Transverse Wave Speed Research Articles

Singularity characteristic analysis for anti-plane accelerated propagating V-notches

By introducing the displacement asymptotic expansion around the vertex of an anti-plane V-notch into the elasto-dynamics equation, the singularity characteristic analysis for an accelerated propagating V-notch is transformed into a problem of solving a characteristic ordinary differential equation. The singularity can be generated once the interpolating matrix method is applied to solve the established characteristic equation. The singularities for anti-plane single material and bi-material propagating V-notches are investigated under different initial propagating velocities and accelerations respectively. For the single material anti-plane V-notch, the singularity becomes stronger with the decrease of notch opening angle, and it becomes stronger with the increase of the direction angle of initial propagating velocity and acceleration. It turns stronger with the increase of propagating speed when the propagating direction of initial velocity is greater than 45°, otherwise, the opposite conclusion may be drawn on the other hand. For the bi-material anti-plane V-notch, the singularity becomes weaker with the increase of propagating acceleration and it becomes stronger with the increase of the ratio of transverse wave speed.

Surface Magnetoacoustic Waves in Magnetostrictive Media

It is known that in absence of external magnetic field it is always possible to excite a surface Love wave in a two-layered medium, whose speed is less than the speed of transverse bulk waves in the substrate and greater than the speed of these bulk waves in the layer. This paper is devoted to the issues of existence and propagation of surface magnetoacoustic waves in layered magnetostrictive half-spaces. It is shown that besides the noted pure elastic waves, the new type of surface magnetoacoustic wave exists, which existence is exclusively conditioned by magnetostrictive properties of medium. It is established that the speed of this new wave can be less than the speed of transverse bulk waves in the layer. It is also established that the new wave propagates with dispersion.

Reference-Free Method for Thickness Gaging of a Test Object and Measuring the Speed of Longitudinal and Transverse Waves in It Based on Echo Signals Picked by an Antenna Array

A reference-free method is proposed for determining the speed of longitudinal and transverse vertically polarized waves and the thickness of a test object based on comparing the measured and calculated echo signals reflected from the boundaries of the test object when using an antenna array operating on a zero tilt angle wedge in the double scanning mode. Results of numerical and model experiments confirming the efficiency of the method are presented. Using this method in a model experiment, it has proved possible to measure the thickness of a test object and the speed of longitudinal and transverse waves in it with a relative error (accuracy) of approximately 0.25%. The method can be used to characterize anisotropic properties of test objects, providing information about their physical and mechanical properties.

Nonlinear Bayesian inversion for estimating water pipeline dimensional and material parameters using acoustic wave dispersion

Monitoring pipeline thinning and material degeneration is becoming important for water-filled pipeline condition assessment. In this paper, an inverse method is proposed for estimating a pipeline's dimensional and material parameters using the dispersion characteristics of its modal wavenumbers. The inverse method is established by matching observed wavenumber dispersion characteristics of the water-filled pipeline with forward model predictions, where pipeline inner radius, thickness and density, and longitudinal and transverse wave speeds of the pipeline wall material are taken as unknown parameters. To account for the strong nonlinearity of the inverse problem and improve inversion efficiency, a Bayesian inversion scheme is formulated using a parallel-tempering Markov chain Monte Carlo approach. The characteristics and the performance of the proposed inverse method are investigated by systematic simulations which cover the impact of the number of modes utilized, dispersion frequency interval and observation errors. Laboratory experiments are utilized to validate the inversion method using wavenumber dispersion observations (below 50 kHz) from three metallic pipelines all with the same outer radius but different wall thicknesses and materials. The uncertainties of the estimated dimensional parameters are found to be lower than 0.2 mm and different materials are successfully distinguished and identified for the three pipelines.

