A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves.

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing.

Ultrasonic polar scans: numerical simulation on generally anisotropic media.

Ultrasonic polar scans are based on the recording of the reflected or transmitted amplitude of sound, impinging a fiber reinforced composite from every possible angle of incidence. The mechanical anisotropy of such materials makes the reflection coefficient direction dependent, whence an ultrasonic polar scan forms a fingerprint of the investigated material. Such scans have already proved to be very valuable in the characterization of composites. Simulations have been performed for single layered and multi-layered systems, for pulsed and harmonic waves. Fiber reinforced composites are mostly orthotropic. The current report presents simulations not only on orthotropic materials but on materials of any kind of anisotropy. These extended numerical simulations are not only valuable in the characterization of highly sophisticated composites, but may also be used to characterize thin slices of crystals and even layered crystals.

Fringed sound fields and their interaction with liquid-solid interfaces.

On the one hand, it is well known that Gaussian beams possess 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.

Enhanced anisotropy in Paratellurite for inhomogeneous waves and its possible importance in the future development of acousto-optic devices.

The anisotropic feature of most crystals, involves a direction dependent wave velocity for each of the possible modes. Paratellurite (Tellurium dioxide) is extraordinary because, for one of the propagation modes, i.e. the quasi shear horizontal (QSH) mode, the anisotropy is exceptional. This results, on the one hand in a very strong directional dependent sound velocity and on the other hand, in a low wave velocity in certain directions, resulting in a high figure of merit for the acousto-optical interaction. In the case of inhomogeneous waves, the slowness surfaces change their shape and magnitude, for all crystals. However, for paratellurite, this effect is again extraordinary. As soon as a relatively small inhomogeneity is considered, the sound velocity for the QSH mode becomes really exceptionally anisotropic, resulting in a slowness surface that is almost spherical, covered by pins. The velocity corresponding to those 'pins', is much lower than in the case of homogeneous plane waves, which is very promising for the future development of acousto-optic cells involving an even higher figure of merit.

The history and properties of ultrasonic inhomogeneous waves.

This paper gives a historical survey of the development of the inhomogeneous wave theory, and its applications, in the field of ultrasonics. The references are listed predominantly chronologically and are as good as complete. Along the historical description, several scientific features of inhomogeneous waves are described. All topics of inhomogeneous wave research are taken into account, such as waves in viscoelastic solids and liquids, thermoviscous liquids and solids, and anisotropic viscoelastic materials. Also inhomogeneous waves having complex frequency are described. Furthermore, the formation of bounded beams by means of inhomogeneous waves is given and the diffraction of inhomogeneous waves on periodically corrugated surfaces. The experimental generation of inhomogeneous waves is considered as well.

The radiation mode theory in ultrasonics.

This paper describes the history and the state of the art in radiation mode theory (RMT) in ultrasonics. The RMT originates from electromagnetism in which it has proved to be very efficient in the field of wave guides and discontinuities. In ultrasonics, the RMT made its entrance only a decade ago and has already proved to be very efficient in describing the interaction of sound with discontinuities such as a step on a plate, a liquid wedge, the extremity of a plate and much more. It is likely that the development of the RMT for two-dimensional (2-D) isotropic media has come almost to an end. This paper lists the results obtained so far. Further extensions to more complicated media are to be expected in the coming decade.

Schlieren photography to study sound interaction with highly absorbing materials.

Strong absorption of sound is often caused by the conversion of sound energy into heat. When this happens, it is not possible to study the interaction of sound with the absorbing material by means of reflected sound characteristics, because there is no reflected sound. Detecting for example the distance that sound travels in a strongly absorbing material, can be done by heat detection systems. However, the presence of temperature detectors in such materials interferes with the sound field and is therefore not really suitable. Infrared measurements are a possible option. Another option is the use of Schlieren photography for simultaneous visualization of sound and heat. This technique is briefly outlined with a 3 MHz sound beam incident on a highly absorbing sponge.

On the theoretical possibility to apply an acoustic diffraction grating as a complex frequency filter device for electronic signals.

In electronics, it is well known that filtering devices can be made that are able to decompose a signal instantaneously into a number of real frequency components. This procedure is equivalent to a numerical real time Fourier transform. However, it is also known that an electronic signal can be decomposed not just in real frequency components, but also in complex frequency components. The current paper shows that it is theoretically possible to create a device, made of a periodically rough surface and a system that transforms the electronic signal into acoustic waves, that can be used to measure the amplitude attributed to considered complex frequency components of an electronic signal, in real time. This 'thought device' is mainly based on the directivity of diffracted sound and the complex frequency dependence of this directivity.

