Longitudinal Wave Propagation Research Articles

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.

Ultrasonic Evaluation of Porosity in Out-of-Autoclave Carbon Fiber–Reinforced Polymer Composite Material

Ultrasonic longitudinal wave propagation is studied in out-of-autoclave (OoA) carbon fiber–reinforced polymer composite material with varying levels of porosity contents. A combination of cure pressures and a solvent is used to produce specimens with void contents in the range of 0% to 22%. Ultrasonic measurements are made in through-transmission mode, and the data is processed to study various aspects of wave interaction with porosity in OoA specimens. The specimens with a wide range of void contents have enabled the study of broader trends of ultrasonic center frequency, wave velocity, and attenuation with respect to porosity. Results show ultrasonic center frequency and wave velocity are decreased linearly as the void content increases. The relationship of ultrasonic wave attenuation can be approximated by a logarithmic relationship when considering the full range of void content studied. Strength measurements of specimens with varying void contents are made using the flatwise tensile (FWT) test. It is observed that the strength rapidly decreases with increasing porosity. Correlations made between FWT strength, ultrasonic wave velocity, and attenuation are best described by logarithmic relationships. The data shows a potential for inferring strength knockdowns due to the presence of porosity based on ultrasonic measurements.

Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube

Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube

Elastic three-dimensional metaframe for selective wave filtering and polarization control

We experimentally achieve selective wave filtering and polarization control in a three-dimensional elastic frame embedding local resonators. By connecting multi-resonating elements to a frame structure, a complete low-frequency, subwavelength bandgap with strong selective filtering properties is obtained. Theory and experiments demonstrate the metaframe capability to selectively stop transverse waves while allowing longitudinal wave propagation as in “fluid-like” elasticity. This peculiar behavior, together with the complete bandgap structure, may open opportunities in the context of wave control, envisaging concurrent applications for three-dimensional filters and elastic wave polarizers.

Effects of the magnetic field on the viscoelastic wave propagation and dynamic material properties

In this paper, the longitudinal wave propagation of a thin ferromagnetic (Fe-Cr-Al alloy) rod under the transverse magnetic field is investigated analytically without ignoring the viscoelastic characteristics of this alloy. The analysis is based on the Bernoulli-Euler rod theory and a 4-element viscoelastic model based on the experimental observation. The viscoelastic wave characteristics and the behaviours of dynamic material properties under the magnetic field are investigated. The analytically results show that the longitudinal wave propagation and the dynamic material properties of the rod are affected by the magnetic field existence (for magnetic field magnitude values greater than about 107A/m), except the imaginary part of the complex elasticity modulus. Furthermore, in a large frequency range, depending on the ratio of the group velocity to the phase velocity an abnormal dispersion characteristic is observed.

Bright-dark wave envelopes of nonlinear regularized-long-wave and Riemann wave models in plasma physics

The nonlinear regularized-long-wave (RLW) and the Riemann wave (RW) models are physically significant in plasma physics and in further study of nonlinear dispersive waves, namely shallow water, ion-acoustic and magneto-sound waves in plasmas, anharmonic lattice and pressure waves in liquid-gas bubble mixtures, tidal and tsunami waves in rivers and oceans, longitudinal electromagnetic wave propagation in plasma, etc. The advanced generalized (G'/G)-expansion scheme is facilitated in this article for retrieving the bright-dark exact solitary wave solutions generated in the form of hyperbolic, trigonometric, and rational structures to the above-stated models. To figure out the internal contrivance of the solutions, 3D and contour plots concerning bright parabolic wave shape, compacton wave shape, bell-shaped soliton, kink wave type soliton, dark anti-parabolic wave shape, anti-compacton wave shape, bright propagation of solitary wave shape solutions are depicted for definite free parametric values. The characteristic feature of the wave envelops fluctuates taking into consideration the changes of free parameters and they are essentially dominated by the linear and nonlinear impact.

Boundary Reflections of Rolling Waves in Cubic Anisotropic Material

Rolling waves have unconventional circular polarizations enabled by the equal-speed propagation of longitudinal and transverse waves in elastic solids. They can transport non-paraxial intrinsic (i.e. spin) mechanical angular momentum in the media. In this work, we analyze the rolling wave reflections and their effects on the non-paraxial spins in a cubic elastic half-space with an elastically supported boundary. Reflected waves from both normal and general oblique incidences are investigated. We show that, by adjusting the stiffness of the elastic boundary, we can precisely control the spin properties of the reflected waves, paving the way towards a broad category of spin manipulation techniques for bulk elastic waves.

