Attenuation Of Longitudinal Waves Research Articles

Unifying temperature definition in atomistic and field representations of conservation laws

In this work, a field representation of the conservation law of linear momentum is derived from the atomistic, using the theory of distributions as the mathematical tool, and expressed in terms of temperature field by defining temperature as a derived quantity as that in molecular kinetic theory and atomistic simulations. The formulation leads to a unified atomistic and continuum description of temperature and a new linear momentum equation that, supplemented by an interatomic potential, completely governs thermal and mechanical processes across scales from the atomic to the continuum. The conservation equation can be used to solve atomistic trajectories for systems at finite temperatures, as well as the evolution of field quantities in space and time, with atomic or multiscale resolution. Four sets of numerical examples are presented to demonstrate the efficacy of the formulation in capturing the effect of temperature and thermal fluctuations, including phonon density of states, thermally activated dislocation motion, dislocation formation during epitaxial processes, and attenuation of longitudinal acoustic waves as a result of their interaction with thermal phonons.

Longitudinal wave attenuation and bandgap analysis of a novel type hybrid tunable resonator metamaterial

Achieving vibration suppression or wave attenuation of tunable local resonance metamaterials without physical modification of the resonator has received a lot of attention recently. In this paper, a hybrid tunable metamaterial with a resonator containing a lever mechanism, an electromagnetic device, and a feedback system is proposed to achieve tunable bandgap and longitudinal wave attenuation. Unlike ordinary metamaterials, inertial amplification mechanisms and negative stiffness elements are involved in our proposed metamaterials. The function of the electromagnetic device and the feedback control are considered to theoretically derive the dispersion relation. The effective mass, the effective stiffness, the displacement transmission rate, and the band structure of the proposed metamaterial are analyzed, and the contributions of some key parameters on the bandgap are investigated. The accuracy of the analytical band structure is verified by the wave transmittance curves obtained by numerical simulation and the transient displacement response of a single oscillator. The results show that the proposed metamaterial yields broadband tunable bandgap in the low-frequency range, which enables the isolation of low-frequency longitudinal vibrations. This study provides a novel option for constructing integrated metamaterials to achieve vibration suppression and wave attenuation.

Low-temperature relaxation of various samarium phosphate glasses

Abstract Glasses constructed, (1 − x) (0.6595P2O5–0.0958ZnO–0.2447PbO) · xSm2O3 with x = 0.00, 0.0045, 0.0089, 0.0132, and 0.0261 mol%, had been created to investigate the attenuation of longitudinal ultrasonic waves at 2, 4, 6, and 14 MHz frequencies between 120 and 300 K. At a variety of temperatures, clear peaks of a large absorption curve have been seen. These peaks are dependent on the structure of the glass as well as the switching frequency. Maximum peaks have been shown to shift to higher temperatures, and the increase in overall frequency points to the presence of some kind of relaxation process. A thermally induced relaxation process is responsible for producing a calm approach, which has been identified as a result of this mechanism. A quiet approach has been defined as a consequence of a thermally triggered relaxation mechanism. The variance of the mean energy of activation of the mechanism counts on primarily the amount of Sm2O3 mol%. Such dependency has been evaluated based on the loss of normal linear solid form, attaining low dispersion, and a large allocation of Arrhenius kind relaxation through temperature-autonomous relaxation power. The measured acoustical energy of activation values have been quantifiably represented based on the number of loss centers (amount of oxygen atoms that now move at a double-well potential).

Bandgap regulations of longitudinal wave for a nonlinear metastructure isolator with high-static-low-dynamic stiffness

Linear structures are inherently difficult to exhibit mechanical properties with high-static-low-dynamic stiffness (HSLDS), which means that linear isolators with these structures struggle to have both high-quality load-bearing capacity and low-frequency isolation ability at the same time. To address this issue, we have designed a high-load-capacity local resonance (LR) nonlinear metastructure isolator for low-frequency vibration isolation of target objects. We reveal the regulation mechanism of longitudinal wave attenuation in such metastructures and conduct comparative study by finite element method (FEM) and experiments for a 3D printed prototype metastructure. The results show that in specific excitation frequencies, the LR nonlinear metastructure with a cantilever beam oscillator having a natural frequency of 11.7 Hz triggers a LR mechanism. Under the action of the nonlinear isolator, the vibration transmissibility is as low as 10 % at the center frequency of the bandgap under the base excitation. Furthermore, the dispersion equation of such nonlinear metastructures is derived, and through the analysis of the regulation of bandgaps, the variation trend of the transmissibility of nonlinear metastructure isolators is effectively predicted. The calculation method and design idea of this metastructure isolators provide a new approach for vibration isolation.

