Longitudinal Wave Propagation Research Articles

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.

Radiation pressure and galactic cosmic rays-driven gravitational instability in rotating and magnetized viscoelastic fluids

This paper studies the combined effects of radiation and galactic cosmic ray pressures on the gravitational instability of magnetized and rotating viscoelastic fluids. The dispersion relations are derived using the normal mode analysis and discussed in the hydrodynamic (weakly coupled fluid) and kinetic (strongly coupled fluid) limits. These dispersion relations are analyzed separately for transverse and longitudinal wave propagation modes. Jeans instability criteria are obtained for kinetic and hydrodynamic limits for both modes of wave propagation, and it is found that the critical Jeans wavenumbers in each case are modified due to the presence of viscoelastic effects, radiation and cosmic rays pressures, and Alfvên wave velocity. It is also observed that the radiation pressure, cosmic ray pressure and viscoelastic parameters suppress the growth rate and thus have stabilizing effects on the Jeans instability. However, cosmic ray diffusion has a destabilizing effect on the onset of gravitational instability. The effects of various parameters on the growth rate of instability are calculated numerically and the outcomes are depicted graphically. The results of the present analysis shall be helpful in understanding the impact of cosmic rays and radiative mechanisms on the gravitational collapse in the viscoelastic region of molecular cloud clumps.

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

Analysis of propagation and resonance properties of longitudinal leaky surface acoustic wave on LiNbO3/SiC bonded structure

Abstract The propagation and resonance properties of longitudinal leaky surface acoustic waves (LLSAW) on a bonded structure comprising an X-cut LiNbO3 (LN) thin plate and a 4H-SiC support substrate are theoretically investigated. The strong LLSAW responses with high Q factors were obtained at the LN thin-plate thickness h where the LLSAW phase velocity was slower than the bulk shear wave of 4H-SiC of 7126 m/s, and a fractional bandwidth (FBW) of 9–10% was obtained for the normalized Al film thickness by wavelength h Al/λ = 0.06–0.07 and h/λ = 0.30–0.40. Moreover, even at h/λ with a faster phase velocity than the bulk shear wave of 4H-SiC, the strong LLSAW responses without spurious response owing to the LLSAW higher-order mode were obtained. Finally, h Al/λ = 0.031 and h/λ = 0.19 were extracted to obtain a phase velocity of 7800 m/s, high Q factors, and FBW of 7.6%.

Thermoelastic wave generation and its longitudinal wave propagation measurement by a microscopic optical interferometer

Laser ultrasonics is a noncontact measurement method that uses a laser-induced elastic wave source in combination with an optical surface displacement-tracking system. This study compared the performances of two optical interferometers with different characteristics when applied to measurement of pulsed thermoelastic waves. The surface displacement-tracking system was designed to measure the center of the microscopic view. A pulsed laser beam irradiated a black ink layer to generate the thermoelastic waves. The out-of-plane displacement on the axially opposite side was then measured using either a Michelson interferometer or a Sagnac interferometer. The objective lens of the system was of a type commonly used in biological observations. The Michelson interferometer estimated a maximum displacement of 0.43 nm and a maximum sound pressure of 24.7 kPa. The signal-to-noise ratios from 16 averages were 14.9 dB (Michelson interferometer) and 19.2 dB (Sagnac interferometer). Furthermore, this paper compares the performance of the numerically estimated Sagnac interferometer outputs calculated from the measured Michelson interferometer outputs with the experimentally obtained Sagnac interferometer outputs. The numerically estimated Sagnac interferometer’s output was shown to be identical to the experimentally acquired output. The Michelson interferometer requires a higher average operating frequency (i.e., it needs a longer data acquisition time), although this interferometer does offer superior displacement output linearity. This property enables calculation of the sound pressure from the displacement amplitude. These findings indicated that combination of the measurement points of the Sagnac interferometer with those of the sparsely distributed Michelson interferometer reduced the measurement time when compared with a single use of the Michelson interferometer while also maintaining the data acquisition quality.

