Characteristic Wave Speeds Research Articles

Research on features and localization of AE signals from the mechanical body of industrial robots based on WD-EMD

Abstract In order to reveal the propagation characteristics of acoustic emission (AE) signals in the body of industrial machinery, the characteristic frequencies and wave speeds of AE signals propagated on the interior and exterior surfaces (IS and ES) of the body were extracted. Subsequently, an algorithm utilizing characteristic frequency and time difference of arrival (TDOA) is proposed for the identification and localization of AE sources. Initially, an AE source is induced on the IS and ES of the body using the pencil-lead break method in accordance to ASTM standards, and the AE signal is captured by two piezoelectric sensors at a sampling frequency of 3 MHz. Then, to avoid the limitations of wavelet decomposition using self-selected wavelet scale and the problem that a single indicator cannot properly evaluate the correlation between independent mode functions (IMFs) with the original signal, this paper will conduct 4-layer wavelet decomposition of the original signal according to the response frequency range of the sensor, and select the wavelet details within the stable range of the response frequency of the sensor for preliminary reconstruction,and then the empirical mode decomposition (EMD) method is used to decompose the de-noised AE signal into 7 IMFs, and the AE waveform is reconstructed by the combined information of correlation coefficient and variance accounted for. Secondly, the reconstruction method combined with EMD analysis and a single index is compared with the proposed method in this paper to verify the reliability of the proposed method. In addition, the frequency domain characteristics of AE signal propagation process on the IS and ES of the body are extracted. Finally, based on the TDOA principle, the propagation speed of AE signal on the IS and ES of the body is calculated. Based on the geometric relationship between the AE source and two sensors, an algorithm for the location of the AE source is proposed. The results show that the proposed signal reconstruction method can effectively extract the features of AE signals, and the average positioning accuracy of the localization algorithm based on characteristic frequency and TDOA reaches 0.86%.

Resonance with surface waves induces forbidden velocity bands in dislocation glide

We use molecular dynamics simulations to demonstrate a pronounced influence of free surfaces on the mobility of dislocations at near-sonic velocities. By correlating instantaneous velocities v and resolved stresses τ, we show that the mobility relations of both edge and screw characters are composed of multiple ranges of stable uniform motion separated by bands of forbidden velocity. The lower limiting velocity for uniform motion of both edge and screw dislocations is the Rayleigh wave speed, cR. When forced to propagate at an average velocity greater than cR, dislocations exhibit cyclic, intermittent jumps in instantaneous velocity between cR and higher velocity branches of the mobility relation. Bands of forbidden velocity may be calculated directly from the velocity dependence of dislocation drag functions, which contain peaks near cR and—in the edge case—one other characteristic surface wave speed, which we associate with shear-horizontal (SH) waves. We propose that peaks in the drag function are due to resonance of free surface vibrations forced by nearby moving dislocations.

Influence of phase transformation on stress wave propagation in thin-walled tubes

Phase transformation can change the properties of a material and significantly affect the stress wave propagation features. This study presents an analytical model of coupled stress wave propagation in pseudo-elastic shape memory alloy thin-walled tubes subjected to combined longitudinal and torsional impact loading. An incremental constitutive model considering the effect of the hydrostatic pressure and deviatoric stress was employed to describe the mechanical behavior of SMA. The phase transformation ellipses shift along the σ-axis in the σ – τ plane due to the asymmetry of tension and compression induced by the hydrostatic pressure. The generalized characteristic theory was used to obtain the characteristic wave speed,simple wave solution, and the differential equation determining the stress path. The numerical results showed that the wave structure in the thin-walled tube is affected by the initial stress state and the final loading state. For the initially static and unstressed thin-walled tube, there is a special region on the σ–τ plane. When the combined longitudinal and torsion impact load lies in this region, an elastic compression wave, elastic shear wave and coupled phase transformation fast waves appear in the thin-walled tube in turn. The abnormal phenomenon is not observed in the conventional elastoplastic tubes.

Elastoplastic stress wave propagation in functionally graded material due to combined compression and shear

In the present paper, an analytical model for the propagation of stress waves in a functionally graded half-space subjected to combined compression and shear impact loading is established. The functionally graded materials (FGMs) based on the elastic–plastic model (the Tamura–Tomota–Ozowa model) are assumed to be continuously graded according to a power-law function of the volume fractions of the constituents. Based on generalized characteristics theory, the characteristic wave speeds were obtained and analyzed. The finite difference method was implemented to discretize the governing equations. Typical numerical examples for FGMs with positive and negative gradients are presented. The numerical examples reveal that the FGMs have the function of managing stress waves. Unlike traditional elastoplastic materials, the wave structures of FGMs will also change depending on such factors as the initial stress state, the amplitude of the loading, and the gradient distribution of the material.

