Nico F. Declercq

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.

Minimum variance guided wave imaging in a quasi-isotropic composite plate

Ultrasonic guided waves are capable of rapidly interrogating large, plate-like structures for both nondestructive evaluation and structural health monitoring (SHM) applications. Distributed sparse arrays of inexpensive piezoelectric transducers offer a cost-effective way to automate the interrogation process. However, the sparse nature of the array limits the amount of information available for performing damage detection and localization. Minimum variance techniques have been incorporated into guided wave imaging to reduce the magnitude of imaging artifacts and improve the imaging performance for sparse array SHM applications. The ability of these techniques to improve imaging performance is related to the accuracy of a priori model assumptions, such as scattering characteristics and dispersion. This paper reports the application of minimum variance imaging under slightly inaccurate model assumptions, such as are expected in realistic environments. Specifically, the imaging algorithm assumes an isotropic, non-dispersive, single mode propagating environment with a scattering field independent of incident angle and frequency. In actuality, the composite material considered here is not only slightly anisotropic and dispersive but also supports multiple propagating modes, and additionally, the scattering field is dependent on the incident angle, scattered angle, and frequency. An isotropic propagation velocity is estimated via calibration prior to imaging to implement the non-dispersive model assumption. Imaging performance is presented under these inaccurate assumptions to demonstrate the robustness of minimum variance imaging to common sources of imaging artifacts.

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.

Acoustic diffraction effects at the Hellenistic amphitheater of Epidaurus: Seat rows responsible for the marvelous acoustics

The Hellenistic theater of Epidaurus, on the Peloponnese in Greece, attracts thousands of visitors every year who are all amazed by the fact that sound coming from the middle of the theater reaches the outer seats, apparently without too much loss of intensity. The theater, renowned for its extraordinary acoustics, is one of the best conserved of its kind in the world. It was used for musical and poetical contests and theatrical performances. The presented numerical study reveals that the seat rows of the theater, unexpectedly play an essential role in the acoustics--at least when the theater is not fully filled with spectators. The seats, which constitute a corrugated surface, serve as an acoustic filter that passes sound coming from the stage at the expense of surrounding acoustic noise. Whether a coincidence or not, the theater of Epidaurus was built with optimized shape and dimensions. Understanding and application of corrugated surfaces as filters rather than merely as diffuse scatterers of sound, may become imperative in the future design of modern theaters.

Theoretical verification of the backward displacement of waves reflected from an interface having superimposed periodicity

Experiments are reported by Breazeale and Torbett [Appl. Phys. Lett. 29, 456 (1976)] that visualize ultrasonic backward beam displacement due to the excitation of surface waves by means of diffraction. The authors have simulated these experiments using the concept of inhomogeneous waves. Such waves have proven to be well suited in predicting beam displacements on plane interfaces. It is now found that inhomogeneous waves are even capable of predicting the experimentally observed displacement phenomena on periodic rough surfaces.

Backward displacement of ultrasonic waves reflected from a periodically corrugated interface

Experiments using the schlieren technique to image sound incident on a corrugated, water-brass interface show a backward displacement of the reflected beam at an angle of 22.5°, confirming the observations of Breazeale and Torbett [Appl. Phys. Lett. 29, 456 (1976)]. However, the present theory hypothesizes that this beam displacement results from excitation of a type of leaky surface wave. Further experiments with a sufficiently narrow incident beam reveal a backward displacement also at angles around 44°, resulting from excitation of Rayleigh surface waves, as predicted by the theory of Tamir and Bertoni [J. Acoust. Soc. Am. 61, 1397 (1971)]. Thus, a wide beam gives a backward displacement at 22.5° only. A narrow beam gives a backward displacement also at angles around 44°.

Bloch wave deafness and modal conversion at a phononic crystal boundary

We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.

Phononic crystal diffraction gratings

When a phononic crystal is interrogated by an external source of acoustic waves, there is necessarily a phenomenon of diffraction occurring on the external enclosing surfaces. Indeed, these external surfaces are periodic and the resulting acoustic diffraction grating has a periodicity that depends on the orientation of the phononic crystal. This work presents a combined experimental and theoretical study on the diffraction of bulk ultrasonic waves on the external surfaces of a 2D phononic crystal that consists of a triangular lattice of steel rods in a water matrix. The results of transmission experiments are compared with theoretical band structures obtained with the finite-element method. Angular spectrograms (showing frequency as a function of angle) determined from diffraction experiments are then compared with finite-element simulations of diffraction occurring on the surfaces of the crystal. The experimental results show that the diffraction that occurs on its external surfaces is highly frequency-d...

Reflection of plane elastic waves in tetragonal crystals with strong anisotropy

Propagation and reflection of plane elastic waves in the acousto-optic crystals tellurium dioxide, rutile, barium titanate, and mercury halides are examined in the paper. The reflection from a free and flat boundary separating the crystals and the vacuum is investigated in the (001) planes in the case of glancing acoustic incidence on the boundary. The analysis shows that two bulk elastic waves may be reflected from the crystal surface. The energy flow of one of the reflected waves in paratellurite and in the mercury compounds propagates in a quasi-back-direction with respect to the incident energy flow. It is proved that energy flows of the incident and reflected elastic waves are separated by a narrow angle of only a few degrees. It is also found that the relative intensity of the unusually reflected waves is close to a unit in a wide variety of crystal cuts. General conclusions related to acoustic propagation and reflection in crystals have been made based on the examined phenomena in the materials.

Theory of the backward beam displacement on periodically corrugated surfaces and its relation to leaky Scholte-Stoneley waves

A demonstration of the capability of the inhomogeneous wave theory to simulate backward displacement of ultrasonic-bounded beams [M. A. Breazeale and M. Torbett, Appl. Phys. Lett. 29, 456 (1976)] has been demonstrated recently [N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, Appl. Phys. Lett. 82, 2533 (2003)]. The current report applies the theory of the diffraction of inhomogeneous waves and shows how this theory is capable of simulating, explaining, and understanding the experiments mentioned above. The theory reveals the existence of leaky Scholte-Stoneley waves, a phenomenon suggested theoretically [N. F. Declercq, J. Degrieck, R. Briers, and O. Leroy, J. Acoust. Soc. Am. 112, 2414 (2002)] and observed experimentally [A. A. Teklu, M. A. Breazeale, J. Acoust. Soc. Am. 113, 2283 (2003)]. Moreover, the present paper shows that the classical Fourier decomposition of bounded beams is unable to simulate the backward beam displacement. This work also elucidates the nature of Wood anomalies in Diffracti...