Optical soliton solutions of generalized Pochammer Chree equation

This research investigates the utilization of a modified version of the Sardar sub-equation method to discover novel exact solutions for the generalized Pochammer Chree equation. The equation itself represents the propagation of longitudinal deformation waves in an elastic rod. By employing this modified method, we aim to identify previously unknown solutions for the equation under consideration, which can contribute to a deeper understanding of the behavior of deformation waves in elastic rods. The solutions obtained are represented by hyperbolic, trigonometric, exponential functions, dark, dark-bright, periodic, singular, and bright solutions. By selecting suitable values for the physical parameters, the dynamic behaviors of these solutions can be demonstrated. This allows for a comprehensive understanding of how the solutions evolve and behave over time. The effectiveness of these methods in capturing the dynamics of the solutions contributes to our understanding of complex physical phenomena. The study’s findings show how effective the selected approaches are in explaining nonlinear dynamic processes. The findings reveal that the chosen techniques are not only effective but also easily implementable, making them applicable to nonlinear model across various fields, particularly in studying the propagation of longitudinal deformation waves in an elastic rod. Furthermore, the results demonstrate that the given model possesses solutions with potentially diverse structures.

Stress wave attenuation in chocolate

The stress wave attenuation in five types of chocolate (extra dark, dark, milk, white, and ruby) was studied. The main acoustics properties of these chocolates were described in terms of longitudinal and transversal wave velocities. The attenuation of the stress waves was studied using the experimental technique known as the Split Hopkinson Pressure Bar (SHPB). The SHPB set-up consists of a specimen and linear elastic incident and transmission bar. Experimental data have been evaluated both in the time as well as frequency domain. Attenuation of the stress wave was described namely using the frequency dependence of the transmission coefficient of the stress wave. This damping increases with the plastic strain of the tested chocolate specimens. From a technological point of view, the fat content of the chocolate has the highest influence on the reduction of the longitudinal wave propagation velocity. The lowest attenuation was observed for the dark chocolate.

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.

Symmetry analysis, optimal subalgebra, quasi-self-adjointness condition with conservation laws and analytical solutions for the ($$1+1$$)-dimensional Pochhammer–Chree model in longitudinal wave propagation

Symmetry analysis, optimal subalgebra, quasi-self-adjointness condition with conservation laws and analytical solutions for the ($$1+1$$)-dimensional Pochhammer–Chree model in longitudinal wave propagation

Physical mechanism of the variation of longitudinal wave velocity with porosity in seafloor sediments

In order to reveal the response mechanism of longitudinal wave velocity and related parameters, through the statistical analysis of the measurement data of seafloor sediments, it is found that there is a minimum value of the change of longitudinal wave velocity with porosity of seafloor sediments. The minimum values of the empirical formula for the change of longitudinal wave velocity with porosity of sediments in different sea areas and their critical porosity values are uniformly analyzed. The calculation shows that the minimum variation range of longitudinal wave velocity with porosity of sediments in different sea areas is between 1468.59 and 1520.22 m/s, and the corresponding critical porosity value changes between 0.69 and 0.88. The analysis shows that the empirical formulas of different scholars belong to the unified mathematical expression derived from acoustic theory. The study shows that the essential reason for the formation of the minimum of longitudinal wave velocity in seafloor sediment is that the coupling of sediment grains affects the propagation of longitudinal wave. It is further revealed that the physical mechanism of the change of longitudinal wave velocity is that the change of contact or suspension state of seafloor sediment grains in seawater affects the elastic stress-strain relations of sediments.

Laser additive manufacturing of Miura-origami tube inspired quasi-zero stiffness metamaterial with prominent longitudinal wave propagation

ABSTRACT Origami metamaterials have become frontiers of research in many disciplines due to their infinite design space, simple size variation, and topologically variable properties. In this study, a novel metamaterial inspired by Miura-origami tubes with a complex quasi-zero-stiffness (QZS) structure was fabricated via laser powder bed fusion (LPBF). The unit of the QZS metamaterial consists of a two-layer quadrilateral frame and two vertical springs attached to its diagonal points. The geometric accuracy, densification level and mechanical properties of the QZS parts fabricated at various processing conditions were investigated and the optimised processing parameters were determined. The displacement response of the QZS parts was analysed by experiments in conjunction with simulation analysis. The results show that the LPBF-fabricated QZS metamaterials form four extra-wide longitudinal wave band gaps under low frequencies from 660 Hz to 2500 Hz. The proposed LPBF-fabricated QZS metamaterial shows great potential in impeding the longitudinal vibration of engineering structures.

