone was produced on an aluminum thick-walled beam. Experiments were finally carried out using a laser vibrometer to confirm the scattering features of nonlinear elastic waves. It was found that the nonlinear shear bulk waves are mainly generated due to the fundamental surface interaction with local plasticity. Furthermore, the generated nonlinear shear bulk waves propagate at a fixed angle towards the interior of the TWS, which can be measured on the opposite surface. The elucidation of the nonlinear elastic wave generation and propagation characteristics paves the way for an effective sensor arrangement in early damage detection applications.

Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial

A novel hollow star-shaped chiral metamaterial (SCM) is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial, exhibiting a wide band gap over 1 500 Hz. To broaden the band gap, solid single-phase and two-phase SCMs are designed and simulated, which produce two ultra-wide band gaps (approximately 5 116 Hz and 6 027 Hz, respectively). The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave. The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied. Decreasing the concave angle leads to an increase in the width of the widest band gap, and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases. Additionally, the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces, wave propagation directions, group velocities, and phase velocities. Ultimately, the analysis focuses on the transmission properties of finite periodic structures. The solid single-phase SCM achieves a maximum vibration attenuation over 800, while the width of the band gap is smaller than that of the two-phase SCM. Both metamaterials exhibit high vibration attenuation capabilities, which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.

Non-Destructive Inspection Method Using Elastic Waves for Quality Management in the Bending Process Region of BFRTP

In order to establish a sustainable infrastructure, structures must maintain their minimum required performance for an extended period. Typically, existing concrete structures are reinforced with steel, but the susceptibility of steel reinforcements to corrosion, attributed to factors such as carbonation and chlorides, can lead to performance degradation, rendering the specified requirements unmet. As a remedy, there has been a growing interest in using lightweight and corrosion-resistant fiber-reinforced polymer (FRP) bars as an alternative to traditional steel reinforcement in concrete structures. Particularly noteworthy is the use of FRP bars manufactured with thermoplastic resins (FRTP) due to their ease of processing and convenient applicability on construction sites. This study delves into the mechanical behavior evaluation by examining the propagation characteristics of elastic waves in the curved section of basalt FRTP (BFRTP). Multiple BFRTP bars underwent a 180-degree bending process, subject to various conditions, including heat and twist variations. Subsequent measurements focused on the propagation characteristics of elastic waves in the curved sections, emphasizing wave attenuation, frequency features, and propagation velocity. Additionally, bending tensile tests were conducted on the curved bars, and a comparative analysis was performed between the tensile strength and the aforementioned elastic wave propagation characteristics. The results affirm a consistent correlation between the propagation characteristics of elastic waves (amplitude ratio, centroid frequency, velocity) during the traversal of the curved BFRTP section and its tensile strength. Notably, both centroid frequency and velocity exhibited correlation coefficients exceeding 0.7, suggesting their potential efficacy as reliable indicators for estimating tensile strength.

Characteristics of elastic wave propagation and anomalous Doppler effect in the periodic structure of floating slab track

Characteristics of elastic wave propagation and anomalous Doppler effect in the periodic structure of floating slab track

Design of patch-shaped lens with thickness variations for elastic wave focusing in thin-plate structures

In mechanical engineering, focusing on elastic waves is pivotal for applications, such as energy harvesting, shock mitigation, and wave manipulation. While phononic crystals have historically been a key method for managing wave propagation, this study explores a novel technique. This method introduces gradient refractive-index (GRIN) lenses by altering the plate thickness and creating localized high-refractive-index zones. Unlike traditional methods, this localized GRIN approach aims to overcome the fabrication and structural limitations, particularly in thin structures. The patch-shaped lenses offer the potential for elastic wave focusing in thinner structures without any degradation of structural performance. Through numerical analysis, we established design principles and examined the elastic wave propagation and focusing characteristics across various thickness variation profiles. This study conducts a thorough analytical and experimental evaluation of these lenses to confirm their effectiveness, structural robustness, and suitability for optimizing wave concentration in various mechanical engineering applications. The research represents an alternative, innovative, and promising pathway in the field of wave focusing, transcending the traditional constraints of thin plate structures.

