Schoch Effect Research Articles

Evaluation of laminated glass adhesion strength based on Lamb waves through the observation of the Schoch effect

Compared to standard plain glass panes, laminated glass has many advantages, such as improved glass panes’ safety, structural strength, and aesthetics. An essential quality criterium of laminated glass, tunable during production, is the adhesion strength of the interlayer. Traditional quality control is destructive and involves peeling, tensioning, or impacting the specimens, while ultrasound may, if properly applied, reveal the quality parameters nondestructively and reduce production costs. In facilities equipped with ultrasonic phased array transducers, bounded beam effects may be exploited to investigate the considered glass panels. In this work, we provide a proof of concept of a bounded beam effect, known as the Schoch displacement, caused by ultrasonic guided waves, to map variations in adhesion nondestructively. Even though in industrial production lines, one may opt for phased array techniques to measure the effects, in this work, we provide images obtained by acousto-optic Schlieren photography for demonstrative purposes.

Investigation of the Schoch effect based on acoustic collective surface oscillation

In this research, the Schoch effect of periodic addition of a rectangular acoustic grating system on the structures of Helmholtz resonators is investigated. The results reveal that positive and negative Schoch shifts can be obtained in the investigation system. The phase of the effective refractive index of the resonator changes by π rad at the resonance frequency when positive Schoch shifts occur. However, it is the phase of the resonator's reflectance coefficient and not the effective refractive index that varies by 2π rad at the resonant frequency when a negative Schoch shift occurs. The findings also show that the system's resonance frequencies can be adjusted by changing the parameters of the structure. When the effective refractive index of the structure is close to or equal to zero, the corresponding frequency is the resonance frequency. At this frequency, the Schoch effect and a significant acoustic collective surface oscillation are observed.

Negative Schoch displacement of two-dimensional acoustic metamaterials with near-zero refractive index

In this paper, the Schoch displacement at the interface between different two-dimensional triangular phononic crystal metamaterial and natural material is studied by using finite element software. As is well known, the Schoch displacement is highly dependent on the surface wave and leakage wave excited at the interface between different materials. So, the negative Schoch displacement can be more easily obtained by adding a suitable thickness of covering layer at the interface between metamaterial material and natural material. The numerical results show that when the negative Schoch displacement happens, the effective parameters of metamaterials are close to zero. It means that the effective refraction index is near to zero and the reduced frequency of the incident acoustic wave is correlated with the reduced frequency of the band gap. It is also found from the results that the reduced frequency of the incident acoustic wave is located at the edge of the band gap when the negative Schoch displacement occurs. The maximum of the metamaterial effective impedance and the maximum of the reflection coefficient are almost at the same frequency. The phase of the imaginary part of the reflection coefficient has a phase mutation in π rad at the corresponding frequency. The frequency of negative Schoch displacement is located in the first band gap of <i>MK</i> direction and near the upper boundary. The Schoch displacement at the interface between conventional materials is usually positive and negligible in previous reports. In this paper, the negative Schoch displacement is obtained by using the near-zero refraction index metamaterials. This not only enriches the physics contents of Schoch effect but also provides a theoretical reference for designing the acoustic devices based on acoustic wave displacement at the interface.

An antiferromagnet as a tunable single-phase elastic hyperbolic medium with spatial dispersion

For a plane and quasi-plane SH-type bulk wave incident from the outside onto a system of equidistant antiferromagnetic dielectric layers, the inclusion of the spatial dispersion in the antiferromagnet as a hyperbolic magnetoacoustic medium induces a number of resonant refractive anomalies: the effects of total reflection (transmission) and the formation of discrete localized magnon-phonon states against the continuous spectrum, the amplification of the angular Schoch effect, and in the case of a one-dimensional resonant magnetic phonon crystal, the acoustic superradiance effect.

