Attenuation Of Elastic Waves Research Articles

Investigating the impact of shear and bulk viscosity on the damping of confined acoustic modes in phononic crystal sensors

Phononic crystal (PnC) sensors are recognized for their capability to control acoustic wave propagation through periodic structures, presenting considerable potential across various applications. Despite advancements, the effects of fluid viscosity on PnC performance remain intricate and inadequately understood. This study theoretically investigates the influence of shear (dynamic) and bulk viscosity on acoustic wave damping in defective one-dimensional phononic crystal (1D PnC) sensors designed for detecting liquid analytes. Acetic acid with varying viscosities is considered to fill a cavity layer intermediated by a multilayer stack of lead and epoxy. The effects of dynamic and bulk viscosity on the resonance characteristics of the defective mode were analyzed. Numerical results reveal that increased dynamic viscosity leads to substantial broadening and decreased intensity of resonance peaks, accompanied by a shift to higher frequencies due to enhanced elastic wave attenuation and damping. At low dynamic viscosity (η = 0.2 ηd), numerous resonance peaks with varying intensities are observed. However, at higher viscosities (η = 2.0 ηd to η = 10.0 ηd), only one prominent peak appears in the spectrum. The intensity of this resonant peak starts at 98% for η = 2 ηd and decreases to 58.8% as the dynamic viscosity increases to η = 10 ηd. Additionally, the combined effect of dynamic and bulk viscosity introduces further damping, causing a strong shift of the resonance peak to higher frequencies, along with an increase in the full width at half maximum (FWHM) and a decrease in the quality factor (QF). These findings emphasize the necessity of incorporating both shear and bulk viscosity in the design of PnC sensors to enhance their sensitivity and accuracy in practical applications. This theoretical framework provides critical insights for optimizing sensor performance and bridging gaps between theoretical predictions and experimental observations, especially in 1D PnCs, offering potential solutions to challenges in real-world PnC sensor applications.

Meta-arch structure: Designed reinforcement cage to enhance vibration isolation performance

In this study, inspired by the mechanical metamaterials with bandgap properties, a new type of meta-arch structure (MAS) for the attenuation of elastic waves is proposed. In this metastructure, the reinforcement cage, typically employed to enhance the tensile properties of building materials, has been redesigned and transformed into a new structure containing circular tubes with embedded resonant microstructures. The vibration reduction performance of the MAS was illustrated by the frequency response analysis in the simulation calculation, and the generation mechanism of the vibration attenuation band was revealed. The specimens of the complex MAS consisting of gypsum, reinforced steel bars, and tubes were fabricated, and the vibration response experiments were carried out to determine the dynamic properties of the novel MAS. The results show that the designed arch structure exhibits a broad vibration attenuation band without sacrificing its structural bearing capacity. Additionally, the robustness of the band gap is demonstrated by analyzing how changes in the positions of excitation and response points influence the band gap. Moreover, the MAS can be customized for specific application scenarios of vibration reduction according to the parameter analysis. Finally, the experimental results closely align with the numerical estimations, confirming the feasibility of the design method for reducing vibrations. This work provides a new method for the development of building structures for vibration and noise control.

Propagation attenuation of elastic waves in multi-row infinitely periodic pile barriers: A closed-form analytical solution

Periodically arranged media exhibit attenuation zones for elastic waves, and the related periodic structures play a crucial role in the design of seismic isolation and vibration mitigation. From the perspective of wave theory, this paper presents a closed-form analytical solution for the propagation attenuation of elastic waves through infinitely periodic, multi-row pile barriers. The innovative approach begins by deriving the extended Graf’s addition theorem to transform wave potentials across arbitrary coordinate systems, overcoming the constraints of traditional formulas that limit pile centers to linear configurations. Subsequently, it completes the wave function expansion by utilizing the phase differences in the frequency domain of wave fields around different periodic elements, thus skillfully integrating the effects of incident and scattered wave fields. For the first time, this study delivers exact expressions for the scattering of various types of plane waves (SH, SV, and P) by multi-row pile barriers with an infinite periodic array, addressing the complexities of large pile numbers in previous theoretical studies. The proposed solution increases computational efficiency by tens of times and markedly reduces the majority of resource usage, improving the analysis of complex vibration isolation systems involving numerous piles. Building on the accuracy verification and convergence analysis, several numerical examples are conducted to explore the effects of pile row, pile spacing, and pile arrangement on the propagation attenuation. The findings elucidate the mechanisms driving vibration reduction design using periodic wave barrier, furthering its application in engineering structures.