Nonlinear plane waves in saturated porous media with incompressible constituents

We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot–Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible (Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shear-wave type, and nonlinear waves can be classified in a similar way. In the special case of a neo-Hookean skeleton, we derive the explicit expressions for the characteristic wave speeds, leading to the hyperbolicity condition. The sound speeds for a Yeoh skeleton are estimated using a perturbation approach. Then we arrive at the evolution equation for the amplitude of acceleration waves. In general, it is governed by a Bernoulli equation. With the present constitutive assumptions, we find that longitudinal jump amplitudes follow a nonlinear evolution, while transverse jump amplitudes evolve in an almost linearly degenerate fashion.

Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations

This work introduces a new type of constrained algebraic stabilization for continuous piecewise-linear finite element approximations to the equations of ideal magnetohydrodynamics (MHD). At the first step of the proposed flux-corrected transport (FCT) algorithm, the Galerkin element matrices are modified by adding graph viscosity proportional to the fastest characteristic wave speed. At the second step, limited antidiffusive corrections are applied and divergence cleaning is performed for the magnetic field. The limiting procedure developed for this stage is designed to enforce local maximum principles, as well as positivity preservation for the density and thermodynamic pressure. Additionally, it adjusts the magnetic field in a way which penalizes divergence errors without violating conservation laws or positivity constraints. Numerical studies for 2D test problems are performed to demonstrate the ability of the proposed algorithms to accomplish this task in applications to ideal MHD benchmarks.

An Impact Test to Determine the Wave Speed in SHPB: Measurement and Uncertainty

Post-processing the strain waves in split Hopkinson pressure bars to get the stress-strain in the sample requires the knowledge of the characteristic wave speed $$c_0$$ in the measuring bars. In the context of metrology, the measurement uncertainty in the value of $$c_0$$ must be assessed. The aim is to minimize this uncertainty, which depends on the way $$c_0$$ is determined, as it has an impact on the uncertainty in the final stress and strain in the sample. The frequency domain method we introduce is based on an impact test on a single bar. The frequency spectrum of the impact response of the bar clearly exhibits the longitudinal resonant frequencies of the bar. The experimental dispersion curve is deduced from the spectrum and an optimization procedure was applied to determine the wave speed $$c_0$$ along with the Poisson’s ratio and the uncertainty in the wave speed. This method gives a relative uncertainty in $$c_0$$ lower than 0.05%: it is mainly related to the uncertainty in the length of the bar (which is hard to reduce when using standard meter tape), which prevails over the uncertainty in the resonance frequencies of the bar. A precise value of the wave speed $$c_0$$ and of the associated measurement uncertainty is an important step in the context of split Hopkinson pressure bars if we want to precisely assess the final uncertainty in Split Hopkinson pressure bars test results, which is at present scarcely done.

A numerical model for multiphase liquid–vapor–gas flows with interfaces and cavitation

We are interested in multiphase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a hyperbolic single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. First, we present an analysis of the characteristic wave speeds associated to the hierarchy of relaxed multiphase models corresponding to different levels of activation of infinitely fast relaxation processes, showing that sub-characteristic conditions hold. We then propose a mixture-energy-consistent finite volume method for the numerical solution of the multiphase model system. The homogeneous portion of the equations is solved numerically via a second-order wave propagation scheme based on robust HLLC-type Riemann solvers. Stiff relaxation source terms are treated by efficient numerical procedures that exploit algebraic equilibrium conditions for the relaxed states. We present numerical results for several three-phase flow problems, including two-dimensional simulations of liquid–vapor–gas flows with interfaces and cavitation phenomena.

Modelling compressible dense and dilute two-phase flows

Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none are able to cover accurately the entire range, in particular regarding waves propagation. In the present work, an alternative to the Baer and Nunziato (BN) model [Baer, M. R. and Nunziato, J. W., “A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials,” Int. J. Multiphase Flow 12(6), 861 (1986)], initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble model [Marble, F. E., “Dynamics of a gas containing small solid particles,” Combustion and Propulsion (5th AGARD Colloquium) (Pergamon Press, 1963), Vol. 175] based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 characteristic wave speeds as well, but with different velocities. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave speeds as the BN model, but at a given point of space, 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock–particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data showing clear improvements.