In-plane surface waves propagating in a coated half-space based on the strain-gradient elasticity theory

By employing the strain gradient elasticity theory, we investigate the propagation of in-plane surface waves in a coated half-space with microstructures. We first investigate the general case of the present problem, that is, both the surface layer and the half-space are described by the strain-gradient elasticity theory. We formulate the boundary and continuity conditions of the general case and derive the dispersion relations of the surface waves. Then we investigate two special cases: (1) the surface layer is described by the strain-gradient elasticity theory, while the half-space by the classical elasticity theory; (2) the surface layer is described by the classical elasticity theory while the half-space by the strain-gradient elasticity theory. We examine the effects of strain-gradient characteristic lengths on the dispersion curves of surface waves in all cases. This study helps to further understand the propagation characteristics of elastic waves in materials with microstructures.

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.

Band gap tunability and wave propagation of a novel fully symmetric single-phase metamaterial

In this paper, a new type of fully symmetric single-phase metamaterial structure is proposed. Based on the finite element method, the band gap characteristics of different forms of the structure and the generation principle of the band gap are discussed. The analysis of the formation mechanism of the band gap shows that the proposed structure can achieve the purpose of expanding the band gap in the low frequency range by changing the structure and adding inclusions. Then, the variation trend of the band gap frequency range in the case of small deformation of the proposed structure is discussed. In addition, the propagation characteristics of elastic waves in the proposed structure are analyzed according to the variation characteristics of frequency contours, phase velocities and group velocities. Finally, the frequency response spectrum obtained from the propagation of elastic waves in a finite lattice composed of Model No. 3 elements further confirms the role of the proposed structure in suppressing wave propagation. The results show that the proposed structure has good band gap characteristics in a certain frequency range, which can provide ideological guidance for the design of metamaterials for achieve low-frequency sound insulation and vibration reduction.

Study on wave propagation in the modulation structure with gradually changing impedance according to specific waveform based on magneto-rheological fluid

This work proposes a novel hierarchical modulation structure with gradually-changed impedance built by magneto-rheological (MR) fluid and investigates its wave propagation characteristics theoretically and experimentally. Based on the impedance tunable property of the MR fluid, applying multiple magnetic fields to MR fluid realizes the modulation of this proposed structure, and regulating its magnetic field distribution law can effectively change the impedance variation forms in the structure. Establish the elastic wave propagation model of this modulated structure, and analyze the variation trends of its elastic wave propagation characteristics with different impedance distribution patterns, taking the vibration level difference as an indicator. Subsequently, conduct experimental testing for the transmissibility of elastic waves. The results show that the elastic wave transmission characteristics of the proposed modulation structure mainly depend on its impedance variation rate and the frequency of external excitation. On a broader band of the frequency range (20–300 Hz) studied in this paper, the gradual impedance distribution of MR fluid enhances the transmission loss of elastic waves compared to a uniform distribution of its impedance. Moreover, in the lower frequency range (40–125 Hz), the layered modulation structure with a non-monotonic variation of impedance following a wave-like waveform presents more significant attenuation on elastic waves than the structure whose impedance varies monotonously in a gradient waveform. This work contributes to expanding the design thoughts of the structure with gradually changing impedance and providing new ideas and means for the control of elastic waves.

Angular wave propagation through one-dimensional phononic crystals made of functionally graded auxetic nanocomposites

Composites reinforced with graphene origami nanofillers possess negative Poisson's ratio and obtain multifunctional features offering unique mechanical properties such as tunable auxeticity, high impact resistance, better indentation resistance, and improved fracture toughness. This paper introduces such novel nanocomposites into functionally graded multilayered phononic crystals and numerically investigates the propagation characteristics of normally and obliquely incident waves in the structures containing components with negative Poisson's ratio. Theoretical models of present structures are formulated and solved by the state space approach. The transfer matrix method is used to obtain dispersion relations of normally and obliquely incident waves. A comprehensive parametric study is conducted to discuss the propagation characteristics of elastic waves in the structures with auxetic and non-auxetic components which can be tuned by the weight fraction and hydrogen coverage of graphene origami fillers. The results indicate that introducing components with negative Poisson’ ratio into unit cells can significantly affect wave propagation features. Wave modes have different sensitivities to the weight fraction and hydrogen coverage of graphene origami fillers. Weigh fraction can manipulate all wave modes simultaneously, while hydrogen coverage only influences longitudinal modes and keeps transverse modes nearly undisturbed. Theoretical results shed insights into the design of high-performance multifunctional phononic crystals.