Propagation of elastic waves in correlated dispersions of resonant scatterers.

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Machine learning-based optimal design of an acoustic black hole metaplate for enhanced bandgap and load-bearing capacity

This paper introduces a novel machine learning-based optimization strategy for multi-functional acoustic black hole (ABH) metaplates. The primary objective is to achieve a multi-functional metaplate with excellent performance in elastic wave attenuation and load-bearing capacity simultaneously. The paper begins by describing the design of nanocomposite ABH metaplates, presenting a new pathway to realize multi-functional metaplates. Then, a semi-analytical method, based on plate theory and the Bloch–Floquet theorem, is introduced to consider the band structure of the nanocomposite metaplates. Through systematic analysis, the impacts of the ABH effect, nanocomposite reinforcements, and the viscoelastic damping layer on the bandgaps and strain energy compliance are highlighted. Meanwhile, two optimization objectives representing bandgap characteristics and in-plane stiffness are derived respectively. Subsequently, a deep learning surrogate model is employed to establish a relationship involving significant parameters with the optimization objectives. The performance evaluation confirms accuracy and computational speed of the surrogate model. Finally, an optimization strategy based on deep reinforcement learning is proposed to obtain multi-functional metaplates with superior bandgaps, enhanced in-plane stiffness, or both. The robustness and efficiency of the strategy are demonstrated under different tests. The results show that the proposed strategy can achieve identical results as the genetic algorithm and nondominated sorting genetic algorithm-II, while surpassing them in computational efficiency and balancing multiple objectives. The findings of this study serve as valuable references for the future development and application of multi-functional advanced metamaterials.

Elastic surface wave attenuation in layered soil by metastructures

AbstractSeismic metastructures are able to effectively attenuate or convert elastic surface waves, attracting increasing attention in different areas such as civil engineering. However, the effects of the source depth and layered characteristics of viscous soil on metastructures for elastic surface wave reduction with Bragg bandgap mechanism remain challenging, which are the key issues for practical applications. In this work, we calculate the dispersion and transmission of metastructures in layered soil and confirm that the metastructures can effectively attenuate the elastic surface waves within the bandgaps. Then, the influence of the embedded depth of the metastructures, the depth of the vibrating source, layered characteristics of viscous soil on the surface vibration reduction are further discussed. It is found that surface vibration attenuation is enhanced by increasing the embedded depth of the metastructures and the density of the first layer. The width of the bandgap increases with the introduction of soil viscosity. On the contrary, the surface vibration attenuation decreases if the vibrating source is placed at a certain depth which requires the bandgap of bulk waves of the metastructures. This study of the seismic metastructures in layered soil provides a guidance in surface vibration reduction in practice.

Acoustic Emission Monitoring in Prestressed Concrete: A Comparative Study of Signal Attenuation from Wire Breaks and Rebound Hammer Impulses