On the effects of damping on the dynamics of axially moving spatially periodic strings

The paper concerns the analysis of the effects of damping on the linear dynamics of an axially moving non-uniform structure, string with periodically varying mass and damping properties. The string, in particular models transmission chains for drive engines. An expression for the threshold velocity of the string axial motion is determined; if the string moves with a velocity higher than the threshold one, then waves travelling in it are unstable. For a uniform string, the threshold velocity equals to the transverse wave speed. It is shown that pure modulations of the string mass can increase the threshold velocity for waves with certain wavenumbers. By contrast, combined modulations of mass and damping properties lead to reduction of the threshold velocity as compared to the case of the uniform string. And the larger the amplitudes of the modulations, the more pronounced the reduction. This indicates that due to periodic spatial modulations of the string properties, the string dynamics can become unstable even if its axial velocity is considerably lower than the transverse wave speed. Thus, periodic distribution of damping and mass properties can considerably affect design of axially moving structures used in applications.

Effect of Surface Layer Damage on Acoustic Anisotropy

Relations for the principal values of the damage tensor based on data on the speeds of longitudinal and transverse waves are proposed. The relationship of acoustic anisotropy with the principal values of the damage tensor are established. The distributions of local speeds and damage along the thickness of the specimen are studied. It is shown that damage is localized in a narrow surface layer, with local damage maxima far exceeding the average damage value.

Effect of pre-tension on energy absorbed by fabric during projectile penetration

High-strength woven fabrics made of polymeric yarns are widely used for protection against projectile impact, because of their strength, low density and high toughness. Their response to projectile impact is complex, because of the woven architecture and rate-dependent behaviour of constituent yarns. This work is directed at understanding the influence of applying pre-tension to a woven fabric, on the energy absorbed during impact by a spherical projectile. An experimental arrangement that facilitates the application of pre-tension to fabric specimens, is used to investigate fabric performance in terms of the variation of energy absorbed with impact velocity, and how pre-tension affects this. The results show that the relationship between energy absorbed during projectile penetration and impact velocity, displays an increasing-decreasing parabolic-type profile. Below the ballistic limit, fabrics subjected to a higher pre-tension perform better, but for higher impact velocities, fabric subjected to lower pre-tensions absorb more energy. To explain the results, projectile impact is simulated using a numerical model that includes the geometrical features of the fabric and incorporates rate dependence of the yarn material. The model exhibits relatively good correlation with experiments, and yields a fuller understanding of the mechanisms governing fabric behaviour. Results show that the initial increase in energy absorbed by the fabric is mainly due to the transfer of projectile kinetic energy to fabric kinetic energy; pre-tension restrains yarn movement and thus decreases energy absorption. Analysis of the variation of transverse wave speed with impact velocity shows that it increases approximately linearly with impact velocity, and that a higher pre-tension also elevates transverse wave speed. The fabric studied fails rapidly when the impact velocity is sufficiently high; this is caused by stress concentration at the impact point and insufficient time for the transverse wave to propagate through the fabric; failure is aggravated by a higher pre-tension and accounts for the resulting poorer performance for impact velocities significantly higher than the ballistic limit.

Sound speeds in and mechanical properties of (U,Pu)O2− x

ABSTRACT The sound speeds of longitudinal and transverse waves in the uranium–plutonium mixed oxide pellets were measured as functions of porosity, oxygen-to-metal ratio, and plutonium content. The effect of each parameter was well fitted by a linear function and the equations were obtained to calculate the sound speeds. Mechanical properties were evaluated with the sound speeds and the result of Young's modulus showed that porosity was the most important factor to decrease Young's modulus. Temperature dependence on Young's modulus was also evaluated with previously reported thermal expansion. Decrease of Young's modulus with increasing temperature was in good agreement with available literature.

Speed of transverse waves in a string revisited

In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the considered wave pulse and the related velocity and acceleration distributions. In this paper, we derive the named formula by applying Newton’s second law or the work-energy theorem to a finite element of the string, making no assumptions about the shape of the wave. We argue that the suggested method can help the student gain a deeper insight into the nature of waves and the related process of energy transport, as well as provide a new experience with the fundamental principles of mechanics as applied to extended and deformable bodies.