Micromechanics and Ultrasonic Propagation in Consolidated Earthen-Site Soils.

Although nondestructive ultrasonic technologies have been applied in laboratory and field tests in the field of heritage conservation, few studies have quantified the relationship among the real microstructures, micromechanical properties, and macroscopic acoustic responses of earthen-site soils. This paper develops a micromechanics-based multiscale model for quantitatively exploring the ultrasonic propagation characteristics of elastic waves in untreated and consolidated earthen-site soils. Scanning electron microscope images and image processing technology are integrated into the finite-element simulation. The effects of microstructure and wave features on the acoustic characteristics of soils are quantitatively investigated under pulsive loading. The simulation results of untreated and consolidated soils are efficiently compared to ultrasonic test data. It is demonstrated that the integration of microstructure image processing and multiscale modeling can predict the ultrasonic pulse velocity well, which improves the accuracy of laboratory testing and field monitoring and better serves the evaluation and implementation of engineering practice in the field of heritage conservation.

Design and optimization of the dual-functional lattice-origami metamaterials

This study proposes a multi-scale composite lattice-origami metamaterial (MCLOM) to achieve excellent bandgap characteristics and energy absorption capacities. The MCLOMs are constructed by considering the high impedance mismatch of lattice structures, the spatial deformability of origami structures, and the tunability of the components in multi-scale composite materials. Firstly, elastic wave propagation characteristics are analyzed in the Bloch wave framework, revealing the realization of complete bandgaps and their generation mechanism by mode shape analysis and transmission spectrum. Subsequently, an optimization framework integrating the particle swarm optimization (PSO) algorithm is developed to maximize the first bandgap’s bandwidth by adjusting various component parameters. Under optimal distribution, the proposed metamaterials achieve remarkable improvements of 289% and 271% in the design objectives of two lattice-origami metamaterials with 90∘ dihedral angle compared to the initial distribution. It can be demonstrated that non-uniform distributions of multi-scale composite materials are dramatically effective for broadband wave attenuation. Additionally, while striving to widen the bandgap, the energy absorption capacities of structures are also crucial. The effect of the distribution of multi-scale composite materials with the optimal bandgap on the energy absorption performance is investigated. The results reveal that the optimal distribution of the lattice-origami metamaterials yields notable improvements of 48.26% and 34.86% under low-velocity impact, and 37.41% and 25.19% under medium-velocity impact. This work presents innovative concepts and approaches for devising and implementing novel dual-functional metamaterials, undoubtedly propelling the continual progress of material science and engineering technology in the times ahead.

Investigation of long-wavelength elastic wave propagation through wet bentonite-filled rock joints

The saturation of the compacted bentonite buffer in the deep geological repository can cause bentonite swelling, intrusion into rock fractures, and erosion. Inevitably, erosion and subsequent bentonite mass loss due to groundwater inflow can aggravate the overall integrity of the engineered barrier system. Therefore, the coupled hydro-mechanical interaction between the buffer and rock during groundwater inflow and bentonite intrusion should be evaluated to guarantee the long-term safety of deep geological disposal. This study investigated the effect of bentonite erosion and intrusion on the elastic wave propagation characteristics in jointed rocks using a quasi-static resonant column test. Jointed rock specimens with different joint conditions (i.e. joint surface saturation and bentonite filling) were prepared using granite rock discs sampled from the Korea Underground Research Tunnel (KURT) and Gyeongju bentonite. The long-wavelength longitudinal and shear wave velocities were measured under different normal stress levels. A Hertzian-type power model was used to fit the wave velocities, and the relationship between the two fitted parameters provided the trend of joint conditions. Numerical simulations using three-dimensional distinct element code (3DEC) were conducted to better understand how the long-wavelength wave propagates through wet bentonite-filled rock joints.