The propagation of transient waves in two-dimensional square lattices

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete periodic media can be obtained by a method of asymptotic inversion of the Laplace and Fourier transforms in the vicinity of the quasi-front of infinitely long waves; moreover, in this method it is possible to take into account the contribution of short waves. Using this method, we obtain asymptotics of perturbations in lattices in plane and antiplane formulations under a local transient load. Besides, we show that equations describing 2D plane motion of a square lattice can be represented in the form of two linearly independent wave equations, each of which contains one unknown function only. By analogy with the theory of elasticity, one equation describes the propagation of shear waves in the lattice, while the other equation describes the propagation of longitudinal waves. As a result, it is shown that, in a homogeneous infinite lattice, a load can be specified in such a manner that either predominantly longitudinal or predominantly shear waves are formed. The problems under study are also solved by a finite difference method. The qualitative and quantitative correspondence of asymptotic and numerical solutions is shown.

A Study of Longitudinal Waveguide with Band Gap Using Cylindrical and Conical Shape Periodic Structure

This research presents the theoretical and experimental studies for cylindrical and conical periodic structures to control longitudinal wave motion. Many relevant researches exist to stop and pass a certain frequency wave without active devices with periodic structures called metamaterials. To modify or control longitudinal wave propagation, i.e., passing or blocking mechanical wave within specific frequency ranges, repeated mass-spring systems or metamaterials can be applied. By integrating a few identical structural components to form a whole structure, it is possible to make a mechanical filter for wave propagation. Most studies rely on straight bar with cylindrical structure. Thus, with a unit cell that have a cylindrical and conical structure, this research presents the extensions toward the studies of the wave motions for straight and curved bars with finite element simulations and experiment studies. The results show that the hybrid cylindrical and conical periodic structures can be effective in terms of wave motion control and stiffness.

Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

On propagation of harmonic plane waves under the Moore–Gibson–Thompson thermoelasticity theory

ABSTRACT The present work is aimed at a detailed investigation of harmonic plane wave propagation through an isotropic, unbounded and homogeneous thermoelastic medium under the recently proposed Moore–Gibson–Thompson (MGT) thermoelasticity theory. The dispersion relation is derived and its solution for the longitudinal plane wave propagation is obtained analytically. Two different modes of longitudinal wave are identified as elastic and thermal mode waves. The asymptotic expressions of various important characteristics of the wave fields such as phase velocity, specific loss and penetration depth for both the waves are obtained for limiting cases of very high and low frequency values. The Whitham stability of harmonic plane waves is established. Further, the computational tool is used to achieve numerical results for these wave characteristics and to illustrate the analytical findings graphically. Some important observations about the prediction of the MGT model in comparison to the other existing models, i.e. classical coupled thermoelastic model, LS model and GN-III model, are highlighted. Effects of material parameters on the propagation of waves are analyzed in a detailed manner. From the theoretical as well as numerical results, it is investigated that the MGT model accounts for finite speed of elastic wave as well as thermal wave.

Longitudinal and shear waves propagation in a periodic foundation with negative Poisson's ratio

The introduction of negative Poisson's ratio materials in engineering has opened new possibilities in materials science, acoustics, and civil engineering. Isotropic elastic foam with a negative Poisson's ratio of -0.7 has been produced which expands laterally when stretched, in contrast to ordinary materials. In this work, a new arrangement of seismic isolation foundation containing a unit cell of concrete - anti rubber and concrete/steel layers is proposed. The novelty lies in application of anti-rubber material as one of the three different layers periodically placed to form a periodic foundation. The auxetic material inclusion in this new arrangement broaden the no pass band of the periodic foundation compared to the earlier investigations. To demonstrate the effectiveness of this metamaterial foundation, an axially loaded column placed under three different foundations are numerically investigated. It is observed that the response of the metamaterial foundation with auxetic inclusion attenuated the elastics waves greatly compared to the foundations with rubber and traditional foundations. The results of the study could be used in developing new foundation materials for vibration attenuation for seismic waves which may cause destruction to engineering structures.