In situ monitoring of dislocation proliferation during plastic deformation using ultrasound

Ultrasound has long been used as a non-destructive tool to test for the brittle fracture of materials. Could it be used as a similar tool to test for ductile failure? As a first step towards answering this question, we report results of local measurements of the speed of transverse waves in aluminum under standard testing conditions at two different probe locations and continuously as a function of applied load. The result, as expected, is independent of stress in the elastic regime, but there is a clear change, consistent with a proliferation of dislocations, as soon as the yield strength is reached. We use a model that blames the change in wave speed on the interaction of elastic waves with oscillating dislocation segments, which quantitatively relates the change in wave velocity with dislocation density Λ and segment length L, thus obtaining a continuous relation between dislocation density and externally applied stress. We took off samples from the probe before, at intermediate, and high loading, and we measured their dislocation density using standard X-ray diffraction and transmission electron microscopy techniques. The results agree well with the acoustic measurements, and the relation between stress and dislocation density is consistent with the Taylor rule. This indicates that monitoring the speed of transverse waves could become a useful diagnostic of dislocation density for metallic pieces in service as well as a tool to test models of plastic behavior.

Exploration of Wave Development during Yarn Transverse Impact

Single yarns have been impacted in a transverse fashion so as to probe the characteristics of resulting wave development. Longitudinal wave speeds were tracked in efforts to directly measure the yarn tensile stiffness, resulting in a slight increase in the modulus of Kevlar® KM2 and Dyneema® SK76. Additionally, the load developed in AuTx® and Kevlar® KM2 yarns behind the longitudinal wave front has been recorded, providing additional verification for the Smith relations. Further effort to bolster the Smith equations has been successfully performed via tracking transverse wave speeds in AuTx® yarns over a range of impacting velocities. Additional emphasis has been placed at understanding the transverse wave development around the yarn critical velocity, demonstrating that there is a velocity zone where partial yarn failure is detected. Above the critical velocity, measurement of early time transverse wave speeds also agrees with the Smith solution, though the wave speed quickly reduces in value due to the drop in tensile stresses resulting from filament rupture. Finally, the Smith equations have been simplified and are compared to the Cunniff equation, which bear a striking resemblance. Due to such a resemblance, it is suggested that yarn critical velocity experiments can be performed on trial yarn material, and the effect of modifying yarn mechanical properties is discussed.

Wave propagation in axially moving periodic strings

The paper deals with analytically studying transverse waves propagation in an axially moving string with periodically modulated cross section. The structure effectively models various relevant technological systems, e.g. belts, thread lines, band saws, etc., and, in particular, roller chain drives for diesel engines by capturing both their spatial periodicity and axial motion. The Method of Varying Amplitudes is employed in the analysis. It is shown that the compound wave traveling in the axially moving periodic string comprises many components with different frequencies and wavenumbers. This is in contrast to non-moving periodic structures, for which all components of the corresponding compound wave feature the same frequency. Due to this “multi-frequency” character of the wave motion, the conventional notion of frequency band-gaps appears to be not applicable for the moving periodic strings. Thus, for such structures, by frequency band-gaps it is proposed to understand frequency ranges in which the primary component of the compound wave attenuates. Such frequency band-gaps can be present for a moving periodic string, but only if its axial velocity is lower than the transverse wave speed, and, the higher the axial velocity, the narrower the frequency band-gaps. The revealed effects could be of potential importance for applications, e.g. they indicate that due to spatial inhomogeneity, oscillations of axially moving periodic chains always involve a multitude of frequencies.