The Schoch effect mechanism analysis and its regulation of two dimensional three components phononic crystal

In this paper, through changing the phononic crystal surface and adjusting the structure of surface layer, we observed the Schoch effect of two dimensional phononic crystal, and the Schoch shift reached 7.1 times of the lattice constant. To further understand the physical mechanism of this kind of phenomenon, the finite element method is used to calculate the band structure of the model. Because of the influences of the surface of structure, there exists a kind of waveguide mode in the passband. Through careful analysis of the band structure and the sound pressure field profile, it is found the kind of waveguide mode makes the incident wave energy go into the waveguide layer which resulting in reflection beam deformation and offset. In addition, through the finite element simulation, the change regulation of the Schoch shift in the phononic crystal is studied by changing the radius of the surface layer and further increase the layer number of the surface layer of the phononic crystal to achieve the control of the Schoch effect of the phononic crystal. The conclusion of this paper can provide some theoretical reference and give some guidance for the design of acoustic sensors based on Schoch effect.

Evanescent wave intensification in surface spin-wave acoustics and magnetic/nonmagnetic interface electrodynamics

A relation is found between the maximum intensification of an evanescent elastic shear wave excited in a magnetic field and the enhancement of the Schoch effect. The conditions necessary for the electromagnetic analog of this relation for the Goos-Hanchen effect in the case of a TM (TE) body wave beam incident from without are determined.

Study by means of liquid side acoustic barrier of the influence of leaky Rayleigh waves on bounded beam reflection

The Schoch effect in ultrasonics, when sound is incident at the Rayleigh angle on a liquid-solid interface, consists of a forward beam displacement of the reflected beam, usually accompanied by a null strip in between the specular portion and the nonspecular reflected beam portion. It is a widely accepted idea that the effect is caused by reflected sound in combination with a sound field emitted by leaky Rayleigh waves. The current work presents an experimental technique to separate and investigate both fields separately by applying an acoustic barrier. The experiments are based on acousto-optic Schlieren photography.

New mechanism of the schoch effect in nonmagnetic dielectrics

A new type of a linear relation between the components of the magnetic field vector and those of the elastic strain tensor (a dynamic piezomagnetic interaction) is proposed. This relation is irrespective of the crystal symmetry and of the presence of a magnetic structure in the dielectric medium. This leads to anomalies in the reflection of a beam of shear bulk waves incident from the depth of the nonmagnetic dielectric medium on either its mechanically free surface or its slip boundary with a semibounded magnetic medium.

Finite element analysis of transmission of leaky Rayleigh waves at the extremity of a fluid-loaded thick plate

A numerical study based on finite element simulations reveals the experimentally indicated fact [N. F. Declercq et al., J. Appl. Phys. 96, 5836 (2004)] that leaky Rayleigh waves propagating along the horizontal surface of a thick fluid-loaded solid plate are transmitted around the corner of the solid plate. The mentioned experiments are based on the so-called Schoch effect, accompanied by the presence of a null strip in the reflected part of the beam, and phenomena occurring when the incident beam, generating the effect, approaches the edge of the solid plate. The referred experiments indicate that leaky Rayleigh waves are generated around the corner of the plate, but the experimental evidence is not fully conclusive whether the effect is caused merely by incident Rayleigh waves on the upper surface or by scattering effects when the incident beam interacts with the corner. The current study first confirms the reported experiments by means of the finite element method and then proofs that the assumption made in the referred paper about Rayleigh waves, being primarily stimulated by the edge of an incident bounded beam rather than the middle, is correct. Ultimately the model is applied to study leaky Rayleigh waves separately from the incident and reflected bounded beams. It is shown that the Rayleigh waves themselves are the physical origin of the transmission of Rayleigh waves rather than scattering effects caused by the incident bounded beam.