A metamaterial cylindrical shell with multiple graded resonators for broadband longitudinal wave attenuation

This paper investigates a metamaterial cylindrical shell with local resonators for broadband longitudinal wave attenuation. A three-component phononic crystal metamaterial cylindrical shell that opens local resonant bandgaps at low frequencies is formed by periodically inserting a lead column coated with soft rubber into an ordinary cylindrical shell. First, the governing equations of elastic wave propagation in cylindrical shell structures are derived through coordinate transformation. Subsequently, numerical models of the metamaterial cylindrical shell are established, and the dispersion relation and vibration transmission characteristics of this structure are calculated using the Finite Element Method (FEM). Finally, in order to further broaden the bandgaps and the strong suppression range of the structure, a multiple-graded-resonator metamaterial cylindrical shell with three different local resonators is also proposed. These local resonators have different start frequencies and locations of their longitudinal wave bandgaps, so they can be combined to produce a wider overall bandgap. Numerical results show that this kind of multiple-graded-resonator metamaterial cylindrical shell has a good vibration suppression effect on longitudinal waves in the range of approximately 180–710 Hz and the vibration suppression effect can reach −40 dB at best. In addition, experimental results on vibration transmission characteristics show good agreement with the numerical results. This work provides a new idea and method for the development of acoustic metamaterials to obtain broadband and low-frequency bandgaps for cylindrical shell structures.

Experiment and simulation for ultrasonic wave propagation in multiple-particle reinforced composites

The study of ultrasonic wave propagation is a crucial foundation for the application of ultrasonic testing in particle-reinforced composites. However, in the presence of the complex interaction among multiple particles, the wave characteristics are difficult to be analyzed and used for parametric inversion. Here we combine the finite element analysis and experimental measurement to investigate the ultrasonic wave propagation in Cu-W/SiC particle-reinforced composites. The experimental and simulation results are in good agreement and quantitatively correlate longitudinal wave velocity and attenuation coefficient with SiC content and ultrasonic frequency. The results show that the attenuation coefficient of ternary composites (Cu-W/SiC) is significantly larger than that of binary composites (Cu-W, Cu-SiC). This is explained by numerical simulation analysis via extracting the individual attenuation components and visualizing the interaction among multiple particles in a model of energy propagation. The interaction among particles competes with the particle independent scattering in particle-reinforced composites. SiC particles serve as energy transfer channels partially compensating for the loss of scattering attenuation caused by interaction among W particles, which further blocks the transmission of incident energy. The present work provides insight into the theoretical basis for ultrasonic testing in multiple-particle reinforced composites.

Acoustic properties for Ga–Sn–Zn liquid metal coupler with low melting point and high acoustic impedance

Acoustic properties of Ga–Sn–Zn (GSZ) liquid alloy coupler with high acoustic impedance were investigated to evaluate materials with high acoustic impedance. GSZ liquid alloy was prepared and its longitudinal wave velocity and attenuation coefficient were measured using the plane-wave ultrasonic material characterization system. Density of the GSZ liquid alloy was also measured by a constant volume expansion method. The acoustic impedance of the GSZ was 12 times higher than that of the water. Attenuation coefficient of GSZ is much smaller than that of water, exhibiting 7.6 dB mm−1 for water and 0.5 dB mm−1 for GSZ at 200 MHz. Considering the reflection and transmission coefficients at each medium boundary calculated from the experimentally obtained acoustic impedance, it was suggested that the amplitude of the reflected wave from the back surface of the Ir sample can be made about 30 times larger with the GSZ coupler than with the water coupler.