An investigation of intersonic fracture using a phase field model

Under certain circumstances, cracks can grow faster than the slowest characteristic wave speed of the material. This so-called intersonic or transonic fracture phenomenon is studied in the present work by means of a phase field fracture model. The model makes use of a regularized representation of the fracture surface. This kind of models intrinsically fulfill the boundary conditions at the evolving crack surface and implicitly govern the crack evolution by a set of partial differential equations. The set includes the momentum balance as well as a phase field equation and is solved by means of a finite element scheme in this work. The simulated crack speeds agree well with experiments and molecular dynamic simulations reported in the literature.

Modeling of ultra-high-speed impact at the surface of an elastic half-space

A Semi-Analytical (SA) method is used to model impact loading at the free surface of an elastic half-space. The inertial effects are taken into account in the form of Green’s functions, also called influence coefficients. The influence coefficients are first computed and the simulation of an elastic shock with time-dependent surface pressure is performed. The effect of material properties, characteristic wave speed, the spatial distribution of the load, the impact size and the temporal form of the load is analyzed. It is observed that the dynamic response of a material which is submitted to dynamic loading depends strongly on the characteristic wave speed. The influence of the pressure pulse duration and peak magnitude is found to be also very significant, whereas the effect of the spot size and spatial distribution of the pressure is less significant.

Vibration analysis of pile-supported embankments under high-speed train passage

Soft ground improvement using piles has increasingly been used as a rapid construction technique for railway and highway embankments over soft soil areas. While most studies conducted so far have addressed only issues of stability and settlement of pile-supported embankments under static loading, very limited attention has been paid to understanding their behaviors under transient loading of moving vehicles. In this study, vibration behaviors of this embankment system under high-speed train passage are investigated through three-dimensional finite element simulation. They include (1) characteristics of the surface wave field at high train speeds, (2) the dependence of vibration amplitude on the train speed and the phenomenon of critical speed, and (3) response at some typical locations in the system when the train moves at the critical speed. The study shows that there are breaks in the simulated wave fronts as transiting between different materials due to the difference in the Rayleigh wave speed among the materials relative to the train speed, and that the increase in train speed is accompanied by the increase in phase shift between the train load and the displacement pattern beneath the load. It is shown that the critical speed of the system is governed by the embankment, instead of the soft soil as commonly observed in previous studies in which the ground is not improved. Namely the vibration amplitude is maximally amplified when the train speed approaches the characteristic Rayleigh wave speed of the embankment material. In addition, the results also suggest that the sloping surfaces on the ballast and embankment along with the piles form a ‘trapping’ effect by which most of the train-induced waves, especially higher-frequency waves, incident to the sloping surfaces are trapped and dissipated within the pile-supported embankment system, and thus significantly reducing vibration amplitudes outside the embankment.

Harmonic balance methods applied to computational fluid dynamics problems

In this paper, we briefly review the classical harmonic balance method, and describe the adaptation of the method required for its application to computational fluid dynamics models of unsteady time periodic flows. We describe several variations of the method including a classical balancing method with pseudo time relaxation, the nonlinear frequency domain form and the time spectral form. We show that the maximum stable Courant–Friedrichs–Lewy (CFL) number for explicit schemes is dependent on the grid reduced frequency, a non-dimensional parameter that depends on the cell size, characteristic wave speed, and the highest frequency retained in the harmonic balance analysis. We apply the harmonic balance methods to several nonlinear unsteady flow problems and show that even strongly nonlinear flows can be modelled accurately with a small number of harmonics retained in the model.

Classical and semirelativistic magnetohydrodynamics with anisotropic ion pressure

We study the magnetohydrodynamics (MHD) equations with anisotropic ion pressure and isotropic electron pressure under both the classical and semirelativistic approximations in order to develop a numerical model. The dispersion relation as well as the characteristic wave speeds are derived. In addition to the exact wave speed solutions, we also provide efficient approximate formulas for the semirelativistic magnetosonic speeds. The equations are discretized with the Rusanov and Harten-Lax-van Leer numerical schemes and implemented into the BATS-R-US MHD code. We perform a set of verification tests.