Longitudinal Wave Propagation in Axially Graded Raylegh–Bishop Nanorods

Longitudinal Wave Propagation in Axially Graded Raylegh–Bishop Nanorods

Numerical and experimental investigations on quasi-static component generation of longitudinal wave propagation in isotropic pipes

In this paper, the quasi-static component (QSC) generation of longitudinal waves propagating in an isotropic pipe is investigated numerically and experimentally. The three-dimensional (3D) finite element (FE) simulations are first carried out to gain physical insights into the characteristics of QSC generation from longitudinal wave travelling in an isotropic pipe with weak material nonlinearity. By applying the axial displacement excitation in the FE model, L(0, 1) mode and L(0, 2) mode are excited simultaneously. Then, the generated QSC pulses are extracted using the phase reversal approach for analysis. It is found that the QSC pulses generated by L(0, 2) mode and L(0, 1) mode are L(0, 1) mode. Meanwhile, the shapes of QSC pulses at different locations are extracted and compared. In this study, a data pre-processing method is proposed to handle numerically calculated and subsequent experimentally measured displacement signals, and a nonlinear acoustic parameter is defined to evaluate the incipient damages. After that, an experiment is conducted to measure the QSCs induced by the propagation of longitudinal waves in an aluminum pipe. The experimental results indicate that the propagation of longitudinal waves in the aluminum pipe can induce the QSCs. Different levels of corrosion are created on the surface of the aluminum pipe and are assessed by the generated QSCs. The results show that the nonlinear acoustic parameter has a monotonically increasing trend with the growing severity of corrosion. The QSCs generated by longitudinal wave can be used to detect and evaluate the early-stage surface corrosion in the aluminum pipe.

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.

A homogenized model for free vibration analysis of finite phononic crystal rods using strain gradient theory

While extensive research has been conducted on elastic wave propagation in infinite phononic crystal (PC) rods, practical applications often involve PC rods of finite length. Therefore, it is essential to consider not only their functional properties, such as wave filtering, but also their mechanical behavior, including free vibration. Motivated by this concern, this study aims to establish a homogenized model for a finite-length PC rod based on the strain gradient theory (SGT) and provide simple closed-form expressions for its natural frequencies. To achieve this objective, an innovative method is developed to determine the material length scale parameters within the SGT. The investigation begins by analyzing the propagation of longitudinal waves in an infinite PC rod. By using the dispersion obtained from Bloch’s theorem as a benchmark, it is demonstrated that the material length scale parameters associated with strain energy and micro-inertial effects in the SGT can be effectively determined by fitting the dispersion obtained from the SGT to the benchmark dispersion obtained from Bloch’s theorem. With the determined parameters, the study proceeds to investigate the free vibration of a finite PC rod. The natural frequencies obtained from both the classical continuum theory (CCT) and the SGT are compared with those calculated by finite element (FE) simulations, which are based on an actual periodic structure and serve as a reliable benchmark. This comparison clearly highlights the superiority of the developed mesoscopic model based on the SGT in accurately predicting the natural frequencies, particularly for higher-order modes, compared to the CCT.

Experimental evidence of nonreciprocal propagation in space-time modulated piezoelectric phononic crystals

A nonreciprocal system composed of a one-dimensional piezoelectric phononic crystal whose periodic electrical conditions are modulated in time is presented. One-way longitudinal wave propagation is studied experimentally and compared to finite element temporal simulations. The modulation is performed by prescribing grounded or floating potential conditions on a periodic set of electrodes through external circuits. This approach makes it possible to consider a wide range of modulation speeds, and the large number of unit cells of the phononic crystal allows us to characterize experimentally the full dispersion curves of the system. This permits to observe the presence of directional bandgaps and to follow the shift in frequencies of these bandgaps as a function of the modulation speed. The experiments show the linear evolution of the central position of the bandgaps with the increase in the modulation speed, as well as their progressive closure, over a wide range of frequencies. Experiments are also used to estimate the evolution of bandgaps in a dispersive system, a problem discussed in several theoretical works but never observed experimentally. This work may constitute the foundation for experimental analysis of Floquet acoustic metamaterials, accelerated-modulation space-time metamaterials, or acoustic analog of the event horizon.