Influence of boundary conditions on acoustic emission propagation characteristics of Zelkova schneideriana

To study the propagation characteristics of acoustic emission signals in Zelkova schneideriana under different boundary conditions, three types of boundary conditions were generated by applying aluminum plates and sound-absorbing cotton on the surface of Zelkova schneideriana specimens. Firstly, the sudden and continuous acoustic emission (AE) sources were simulated by PLB (pencil–lead break) tests and signal generator on the specimen surface, and the AE signals were collected by 5 sensors equally spaced on the surface of the specimen, and the sampling frequency was set to 500 kHz. Then, the detailed signals of different frequency bands were obtained by wavelet decomposition, and TDOA (the time difference of arrival) and correlation analysis method were used to calculate the time difference of longitudinal wave and surface transverse wave and the corresponding propagation velocity, respectively. Finally, the pulse trains with different energy levels generated by the signal generator were used as AE sources to study the attenuation law of AE signal energy with distance under different boundary conditions. The results show that the boundary changes can lead to a significant increase in the surface transverse wave velocity, and have no significant effect on the longitudinal wave velocity. At the same time, the energy attenuation of surface and longitudinal waves is faster after the aluminum plate and sound-absorbing cotton are affixed, and the distance of longitudinal waves attenuation to 90% is reduced from 186 to 139 mm, and the distance of surface transverse waves propagation is reduced from 312 to 226 mm.

Assessment of flaws in cold sintered ZnO via longitudinal ultrasonic wave speed and attenuation measurements

The cold sintering process (CSP) is a low temperature processing technique that utilizes a transient phase to synthesize dense ceramics. However, some CSP parts contain microflaws that arise due to pressure gradients and inhomogeneities in temperature and distribution of the transient phase. This work uses high frequency ultrasound (20 MHz) to verify the presence of defects larger than 15 μm in effective radius in CSP ZnO samples of varying densities (84–97%). The acoustic data were compared to X-ray Computed Tomography (XCT) images to validate the findings. Acoustic metrics used in this work include wave speed, which is affected by differences in the effective elastic properties of the medium, and attenuation, which is wave energy loss due to scattering from defects, including those smaller than the wavelength. Wave speed maps were inhomogeneous suggesting density gradients which were verified with SEM. Areas of high attenuation (> 300 Np/m) are present in all samples independent of relative density and correspond to defects identified in XCT ranging from 15 μm to 50 μm in effective radius. This suggests the presence of microflaws possibly due to the inhomogeneous removal of the transient phase. However, some high attenuation spots do not correspond to visible defects in XCT which suggests the presence of features such as texturing which are undetectable with XCT. These results show the viability of high frequency ultrasound for defect detection in cold sintered ZnO.

Integrating ultrasound and x-ray computed tomography to evaluate the microstructure of binder jet stainless steel 316L components

Binder jet printing (BJP) is a promising additive manufacturing method with benefits in sustainability, material selection, and geometric design freedom. However, issues related to part quality persist, necessitating reliable inspection and characterization strategies. Traditional protocols involving sectioning and extensive sample preparation may miss crucial information about a components’ microstructure due to volumetric variations. This study explores ultrasonic inspection of binder jet SS316L tensile specimens containing spatially varying grain size and porosity by measurement of longitudinal wave speed and attenuation. The ability of ultrasound to detect porosity is evaluated by cross referencing wave speed and attenuation data with porosity data gathered from x-ray computed tomography (XCT). Three-dimensional pore volumes were collapsed into two-dimensional maps such that ultrasound and XCT could be compared in a point-by-point fashion. After tensile testing, the location of failure was compared against wave speed and attenuation extremes. The results show the potential of ultrasound as well as important considerations related to the inspection of additively manufactured parts with complex microstructures.

ON THE INFLUENCE OF THE PARAMETERS OF GLOBULAR GRAPHITE INCLUSIONS ON THE ACOUSTIC CHARACTERISTICS OF CAST IRON AND ULTRASONIC LONGITUDINAL WAVE SIGNALS

Based on analytical models, the dependence of the velocity and attenuation coefficient of the longitudinal ultrasonic wave in cast iron with globular graphite on the average size of graphite elements and its volume content is shown. Computer modeling of acoustic paths for a medium – cast iron with globular graphite for standard normal probes was carried out to assess the influence of such a medium on the characteristics of the transmitted and recorded signals during ultrasonic testing. Calculations of directivity characteristic of probes with normalization of each directivity characteristic to its maximum for steel and cast iron with globular graphite, a slight change in the width of the directivity characteristics due to the lower velocity of longitudinal waves in cast iron compared to steel. It is established that the amplitude of the bottom signal in cast iron with globular graphite can exceed its values for structural steel. Evaluation of the nonlinearity of attenuation for cast iron with globular graphite showed that it is very small. The features of DGS-diagrams for cast iron with globular graphite are noted, associated with higher attenuation of longitudinal waves than in steel, as well as with lower velocities of their propagation.