Acoustic emission monitoring (AEM) has emerged as an effective technique for detecting wire breaks resulting from, e.g., stress corrosion cracking, and its application on prestressed concrete bridges is increasing. The success of this monitoring measure depends crucially on a carefully designed sensor layout. For this, the attenuation of elastic waves within the structure’s material is ideally determined in situ through object-related measurements (ORMs) with a reproducible signal source, typically a rebound hammer. This assumes that the attenuation coefficients derived from rebound hammer tests are comparable to those from wire breaks, thus allowing their results to be directly applied to wire break detection without further adjustments. This study challenges this assumption by analysing attenuation behaviour through an extensive dataset. Employing time-domain and frequency analysis, the research generates attenuation profiles from laboratory experiments and in situ measurements across various girders and bridge structures, extracting the slope and residual standard deviation (RSD). While generally validating this approach, the findings highlight differences in attenuation behaviour from among wire break signals and rebound hammer impulses, whereby the latter potentially underestimates the relevant attenuation of wire breaks by approximately 20%. Consequently, a transfer factor is proposed to adjust ORM results obtained with the rebound hammer for wire break scenarios. It consists of a scaling factor of 1.2 to modify the average attenuation coefficient and a constant term of ±1.0 dB/m to cover a 95% confidence interval, and thus, account for sample scattering. Moreover, the anisotropic attenuation behaviour across different structures was studied, showing that transverse attenuation consistently exceeds the longitudinal, significantly influenced by structural features such as voids. In prefabricated concrete bridges with in situ-cast concrete slabs, transverse signal transmission remains unhindered across multiple elements. Finally, the results provide a valuable reference for the design of sensor layouts in bridge monitoring, particularly benefiting scenarios where direct in situ experiences are lacking.

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.

Effects of grain size distributions on scattering attenuation of elastic waves in polycrystalline materials

Effects of grain size distributions on scattering attenuation of elastic waves in polycrystalline materials

Elastic Wave Propagation Control in Porous and Finitely Deformed Locally Resonant Nacre-like Metamaterials.

Recent studies have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformation effects, leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, in porous periodic nacre-like microstructures, microscopic and macroscopic instabilities may occur for a given uniaxial loading process and, as a consequence, wave attenuation properties may evolve as a function of the microstructural evolution, designating it as metamaterials. The numerical outcomes provide new opportunities to design bioinspired, soft composite metamaterials characterized by high deformability and enhanced elastic wave attenuation capabilities given by the insertion of voids and lead cores.

Pine-like elastic metamaterials for urban seismic Rayleigh wave attenuation

Preventing urban regions from seismic wave destruction is of paramount significance because it is closely related to urban lifeline and prosperity of cities. Almost all conventional seismic resistance approaches rely on the stiffness and strength of buildings, which require excessive structural components with additional self-weights. In this study, we propose a pine-like seismic metamaterial for efficient attenuation of surface Rayleigh waves. The pine arrays in suburban regions demonstrate an ability to convert Rayleigh waves to shear bulk waves or attenuate waves on the surface via local resonation. This property originates from a gradient design of pine arrays, where a scale ratio is defined to tune the geometric properties of each pine unit. Specifically, a gradient pine array with a scale ratio smaller than one can interact with the Rayleigh waves and convert them to shear waves that propagate deep to underground. The transmission ratio of the entire system indicates a broadband wave attenuation at subwavelength scale. It reveals that the pine is able to couple with a certain elastic Rayleigh wave whose wavelength is much larger than the lattice constant, which is rarely achieved in any conventional civil engineering structures such as open trench barriers and filled trench barriers. Additionally, a numerical model of an urban region and suburban pine array is established and analyzed. Infrastructures and structures in a city that suffer direct Rayleigh wave interference run into a high risk of structural destruction as compared to urban structures protected with suburban metamaterial pine arrays. Finally, two real earthquake wave signals are used to validate the efficiency of the pine arrays in dissipating earthquake energy. The approach in this paper can be extended to deal with more complex naturally available structures for examining the elastic wave attenuation abilities of these novel structures.