Highly efficient gas sensor based on quasi-periodic phononic crystals

Highly sensitive gas sensors have been introduced for the sensing of air, NH3, O2, CO2, or CH4 gases. The quasi-periodic structures of simple and generalized Fibonacci, simple and generalized Thue-Morse, Rudin-Shapiro, and symmetry structures have been regarded composed of diverse materials of PDMS, Epoxy, Al, and Steel and the detection gas. The proposed quasi-periodic structures have been investigated for maximum 10 alternating layers of solid-fluid arrangement with thickness ratio of (dsoild:dfluid)=(9:1). The study has been carried out by the transfer matrix method for the longitudinal wave propagation and the FC(5,1) and RS(4) structures composed of Al and Steel as solid material presented single peak shift for different gas infiltration. The sensitivities of 0.5988 MHz.m3. kg−1, 0.7777 MHz.m3. kg−1, 0.8738 MHz.m3. kg−1, and 0.9346 MHz.m3. kg-1 have been obtained in the frequency range of MHz for pure CO2, O2, NH3, and CH4 gases, respectively. Also, the best layer sequence for highly efficient gas sensor in 1D phononic quasi-crystals has been obtained, discussed, and optimized to get high quality factor.

CREEPING SURFACE LONGITUDINAL ACOUSTIC WAVE: MAIN PROPERTIES AND APPLICATION POSSIBILITIES

Creeping ultrasonic waves have long been successfully used for flaw detection of near-surface and near-bottom zones of metal products. However, due to the fact that the creeping wave generates a lateral transverse wave directed into the metal volume at the third critical angle, it is also possible to test internal defects in principle. At known velocities of propagation of longitudinal and transverse waves in the metal, the third critical angle is easily calculated. Therefore, the time of propagation of the ultrasonic signal along any trajectory between points on the surface and in the volume of the metal can be calculated. Usually, creeping waves are used to test products of plane-parallel shape. There are no cases of their application on curved surfaces in the literature. It is possible that the creeping wave can also propagate over a concave surface. The aim of the article is to test experimentally new ways of using creeping waves. The propagation trajectories of the creeping and lateral transverse waves were studied on a steel plate. The time of passage of the ultrasonic signal along such trajectories of different lengths was measured, and the measurement results were compared with the calculated time values. The measured and calculated values coincided with accuracy sufficient for the coherent accumulation of echo signals that passed through the metal part of the path by the creeping wave and another part of the path by the lateral transverse wave.The propagation of the creeping wave over a concave surface was studied on a steel sample with cylindrical faces of different radii. As a result, it turned out that on a concave surface, the creeping wave propagates at the same speed of longitudinal waves as on a flat surface, but it decays much more strongly with distance. Studies have shown that creeping waves can be used in ultrasonic tomography, where a preliminary calculation of the propagation trajectories of ultrasonic signals is required. The propagation of creeping waves over concave surfaces extends the capabilities of the TOFD method to the area of intube testing

Harnessing bulging or sloshing modes to design locally resonant liquid-solid metamaterials

This paper proposes harnessing bulging or sloshing modes to design locally resonant liquid-solid metamaterials that can be applied to vibration isolation engineering. The longitudinal dynamic effective mass of the proposed bulging or sloshing cell is analyzed through the assumed mode method and the finite element simulation. The meta-structure consisting of a sequence of unit cells is studied as well. In a certain frequency regime, the proposed bulging metamaterial can block the propagation of elastic longitudinal waves and convert the energy of the host structure to the bending energy of localized covering plates. This longitudinal-to-transverse conversion is triggered by the coupled vibration of the internal liquid and the covering plate. This feature can be applied to energy harvesting. In terms of the sloshing metamaterial, it can attenuate elastic longitudinal waves in an extremely low-frequency range. The local resonance frequency and the bandwidth of the sloshing metamaterial can be tuned by altering the liquid height. Additionally, we exhibit equivalent pendulum-like models to understand the vibration behavior of the bulging and sloshing cells. The proposed liquid-solid metamaterials can provide new approaches for vibration isolation and mechanical energy harvesting. The concept presented here may also give inspirations to designing other multi-physics metamaterials.