Fully Automated and Robust Tracking of Transient Waves in Structured Anatomies Using Dynamic Programming

Tissue stiffness is often linked to underlying pathology and can be quantified by measuring the mechanical transient transverse wave speed (TWS) within the medium. Time-of-flight methods based on correlation of the transient signals or tracking of peaks have been used to quantify the TWS from displacement maps obtained with ultrasound pulse-echo techniques. However, it is challenging to apply these methods to in vivo data because of tissue inhomogeneity, noise and artifacts that produce outliers. In this study, we introduce a robust and fully automated method based on dynamic programming to estimate TWS in tissues with known geometries. The method is validated using ultrasound bladder vibrometry data from an in vivo study. We compared the results of our method with those of time-of-flight techniques. Our method performs better than time-of-flight techniques. In conclusion, we present a robust and accurate TWS detection method that overcomes the difficulties of time-of-flight methods.

Elasticity, hardness, and thermal properties of ZrBn (n=1, 2, 12)

Elasticity, hardness, and thermal conductivity of ZrBn (n=1, 2, 12) were studied in this paper by using the first-principles calculations of plane wave ultra-soft pseudo-potential technology based on the density functional theory (DFT). Deep analysis of elasticity and anisotropy was carried out, indicating that ZrB and ZrB2 are soft (the most anisotropic) and superhard (the least anisotropic) respectively. The transverse wave speed (Vt), longitudinal wave speed (Vl) and the minimum thermal conductivity κmin (both Clark and Cahill model) were calculated. Our investigations show that ZrB is a good heat insulating material and a good lubricant, ZrB12 can be served as a good high-temperature-resistant material and superconducting material, and ZrB2 is a good wear-resistant material.

Localization of CO2 leakage from transportation pipelines through low frequency acoustic emission detection

Carbon Capture and Storage is a technology to reduce greenhouse gas emissions. CO2 leak from high pressure CO2 transportation pipelines can pose a significant threat to the safety and health of the people living in the vicinity of the pipelines. This paper presents a technique for the efficient localization of CO2 leakage in the transportation pipelines using acoustic emission method with low frequency and narrow band sensors. Experimental tests were carried out on a lab scale test rig releasing CO2 from a stainless steel pipe. Further, the characteristics of the acoustic emission signals are analyzed in both the time and the frequency domains. The impact of using the transverse wave speed and the longitudinal wave speed on the accuracy of the leak localization is investigated. Since the acoustic signals are expected to be attenuated and dispersed when propagating along the pipe, empirical mode decomposition, signal reconstruction and a data fusion method are employed in order to extract high quality data for accurate localization of the leak source. It is demonstrated that a localization error of approximately 5% is achievable with the proposed detecting system.

Effect of twist on transverse impact response of ballistic fiber yarns

A Hopkinson bar was employed to conduct transverse impact testing of twisted Kevlar KM2 fiber yarns at the same impact speed. The speed of Euler transverse wave generated by the impact was measured utilizing a high speed digital camera. The study included fiber yarns twisted by different amounts. The Euler transverse wave speed was observed to increase with increasing amount of twist of the fiber yarn, within the range of this investigation. The higher transverse wave speeds in the more twisted fiber yarns indicate better ballistic performance in soft body armors for personal protection.

Reflection at the free surface of piezoelectric thermo-microstretch viscoelastic medium without energy dissipation

The present paper is aimed to model and study the characteristics of various reflected waves in a homogeneous isotropic piezoelectric thermo-microstretch viscoelastic solid within the context of theory of thermoelasticity without energy dissipation. It is shown that there exists three sets of coupled longitudinal and two sets of coupled transverse waves with different speeds in a two-dimensional model of the solid. The speeds of all the existing waves are found to be complex valued and frequency dependent. The speeds of coupled longitudinal waves are found to be influenced by the electric effect, while the speeds of transverse waves remain unaffected to the electric effects. Reflection coefficients and energy ratios of various reflected waves are presented when (1) a set of coupled longitudinal waves is made incident and (2) a set of coupled transverse waves is made incident. The numerical computations have been carried out to calculate the phase speeds, reflection coefficients and energy ratios with the help of Matlab programming for aluminum-epoxy like material. The numerical values of the modulus of reflection coefficients and phase speeds are presented graphically to exhibit the viscous effects. The energy ratios as functions of angle of incidence are also shown graphically. Some particular cases of interest have been inferred from the present study.