Fast beating null strip during the reflection of pulsed Gaussian beams incident at the Rayleigh angle

It is well known that harmonic bounded Gaussian beams undergo a transformation into two bounded beams upon reflection on a solid immersed in a liquid. The effect is known as the Schoch effect and can be found at the Rayleigh angle for thick plates and at the different Lamb angles for thin plates. Here, a study is made on the effect of pulsed Gaussian beams reflected on solids. It is found experimentally that the Rayleigh wave phenomenon still generates two reflected bounded beams, whereas Lamb wave phenomena do not generate this effect. This fact may be explained intuitively by realizing that the Rayleigh phenomenon is a coincidental phenomenon that is generated in situ, whereas the Lamb wave phenomenon is a non-coincidental phenomenon that is generated only after incident sound is influenced by both sides of a thin plate. Another explanation is the fact that Rayleigh waves are not dispersive, whereas stimulation and propagation of Lamb waves is frequency dependent. A pulse contains many frequencies and therefore only a fraction of the incident pulse is transformed into a Lamb wave. In this paper, numerical simulations are performed that show that actually the Schoch effect does occur neither for Rayleigh waves, nor for Lamb waves. As a matter of fact, a pulse, incident at the Rayleigh angle, generates two reflected lobes with a null zone of a different kind. The null zone is beating several times during the passage of each pulse. This results in a ‘null zone’ having a lower mean intensity than any of the two lobes, still less outspoken than for the case of harmonic incident bounded beams. This effect does only occur for Rayleigh wave generation and is much less outspoken for Lamb wave generation.

Fringed sound fields and their interaction with liquid–solid interfaces

On the one hand, it is well known that Gaussian beams posses the ability to stimulate Rayleigh waves, resulting in the Schoch effect, a lateral beam displacement. This effect, often characterized by a reflected sound pattern consisting of two anti-phase beams, is due to the re-radiation of sound because of the stimulation of leaky Rayleigh waves. On the other hand, fringed sound beams are characterized by the fact that they consist of a number of neighboring anti-phase narrow beams. They are a first approximation of a sound field originating from a phased array of harmonic vibrating crystals in which each crystal vibrates in anti-phase compared to its neighbor. The individual lobes within the fringed sound pattern diverge much less than standard Gaussian beams of the same size. The current study investigates the interaction of fringed beams with a liquid–solid interface. It is found that under certain conditions, a fringed beam, incident at the Rayleigh angle, produces a reflected sound pattern that contains a wide lobe that is not fringed. It is also shown that under other conditions, contrary to the famous forward displacement of the reflected sound for incident Gaussian beams, a strong backward displacement occurs for fringed beams.

The double-sided ultrasonic beam displacement

It is a well-established idea in optics as well as in ultrasonics that a bounded Gaussian beam, when reflected from an interface, can be displaced in the forward or in the backward direction, depending on the propagation direction of leaky waves that are generated by the incident beam. Such a displacement is often accompanied by the so-called Schoch effect characterized by a null strip in between a specular and a nonspecular reflected beam, and a trailing field that is much further displaced. The current letter shows experimentally and numerically that a simultaneous forward and backward displacement is possible accompanied by two null strips and being only the result of forward propagating Lamb waves.

The Schoch effect to distinguish between different liquids in closed containers

In different industrial branches, it is necessary to characterize liquids in closed containers. For small cans, accessibility to both sides is almost trivial. However, in industries in which larger containers are used, and especially in the dock industry, only one side is accessible practically; and damping often prevents through-transmission ultrasonic measurements or pulse echo techniques. It is known that built-in sensors can be used to determine density and wave velocity of liquids; but normally containers are not equipped with such sensors. It is also known that differences in the reflection coefficient at a solid-liquid interface can determine the density and sound velocity of liquids, but only if the difference in acoustical impedance between the solid and the liquid is small. For most containers this condition is not provided; therefore, a more sensitive method is needed. This paper reports simulations that show how identical containers, having different liquids inside, can be distinguished from one another by means of differences in the Schoch effect at a Lamb wave angle of incidence for harmonic-bounded ultrasonic beams.

Frequency band gap for Rayleigh waves on coated substrates

The Rayleigh wave velocity for a coated substrate must have a value in between the ones for the substrate material and the coating material. Nevertheless, Adler and McCathern [J. Appl. Phys. 49, 2576 (1978)] have performed measurements, based on the Schoch effect, on a stainless steel substrate covered with an aluminum oxide coating that contradict this phenomenon. The current letter describes the frequency band gap effect for Rayleigh waves on coated substrates and explains how this phenomenon is related to the cited measurements. The existence of such a gap can be very important for the development of frequency filters.