Numerical simulation of seismic waves in 3-D orthorhombic poroelastic medium with microseismic source implementation

SUMMARY We have carried out microseismic forward modelling in orthorhombic poroelastic medium. The seismic response to isotropic (ISO) source, double couple (DC) source and compensated linear vector dipole (CLVD) source was solved by finite-difference algorithm in time domain, respectively. We used analytical solution to test our numerical algorithm and find that the match between the analytical solutions and numerical solutions is sufficiently close. We then designed several different models to calculate the seismic response and analyse the effect of medium parameters and source mechanism on the propagation of seismic waves. We observed from the modelling results that ISO source excites two kinds of waves in isotropic medium, which are fast longitudinal wave and slow longitudinal wave, while the DC and CLVD sources excite three kinds of waves in isotropic medium, including a transverse wave in addition to the fast and slow longitudinal waves. All of these three kinds of sources generate four kinds of seismic waves in orthorhombic poroelastic medium. These are two separable transverse waves in addition to the fast and slow longitudinal waves. The fluid viscosity and medium tortuosity has an effect on the propagation of the slow longitudinal wave. The slow longitudinal wave appears in propagating mode under the effect of low fluid viscosity and appears at the source location in a static mode under the effect of high fluid viscosity. The wavefield snapshot of the slow longitudinal wave has a circular shape when the tortuosity is isotropic, whereas it has an oval shape when the tortuosity is anisotropic. As far as the anisotropic parameters are concerned, the anisotropy of the fast longitudinal wave is more sensitive to the value of $\varepsilon ( {{\varepsilon _1},{\varepsilon _2}} )$, while the value of ${\rm{\delta }}( {{{\rm{\delta }}_1},{{\rm{\delta }}_2},{{\rm{\delta }}_3}} )$ has more effect on the anisotropic behaviour of the two separable transverse waves.

Effect and identification of parametric distributed uncertainties in longitudinal wave propagation

Uncertainties play an important role in dynamic systems regarding their vibration and wave propagation behaviour. Stochastic methods have been used to address the randomness incorporated in numerical models. The spectral element method (SEM) is suitable to perform vibration and wave propagation analysis based on large frequency ranges with accuracy and low computational cost. This paper explores the longitudinal wave propagation considering uncertainties in the media aside from demonstrating and quantifying the effect of randomness inherent in the material. The stochastic Love rod spectral elements are proposed, and the parameters were assumed to be spatially distributed alongside the structure expressed as a random field. It is expanded using the Karhunen-Loève spectral decomposition and memoryless transformation. The Wentzel-Kramers-Brillouin (WKB) approximation is a powerful tool to evaluate local impedance changes slowly. It is used to indicate and quantify a changing rate related to material properties varying along the rod. Numerical examples analyse wave propagation in a longitudinal waveguide with distributed parameters.

Dispersion of Elastic Waves Propagating in a Fluid-Saturated Porous Medium with Cavities

The propagation of plane longitudinal waves in a fluid-saturated porous medium with cavities is considered in linear elastic approximation. It has been shown that as distinct from the classical porous medium (Biot’s medium) where two longitudinal dispersionless waves can propagate (a fast wave and a slow wave), in the porous-cavity media three dispersive longitudinal waves propagate and one of them is solely induced due to cavities in the material. The study of waves is carried out by obtaining and analyzing the dispersion equation, phase velocity and group velocity. The frequency spectrum density is considered, which enables to identify the degree of dispersion expressiveness. At certain values of the system parameters some regions of strong and weak dispersion, regions of normal and anomalous dispersion have been identified.

Measurement of Stress Waves Propagation in Percussive Drilling.

This work describes the results of a test campaign aimed to measure the propagation of longitudinal, torsional, and flexural stress waves on a drill bit during percussive rock drilling. Although the stress wave propagation during percussive drilling has been extensively modeled and studied in the literature, its experimental characterization is poorly documented and generally limited to the detection of the longitudinal stress waves. The activity was performed under continuous drilling while varying three parameters, the type of concrete, the operator feeding force, and the drilling hammer rotational speed. It was found that axial stress wave frequencies and spectral amplitudes depend on the investigated parameters. Moreover, a relevant coupling between axial and torsional vibrations was evidenced, while negligible contribution was found from the bending modes. A finite element model of the drill bit and percussive element was developed to simulate the impact and the coupling between axial and torsional vibrations. A strong correlation was found between computed and measured axial stress spectra, but additional studies are required to achieve a satisfactory agreement between the measured and the simulated torque vibrations.

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.