Simulation and analysis of elastic waves in partially saturated double-porosity media based on finite difference method

Double-porosity poroelastic model takes into account the effect of mesoscopic flow induced by rock heterogeneity on dispersion and attenuation of elastic waves, and has obtained good application results in the quantitative explanation of seismic data in heterogeneous reservoirs. Wavefield simulation based on double-porosity model not only helps visualize the propagation characteristics of the elastic waves but also lays the foundation for seismic imaging. In this work, we perform wavefield simulation and analysis based on the Santos-Rayleigh model which incorporates mesoscopic and global flow in a partially-saturated double-porosity medium. Specifically, the mesoscopic flow mechanism is represented with a Zener viscoelastic model. The comparison shows that the Zener model can accurately capture the propagation characteristics of fast P-wave, but fails to describe the attenuation characteristics of slow P3 wave in the low-frequency band. It implies that Zener viscoelastic model and slow wave modes follow different mechanisms. Then the staggered grid finite-difference method is used to simulate wave propagation in a double-porosity medium, and the stiff problem is solved with a time-splitting algorithm, which can significantly improve computational efficiency. Based on the above methods, the correctness of our algorithm is verified with derived analytical solution for a P-wave source in a uniform partially saturated poroelastic medium. Analytical and numerical solutions are in good agreement and mean error is 0.33%. We provide some examples of wavefield snapshots and seismograms in homogeneous and layered heterogeneous media at seismic and ultrasonic frequencies. The simulation results demonstrate the strong attenuation of fast P-wave and no change of S-wave in the seismic band due to mesoscopic flow mechanism, which is consistent with the theoretical prediction of double-porosity model. Moreover, the energy of fast P-wave is concentrated in solid phase while slow waves are stronger in fluid phase. This work contributes to the understanding of broadband elastic wave propagation in a heterogeneous partially saturated porous medium and can be applied to the reservoir imaging with broadband geophysical data.

A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties.

The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

High frequency attenuation of elastic waves transmitted at an angle through a randomly-fluctuating horizontally-layered slab

This paper is concerned with the modeling of elastic waves traveling at small incidence angles through a randomly-fluctuating horizontally-layered slab, in regimes where the wavelength is small compared to the thickness of the slab. The wave propagation problem is reset in a frame following the coherent front, which propagates in a homogenized medium. This homogenized medium is anisotropic because of the layering, and the equations obtained account explicitly for the coupling of quasi-P and quasi-S waves. The resulting model is governed by a set of coupled stochastic ordinary differential equations that can be approximated numerically very efficiently, and yields in particular estimates of the transmission and reflections coefficients of the slab. The latter compare favorably to the coefficients obtained in a full scale numerical simulation of the (micro-scale) wave equation, for a fraction of the cost.

Prediction of dispersion and attenuation on elastic wave velocities in partially saturated rock based on the fluid distribution obtained from three-dimensional (3D) micro-CT images

Elastic wave attenuation in partially saturated porous rock is primarily due to wave-induced fluid flow, which arises from the contrast in compressibility between air and water and is influenced by the water distribution within the rock. We propose a method for constructing a numerical model that predicts mesoscopic dispersion and attenuation. Initially, we use fluid distribution data sourced from 3D X-ray Computed Tomography images to construct the numerical model, utilizing Biot’s poroelastic equations as the governing equations. Subsequently, we implement the finite element method to derive solutions for the numerical model. Our focus is centered on two key challenges: 1) reducing memory cost, and 2) efficiently handling element intersection during the meshing process. The solutions illustrate the evolution of fluid pressure distribution and the frequency-dependent advancement of the elastic moduli, coupled with their corresponding attenuation. Ultimately, we compare these numerical predictions with previously published experimental data from a study on partially saturated Indiana limestone. The considerable agreement between our numerical results and the experimental data confirms the validity of our method, which crucially incorporates the actual fluid distribution (captured from 3D CT images) as a vital input.

Propagation and attenuation of elastic waves in nematic elastomer hollow cylinders

As an intelligent soft material, nematic elastomers (NEs) possess both rubber elasticity and the unique properties of liquid crystals. Such combination gives NEs unusual mechanical response. In this paper, guided waves in nematic elastomer hollow cylinders are investigated. Based on the viscoelasticity theory, the wave governing equations are derived and solved by the Legendre polynomial series approach (LPSA). This approach can directly obtain eigenvalues/eigenvectors characterizing wave propagation and attenuation or field profiles. The effects of circumferential order and radius-thickness ratio on dispersion and attenuation curves are discussed. Besides, dispersion and attenuation curves with different initial director orientations are presented. It is found that the existence of the director results in mode conversions between adjacent flexural longitudinal modes and flexural torsional modes. The results provide important guidance for dynamic design and device analysis of cylinder-shaped nematic elastomer devices.