The Schoch effect as a means to detect the principal axes of a piezoelectric crystal

When a bounded beam is incident on a piezoelectric crystal at the right angle, surface waves are generated which result in the Schoch effect. This effect consists of the appearance of two reflected beams instead of one, with a null strip in between. The characteristics of this Schoch effect are determined by the physical properties of the solid under consideration, but also by the direction of the principal axes. Therefore, the effect can be used to determine those directions. A comparison of theory and experiments on lithium niobate is shown. This method can be used as a practical tool for determining the principle axes, since these are not visible to the eye. [Work supported by The Flemish Institute for the Encouragement of the Scientific and Technological Research in Industry (I.W.T.) and by a NATO Collaborative Linkage Grant.]

Ultrasonic inhomogeneous waves: Three decades of fascination

Inhomogeneous waves are mathematically described as pure homogeneous plane waves except for the important fact that all wave parameters, i.e., wave vector, polarization vector and frequency, can be complex valued. Even though the existence of a complex wave vector was known for a long time, Henry Cooper was the first to study such waves and their interaction with interfaces. It was not until 1980 that researchers became aware of the fact that inhomogeneous waves are mandatory phenomena in the description of reflection/transmission phenomena between lossy media. Later, it was shown that inhomogeneous waves also formed natural building blocks of bounded beams and formed a physical explanation for the Schoch effect. This paper describes this development from a historical point of view and describes scientific properties (e.g., their polarization, dispersion) whenever needed in order to understand the evolution from 1980 until the present. All topics of inhomogeneous wave research are taken into account, such as waves in viscoelastic solids and liquids, thermo-viscous liquids and solids, anisotropic viscoelastic materials, periodically rough materials, the features of complex frequency and the experimental generation of inhomogeneous waves. [Work supported by The Flemish Institute for the Encouragement of the Scientific and Technological Research in Industry (I.W.T.).]

The representation of 3D gaussian beams by means of inhomogeneous waves

There are different methods to mathematically represent a bounded beam. Perhaps the most famous method is the classical Fourier method that consists of the superposition of pure homogeneous plane waves all traveling in different directions and having an amplitude that can be found by the Fourier transform of the required profile. This method works perfectly for 2D as well as for 3D bounded beams. However, some researchers prefer the inhomogeneous wave theory to represent a bounded beam because some phenomena, e.g. the Schoch effect, are explained by this method by means of concepts that agree better with intuition. There are several papers dealing with this method for 2D gaussian beams. Until now, it has never been considered possible to represent 3D gaussian beams as well. The present paper shows a method to overcome this shortcoming and presents different sorts of 3D gaussian beams that are built up by means of inhomogeneous plane waves.

Back reflection of ultrasonic waves from a liquid–solid interface

A new acoustic phenomenon has recently been observed in experiments where a bounded beam of ultrasound is incident upon a smooth liquid–solid interface. A significant amount of coherent radiation is found to be backscattered in the general direction of incidence. The angle of back reflection is observed to be equal to the critical Rayleigh angle or leaky wave angle. Most of these observations were made during experiments on the Schoch displacement effect, and therefore it has been tacitly assumed that the back reflection is strongly dependent upon the angle of incidence, as is the case for the beam shifting in the Schoch effect. We present a theoretical basis for this new phenomenon. A two-dimensional incident beam of Gaussian profile is considered. By a careful analysis we isolate that part of the field on the interface which has Fourier components corresponding to backward propagating waves in the liquid. This subset of the total wave field is then considered separately and it is shown to display a maximum in a certain direction, close to the critical Rayleigh angle. This peak in the angular pattern of the scattered field corresponds to an evanescent reflection boundary. We discuss the dependence of the effect upon certain parameters. The amplitude is shown to decrease as the beam width is increased, and it increases with increasing Schoch displacement. This backscattering is present for all angles of incidence; there is nothing inherently special about the Rayleigh angle.