The eddy-current and ultrasonic investigations of the nickel-base superalloy the gas turbine engine blades after exploitation

The work carried out microstructural, eddy-current and ultrasonic studies of the material of spent blades of gas turbine engines made of nickel-base superalloy. To determine the degree of damage to the material of the spent blades, studies of the microstructure were carried out on a scanning electron microscope. It was found that γ' coagulation occurred in some specimens, which corresponds to overheated material. Acoustic studies of the material were carried out using the ultrasonic pulse echo method. Comparative analysis showed that in such specimens there is a significant decrease in the velocity of propagation and attenuation of longitudinal ultrasonic waves. It is found that the readings of the eddy-current flaw detector in overheated specimens differ more than twice in comparison with non-overheated specimens. This fact can be used for operational non-destructive testing of the actual state of the metal structure by the eddy current method with the aim of further safe operation of gas turbine engines.

Experimental study on wave propagation through granite after high-temperature treatment

This paper presents an investigation of wave propagation through granite after different high-temperature treatments by using a pendulum impact setup. Propagation coefficients (attenuation coefficient and wavenumber) were successfully introduced to describe the attenuation of longitudinal waves through granite after high-temperature treatment. The attenuation rate of the longitudinal wave through the granite after different high-temperature treatments was obtained. In addition, the effects of temperature, amplitude and wavelength of longitudinal waves on the propagation coefficient and attenuation rate were discussed. The experimental results show that the propagation coefficient and the attenuation rate increase with increasing temperature. The attenuation rate decreases with increasing wavelength, while the propagation coefficient is not influenced by the wavelength. Meanwhile, the propagation coefficient and the attenuation rate are not influenced by the amplitude of the longitudinal wave.

Study of acoustic emission propagation characteristics and energy attenuation of surface transverse wave and internal longitudinal wave of wood

Study of acoustic emission propagation characteristics and energy attenuation of surface transverse wave and internal longitudinal wave of wood

Vibration characteristics of innovative reentrant-chiral elastic metamaterials

In this work, an innovative two-dimensional (2D) hybrid auxetic elastic metamaterial (MODEL I) with reentrant triangular and chiral structures is proposed to open the broaden bandgap for vibration attenuation. Furthermore, the hybrid reentrant-chiral lattice with embedded resonators (MODEL II) shows multiple bandgaps at ultra-low frequency. Based on theoretical lumped mass-in-mass method and finite element method, the bandgap and longitudinal elastic wave attenuation are characterized. There is no complete bandgap in classical reentrant triangular lattice (MODEL 0), while the complete bandgaps width for MODEL I and II account for one forth of the concerned frequency range (0–4500 Hz). What more, the lower boundary of the first bandgap for MODEL II is 56% lower than that of MODEL I. The bandgap formation mechanisms are investigated by analyzing the mode shapes on the dispersion curves, and the frequency-dependent energy flow are studied through the iso-frequency contours, phase and group velocities. Finally, the longitudinal elastic wave attenuation of finite-size lattice of MODEL II illustrates ultra-wide vibration attenuation frequency range in the directional bandgaps. This research provides important clues and theoretical guidance for the design of vibration isolators, beam, plates and other renewed devices.

RESEARCH OF STRUCTURE OF SAMPLES OF METAL OF POWER PIPELINES BY ULTRASONIC METHOD

Results of researches of structure of metal of elements of power pipelines before operation by a ultrasonic method are submitted. With use before the developed algorithm of definition of factor of attenuation of longitudinal waves owing to dispersion on structural elements calculations of amplitude of a bottom echo – signal in metal with various in average size of a grain, distribution of grains on the sizes and factor of anisotropy are executed. Influence of parameters of metal on amplitude of an echo – signal is shown. Comparison of theoretical calculation with the data of experiment and results metallography for five samples of elements of pipelines from two grades of metal with a various operating time is carried out and their satisfactory concurrence is shown.

Determination of fiber volume fraction in a cured laminate

Propagation of ultrasonic wave in Carbon Fiber Reinforced Polymer (CFRP) is greatly influenced by the material’s matrix, resins and fiber volume ratio. Laser ultrasonic broadband spectral technique has been demonstrated for porosity and fiber volume ratio extraction on unidirection aligned CFRP laminates. Porosity in the matrix materials can be calculated by longitudinal wave attenuation and accurate fiber volume ratio can be derived by combined velocity through the high strength carbon fiber and the matrix material with further consideration of porosity effects. The results have been benchmarked by pulse-echo ultrasonic tests, gas pycnometer and thermal gravimetric analysis (TGA). The potentials and advantages of the laser ultrasonic technique as a non-destructive evaluation method for CFRP carbon fiber volume fraction evaluation were demonstrated.