Beam-type metastructure with X-shape inertial amplification mechanisms for vibration suppression

A new type of beam-type metastructure periodically attaching single- or multi-stage X-shape inertial amplification (XIA) mechanisms is designed to realize efficient elastic wave attenuation and wide bandgaps benefiting the vibration suppression. Band structures of the unit cell and vibration response of the finite beam are validated numerically and experimentally. Numerical results show that compared with the triangular inertial amplification beams with the same added masses, XIA mechanisms generate wider bandgaps with higher attenuation constants at the same frequency band, for the same inertia amplification (IA) angle or same installation space. Parametric studies reveal that XIA mechanisms lead to the coupling effect of transverse wave and longitudinal wave, and induce a newly emerging bandgap. Moreover, the variations of IA angle, amplification ratio and number of stages apply basically similar effects on band structures, except the IA span. Finally, in order to explore practical applications on vibration suppression of XIA mechanisms, two schemes of multiple mechanisms in a unit cell and the hybrid unit cell are investigated. The proposed designs of XIA mechanisms have the potential to improve the capability of vibration suppression of the structures in engineering practices.

Influence on Elastic Wave Propagation Behavior in Polymers Composites: An Analysis of Inflection Phenomena

Particulate polymer composites (PPCs) are widely applied under different elastic wave loading conditions in the automobile, aviation, and armor protection industries. This study investigates the elastic wave propagation behavior of a typical PPC, specifically a Cu/poly (methyl methacrylate) (PMMA) composite, with a wide range of particle contents (30-65 vol. %) and particle sizes (1-100 μm). The results demonstrate an inflection phenomenon in both the elastic wave velocity and attenuation coefficient with increasing volume content. In addition, the inflection point moves to the direction of low content with the increase in particle size. Notably, the elastic wave velocity, attenuation, and wavefront width significantly increased with the particle size. The inflection phenomenon of elastic wave propagation behavior in PPCs is demonstrated to have resulted from particle interaction using the classical scattering theory and finite element analysis. The particle interaction initially intensified and then reduced with increasing particle content. This study elucidates the underlying mechanism governing the elastic wave propagation behavior of high particle content PPCs and provides guidelines for the design and application of wave-absorbing composites.

Elastic wave velocity of marine sediments with free gas: Insights from CT-acoustic observation and theoretical analysis

The existence of free gas in pores will significantly affect the elastic wave velocity and attenuation coefficient of aqueous sediments. However, because the gas content and distribution are difficult to be accurately obtained through experiments, it is difficult to accurately characterize the relationship between elastic wave velocity and gas content, which may lead to the evaluation error of gas saturation in sediments. In this study, we applied the combined detection technology of X-CT and ultrasonic detection to simultaneously obtain the volume proportion of each phase and acoustic velocity of the selected marine sediments, respectively. On the basis of experiments, the applicability of effective medium theory (EMT), Biot-Gassmann theory by Lee (BGTL) and simplified three-phase equation (STPE) is verified. Meanwhile, the bulk modulus of pore fluid (Kfl) is recalculated by integrating Wood's and Domenico's equations by introducing calibration constant J to adapt to different reservoir conditions. The results show that the elastic wave velocities predicted by BGTL and STPE are more accurate compared with other gas estimation models. When J = −0.8, the acoustic velocity of sedimentary medium predicted by BGTL is more consistent with the experimental data. In addition, we apply the model to the elastic wave velocity data from ODP 204 Hole 1245 and obtain the free gas saturation. The results provide a theoretical and practical application reference for accurately estimating the free gas saturation in marine sediments.