Longitudinal wave propagation in an elastic cylinder embedded in a viscoelastic fluid

Abstract A novel analytical investigation of longitudinal wave propagation in an elastic cylinder embedded in a viscoelastic fluid is proposed. The Maxwell model is used to describe the viscoelastic fluid behavior. With appropriate boundary conditions, a complex dispersion equation of longitudinal wave has been established. The aim of this paper is to study the effect of the fluid rheological properties on the longitudinal wave characteristics (attenuation and velocity). It is shown that the attenuation is the sum of a viscous and non viscous component. The viscosity induced attenuation is predominant at low frequencies. On the other hand, the effect of the liquid amount and elastic cylinder radius on the attenuation and velocity are studied. A critical normalized liquid thickness is highlighted. Beyond this critical value, the influence of the outer boundary condition can be neglected. At last, among other interesting phenomena, it is highlighted that if the Deborah number increases, the attenuation decreases. This variation characterize a stiffening of the viscoelastic medium. In addition, the obtained results show that the viscosity measurement should be performed at low frequencies using small elastic cylinder radius. Accordingly, these investigations are novel and can be applied in geophysics, food industry, medicine, non-destructive testing of materials, design and development of fluid sensors.

Anisotropic mechanical behavior and thermal attributes of antiferromagnetic UX2(X=P, As, Sb) materials: A density functional and elasticity theories study

In this work, we delve into the investigation of mechanical and thermal properties of antiferromagnetic UX2 (X=P, As, Sb), which are structured in the unique anti-Cu2Sb-type tetragonal form. The study’s principal findings revolve around the revelation of distinctive compressibility patterns and an observed preference for shear deformation in these compounds. These patterns are notably marked by a lower compressibility along the [100] direction than the [001] one, and the ease of shear deformation on the (100) plane compared to the (001) one. Intriguingly, our findings identify these compounds as residing on the brink of the brittle/ductile borderline as per Pugh’s ratio and Poisson’s ratio. Furthermore, the mechanical strength in these materials is significantly influenced by shear deformation, a fact indicated by the values of bulk and Young’s modulus. Among the UX2 (X=P, As, Sb) compounds, our analysis of the Debye temperature singles out UP2 as an outstanding performer due to its higher Debye temperature. A noteworthy aspect of this study is the quicker propagation of longitudinal waves over transverse waves, as indicated by the wave velocity and anisotropy calculations. We bring forth an enriched understanding of the anisotropic behavior of these materials in terms of bulk modulus, Young’s modulus, shear modulus, and Poisson’s ratio. The predicted high melting temperatures of the UX2 (X=P, As, Sb) compounds, coupled with the computed heat capacities aligning well with existing experimental data, point towards their potential applicability in high-temperature settings. Collectively, our study not only validates the methodologies employed but also brings to light fascinating new insights into the mechanical and thermal properties of these compounds, deepening our understanding of the intricate interplay between their atomic constitution and physical properties.

Longitudinal wave propagation analysis in Entangled metallic wire materials using an improved wave and finite element method

This paper proposes a novel concept and methodology to study longitudinal wave propagation in entangled metallic wire material (EMWM), a porous structural network consisting of spatial helix wires. The numerical model of EMWM is constructed using representative volume elements (RVE) obtained through X-ray tomography and skeletonization of a standard specimen. By increasing the approximate periodic boundary, the improved wave and finite ele-ment method (WFE) is employed to model EMWM as approximately periodic structures, allowing for numerical simulations of wave propagation characteristics. Frequency bands and resonance modes of EMWM are calculated to analyze the characteristics of one-dimensional wave propagation. The numerical results show that EMWM exhibits unique frequency band characteristics compared to typical periodic porous materials. In the frequency range of 15 to n n 35 kHz, the first pass band corresponds to the tensile-compressive motion of the entire specimen, while the higher pass bands correspond to localized vibrations within the spatial wires. Additionally, the frequency bands can be adjusted across a wide range based on the relative density of EMWM specimens. The improved WFE method and obtained numerical data can facilitate the application of EMWM on high frequency vibration isolation.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.