The effect of viscoelasticity and microplasticity on the P- wave attenuation in dry and water-saturated sandstone: An experimental study

Seismic studies use a viscoelastic model of a standard inelastic body that does not take into account the effect of microplasticity of the rocks. The modern approach introduces the new components, which indeed improves the efficiency of the seismic methods. The aim of this study is to determine the combined effect of viscoelasticity and microplasticity on the longitudinal wave's attenuation. The high-resolution measurements performed on dry and water-saturated sandstone by a pulse frequency of 1 MHz within the strain ranges of ~ (0.3–2.0) × 10-6 under 10 MPa confining pressure. Within the range of 0.5–2.5 MHz at both states of the dry and water-saturated sample, the frequency dependence of P- wave attenuation Qp−1(f) forms a peak due to the viscoelasticity. Microplasticity effect manifests as a non-linear dependence of the wave attenuation Qp−1(ε) on the strain amplitude. By increasing the strain amplitude the attenuation peak in the saturated sandstone shifts towards the higher frequencies and Qp−1- values. The indicators of microplastic deformation on the wave profile are the stress plateau and the stress drop feature. Within the range of 1.5–2.5 MHz frequencies the microplasticity is increased on the attenuation spectrum. The significant difference between dry and water-saturated sandstone can be observed as a change in peak and value of the attenuation. Considering microplasticity in the models and introducing the number of stress plateaus into a wave profile shows a significant effect of this factor on the wave attenuation. Unconventional behavior of the wave attenuation is explained by a joint action of viscoelastic and micro-plastic mechanism. The results of this study can contribute in improvement of the methods of geological interpretation of the seismic and acoustic data.

Characterization of Grain Size in 316L Stainless Steel Using the Attenuation of Rayleigh Wave Measured by Air-Coupled Transducer.

Grain size is an important parameter in evaluating the properties of microstructures in metals. In this paper, the attenuation coefficient of Rayleigh waves is introduced to characterize grain size in heat treated 316L stainless steel. Rayleigh wave attenuation is measured using an angle beam wedge transducer as the transmitter and an air-coupled transducer as the receiver. The results show that the grain size in 316L stainless steel increases due to heat treatment time, the hardness decreases accordingly, and the attenuation coefficient of Rayleigh waves increases. This indicates that the Rayleigh wave attenuation is sufficient in distinguishing the changes in the properties of the heat-treated stainless steel. It is found that compared with the measurement method using an angle beam wedge receiver, the measured results are efficient, more stable and less influenced by the surface state when an air-coupled receiver is used. In addition, comparison results also show that the Rayleigh wave attenuation is more sensitive to changes in material properties than the longitudinal wave attenuation, as the wavelength of the Rayleigh wave is shorter than that of the longitudinal wave at the same frequency.

Longitudinal wave attenuation in polycrystals with elongated grains: 3D numerical and analytical modeling.

This work develops a second-order approximation (SOA) model and a three-dimensional (3D) finite element (FE) model to calculate scattering-induced attenuation for elastic wave propagation in polycrystals with elongated grains of arbitrary crystal symmetry. The SOA model accounts for some degree of multiple scattering, whereas the 3D FE model includes all scattering possibilities. The SOA model incorporates the accurate geometric two-point correlation function obtained from the FE material systems to enable comparative studies between the two models. Also, the analytical Rayleigh and stochastic asymptotes are presented to provide explicit insights into propagation behaviors. Quantitative agreement is found between the FE and analytical models for all evaluated cases. In particular, the FE simulations support the SOA model prediction that grain shape does not exert influence on attenuation in the Rayleigh regime and its effect emerges as frequency increases to the stochastic regime showing anisotropy in attenuation. This attenuation anisotropy intensifies with the increase in frequency, but it exhibits a complicated behavior as frequency transits into the geometric regime. Wavefield fluctuations captured from the FE simulations are provided to help observe these complex scattering behaviors. The proportionality of attenuation to elastic scattering factors is also quantitatively evaluated.