Characteristic wave speeds in the surface Brillouin scattering measurement of elastic constants of crystals

A simple and robust fitting procedure is presented for determining the three elastic constants of a cubic crystal from surface Brillouin scattering measurements carried out in the $⟨100⟩$ and $⟨110⟩$ directions in a (001) surface. The input data utilized are the Rayleigh surface wave velocity, the Lamb shoulder threshold velocity, and the longitudinal lateral wave velocity measured in the two directions. In fitting these velocities, use of simple closed-form expressions is made for the secular functions determining them. Corresponding expressions for the $⟨010⟩$ and $⟨10\overline{1}⟩$ directions in the (101) plane are also provided. The formulas for the Lamb shoulder threshold, which have not previously been available in the literature, should prove to be particularly useful, as they apply also to thin supported film structures. The procedure is applied to the determination of the elastic constants of the ternary semiconductor alloy ${\text{InAs}}_{0.91}{\text{Sb}}_{0.09}$, yielding ${C}_{11}=74.4\text{ }\text{GPa}$, ${C}_{12}=40.5\text{ }\text{GPa}$, and ${C}_{44}=37.8\text{ }\text{GPa}$.

Forward and backward waves in the arterial system: impedance or wave intensity analysis?

Both impedance analysis and wave intensity analysis are used to separate measured pressure and flow waveforms into their forward and backward components. The separation is sensitive to the characteristic impedance or wave speed determined from the data. In all other aspects, the results are identical.

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Reθ varied from 4.8 × 105 to 1.1 × 106. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Reθ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.

Wave speeds, shear bands and the second-order work for incrementally nonlinear constitutive models

The paper discusses the consequences of the incremental nonlinearity of a constitutive model of a solid for the analyses of characteristic wave speeds, acceleration waves, the second-order work criterion and shear band formation. Incremental nonlinearity may entail qualitative changes in the results as compared to incrementally linear models. Certain well-known correlations cannot be established if the constitutive equation is assumed to be incrementally nonlinear. In particular, the spectra of the characteristic wave speeds and the acceleration wave speeds become continuous and are described by different equations. The second-order work criterion as a sufficient condition of uniqueness of the incremental boundary value problem loses its applicability in bifurcation analyses, unless the applicability can be proved for a particular type of nonlinearity. The singularity of the acoustic tensor in the general nonlinear case correlates neither with the vanishing of the second-order work nor with the shear band formation.

On well-posedness of the dynamic problem for an anisotropic fluid-saturated solid

It is known that a high degree of anisotropy in the constitutive behaviour of a solid may result in the loss of hyperbolicity of the dynamic equations in the form of either complex-conjugate or purely imaginary characteristic wave speeds (flutter ill-posedness and shear band formation, respectively). In the present paper we investigate the characteristic wave speeds in the dynamic problem for a transversely isotropic fluid-saturated porous solid. Three cases are considered: a dry solid and a saturated solid under locally undrained and drained conditions. It is shown that, for given constitutive parameters of the solid skeleton, the dynamic problem for a drained solid may become ill-posed due to the flutter-type loss of hyperbolicity, while the dynamic equations for a dry and an undrained solids remain hyperbolic. For a given solid skeleton, the characteristic wave speeds are strongly influenced by the pore fluid compressibility which, in turn, is extremely sensitive to the presence of a small amount of free gas.

X‐Winds in Action

The interaction of accretion disks with the magnetospheres of young stars can produce X-winds and funnel flows. With the assumption of axial symmetry and steady state flow, the problem can be formulated in terms of quantities that are conserved along streamlines, such as the Bernoulli integral (BI), plus a partial differential equation (PDE), called the Grad-Shafranov equation (GSE), that governs the distribution of streamlines in the meridional plane. The GSE plus BI yields a PDE of mixed type, elliptic before critical surfaces where the flow speed equals certain characteristic wave speeds are crossed and hyperbolic afterward. The computational difficulties are exacerbated by the locations of the critical surfaces not being known in advance. To overcome these obstacles, we consider a variational principle by which the GSE can be attacked by extremizing an action integral, with all other conserved quantities of the problem explicitly included as part of the overall formulation. To simplify actual applications we adopt the cold limit of a negligibly small ratio of the sound speed to the speed of Keplerian rotation in the disk where the X-wind is launched. We also ignore the obstructing effects of any magnetic fields that might thread a disk approximated to be infinitesimally thin. We then introduce trial functions with adjustable coefficients to minimize the variations that give the GSE. We tabulate the resulting coefficients so that other workers can have analytic forms to reconstruct X-wind solutions for various astronomical, cosmochemical, and meteoritical applications.