Diffraction of homogeneous and inhomogeneous plane waves on a doubly corrugated liquid/solid interface.

This paper extends the theory of the diffraction of sound on 1D corrugated surfaces to 2D corrugated surfaces. Such surfaces, that are egg crate shaped, diffract incoming sound into all polar directions, which is fundamentally different from 1D corrugated surfaces. A theoretical justification is given for extending the classical grating equation to the case of incident inhomogeneous waves, for 1D corrugated surfaces as well as for 2D corrugated surfaces. Even though the present paper presents a theory which is valid for all angles of incidence, special attention is given to the particular case of the stimulation of surface waves by normal incident sound. The most interesting conclusion is that, depending on the frequency and the incident inhomogeneity, Scholte-Stoneley waves and leaky Rayleigh waves can be generated in different directions. This effect might be of particular interest in the development of surface acoustic wave devices and the basic idea of this steering effect can be of importance for planar actuators.

A useful analytical description of the coefficients in an inhomogeneous wave decomposition of a symmetrical bounded beam.

If a bounded beam is described using a superposition of infinite inhomogeneous waves, the values of the coefficients attributed to each inhomogeneous wave are found using a classical optimization procedure, whence it is impossible to describe the obtained values analytically. In this paper, we develop a new and easy to apply straightforward analytical method to find the appropriate values of the sought coefficients. Supplementary to its analytical and straightforward nature, the method proves to reduce the inherent instabilities found in the inhomogeneous wave decomposition.

On the influence of fatigue on ultrasonic polar scans of fiber reinforced composites.

Ultrasonic polar scans have already proved to be well-suited as a practical means of characterizing fiber reinforced composite plates. The method consists of registering the reflected or transmitted sound amplitude as a function of each possible angle of incidence. It is hence an amplitude measurement by which it differs from more common 'time of flight' measurements. Ultrasonic polar scans are actually a fingerprint of a composite laminate. One of the many promising applications of the ultrasonic polar scan is the monitoring of fiber reinforced composites in service. Especially the progress of fatigue damage can be monitored easily and nondestructively. This paper presents numerical simulations of the influence of fatigue on ultrasonic polar scans as well as some experimental results.

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.

A theoretical study of special acoustic effects caused by the staircase of the El Castillo pyramid at the Maya ruins of Chichen-Itza in Mexico.

It is known that a handclap in front of the stairs of the great pyramid of Chichen Itza produces a chirp echo which sounds more or less like the sound of a Quetzal bird. The present work describes precise diffraction simulations and attempts to answer the critical question what physical effects cause the formation of the chirp echo. Comparison is made with experimental results obtained from David Lubman. Numerical simulations show that the echo shows a strong dependence on the kind of incident sound. Simulations are performed for a (delta function like) pulse and also for a real handclap. The effect of reflections on the ground in front of the pyramid is also discussed. The present work also explains why an observer seated on the lowest step of the pyramid hears the sound of raindrops falling in a water filled bucket instead of footstep sounds when people, situated higher up the pyramid, climb the stairs.

Interaction of a bounded ultrasonic beam with a thin inclusion inside a plate.

A theoretical study of the reflection of a two-dimensional Gaussian ultrasonic beam, incident at a Lamb angle of a plate containing a thin rectangular inclusion at an arbitrary position, is presented on the basis radiation mode theory. The inclusion is parallel to the plate surface and its thickness is assumed to be much smaller than the ultrasonic wavelength. It is shown that the amplitude and phase of the reflected beam profile can be used for accurate inclusion characterization. However, this only holds for certain internal positions of the inclusion and for material combinations that do not strongly perturb the excitation of Lamb waves in the plate. When these conditions are satisfied, it is possible to define the Lamb waves and the associated experimental conditions for which good estimates can be obtained of the position of the beginning point of the inclusion as well as of the length and the thickness of the inclusion.

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence.

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.

The use of polarized bounded beams to determine the groove direction of a surface corrugation at normal incidence, the generation of surface waves and the insonification at Bragg-angles.

Zero order reflected sound from a singly corrugated interface between a solid and a liquid, insonified from the solid side by circular polarized shear waves, can become almost perfect linearly polarized in a direction parallel or perpendicular to the corrugations, depending on the frequency, and can therefore reveal the direction of the corrugations. When narrow bounded beams, formed by a summation of infinite plane waves, are diffracted at certain frequencies, depending on the angle of incidence, or vice versa, one can predict phenomena like backscattering at Bragg-angle incidence and also the creation of Scholte-Stoneley waves.