EFFECTS OF DYNAMIC LOADS landslide-prone slopes in the area of ​​Sochi

This study analyzed the impact of the dynamic loads and vibration impacts from construction machinery and road transport on landslide slopes and soils composing them. To study the effect of the dynamic effects were used geophysical research methods and computational techniques based on the speed of longitudinal and transverse waves and the elastic properties of rocks. These calculations allowed us to obtain the values of stresses in the soil as a result of the impact and value of the natural frequencies of ground, forming the landslide slopes. The results of mathematical calculations based on the work of many scholars of the influence of dynamic loads on the ground. As a result, after an analysis of the materials geophysical data and mathematical calculations in groundwater were identified thicker layers in which the values of natural frequencies coincide with the values of the frequency of exposure.

Modeling unidirectional composites by bundling fibers into strips with experimental determination of shear and compression properties at high pressures

Numerical models of unidirectional panels of ultra-high-molecular weight polyethylene (UHMWPE), like Dyneema® HB80 or Spectra®, have been a difficult challenge. The problem arises from the intimate structure of the material. It is a huge collection of fibers loosely held together by a matrix. For example, for HB80 the fibers are very small in diameter (∼17 μm) but extremely strong (∼3.5 GPa). The amount of matrix is small (∼20% in volume) and very weak. The “natural” scale to use in the numerical model for this material is the fiber scale (∼17 μm). This scale would provide the right sound speed, transverse wave speed, failure strain, strength of the laminate, deflection, slippage between the fibers/layers, etc. which are all essential details if we want to have predictive capability. But even with the very powerful computers available nowadays we are still very far from being able to simulate a real-size laminated target (for example 30 cm wide and 1 or 2 cm thick) at the fiber scale. This paper proposes an “intermediate” scale that bundles or consolidates many fibers together so that the numerical problem is solvable in a few hours (or maximum one or two days for thick targets) of computation in a single board (24 processors). The scale is chosen precisely so that the essential physics of the ballistics problem is kept and the material properties used are the ones measured in the lab for the fiber and matrix. A similar approach was presented in a previous paper for fabrics (Kevlar, Dyneema, and PBO) where a yarn-level model was able to reproduce both the wave propagation patterns and the ballistic limits. This paper first describes new material test results (shear and compression at low and high confinement pressures). These were essential in properly capturing the delamination of the material. Then, for completeness, transverse wave propagation and ballistics results in Dyneema published elsewhere are briefly presented. Finally the numerical model in LS-DYNA is developed and comparison with deflection history and ballistic limits is conferred.

Nonlinear experiments of tuning curve resonances for the vibrational modes of a weakly stretched circular membrane

Nonlinear oscillations of a pre-stretched 11.5 cm diameter latex circular membrane clamped rigidly around the boundary were investigated. The relaxed membrane thickness was 0.4 mm. An 8 cm diameter loud speaker drove the membrane from below using a swept sinusoidal tone. Low drive tuning curve sweeps demonstrated resonant frequencies corresponded to the first three radially symmetric linear drum modes (56, 147.6, and 240.5 Hz) sweeping from 50 to 300 Hz. Regression yielded a transverse wave speed of 10.6 m/s. Incrementally increasing the speaker amplitude (after each sweep) showed the lowest resonant frequency at first decreases, then increases with increasing acoustic drive pressure. Higher modes exhibited frequency increases with drive level. Tuning curve responses were measured using a 6 mm diameter microphone 5 mm above the center of the membrane. Nonlinear tuning curves hysteresis effects occur for higher drive levels sweeping between 50 and 70 Hz. Here, the amplitude sharply falls from a high to a low microphone response at fa = 59 Hz. With the same drive level, a sweep tone starting from 70 Hz to 50 Hz exhibits at fa = 57.5 Hz, a jump from a lower to a higher microphone response. [Goncalves et al., J. Vib. Sound 327, 231 (2009).]