Modelling a simplified device-a wind musical instrument-as an educational tool to study the behavior of a one-dimensional resonator.

The aim of this paper is to show how the analytical modelling of a simplified acoustic device (herein a simplified wind musical instrument) may be a relevant educational way to study several aspects of the behavior of an idealized component [herein a one-dimensional (1-D) resonator], which is the core component of the device considered. A time-dependent source, whether sinusoidal, impulse, or representing approximate valve-effects of the reed, is coupled to the resonator in the analytical modelling. The unavoidable thermo-viscous parietal dissipation, as well as an approximate radiation effect, are accounted for. After a brief presentation of the problem, precisely posed and solved in detail analytically in an approximate manner, results in both the frequency domain and in the time domain are presented. These results include the properties of the transient behaviors (both the starting transient and the transient decay), illustrating the main features of the resonator.

Using heat maps in teaching acoustics: Interaction of incident plane wave or incident beam with a solid plane structure.

Using heat maps provides frame and relevance to topics covered in physical acoustics courses as students can more easily visualize complex ideas and situations. Students can also form a much better understanding of the physical phenomena involved and build more advanced critical thinking when heat maps are used. It is the aim of the paper to provide ways for students to interact with heat maps by using two examples: first, the interaction of a plane wave (not only monochromatic) with an interface separating a fluid and a solid medium and, second, the interaction of an acoustic beam with such an interface (including a solid layer). These heat maps permit both to describe non-specular effects for the reflected acoustic beam due to the generation of a modal wave and, in the case of anisotropic media, highlight the difference between the direction predicted by Snell-Descartes law and that predicted by energy flux.

Raising students' interest and deepening their training in acoustics through dedicated exercises.

The aim of this paper is to briefly present ways to improve the interest of students who begin to attend physical acoustic courses and give examples of exercises (among many others) dedicated to the deepening of their training. Regarding the interest of students who are just beginning, two particular questions arise: how is the attention of these students gained? and how would the students be properly trained when starting out? An attempt to answer these questions is given at the beginning of the paper. Then, the paper continues with a brief presentation of some problems, which are extracted from a three-volume textbook that was published recently, precisely posed, and solved in detail analytically in an exact or approximate manner, even numerically, according to the three levels (bachelor, master, and Ph.D.) while offering an opportunity to deal extensively with the modeling of important topics in acoustics, which are treated as having several ways to be addressed.

Two Elastodynamic Incremental Models: The Incremental Theory of Diffraction and a Huygens Method.

The elastodynamic geometrical theory of diffraction (GTD) has proved to be useful in ultrasonic nondestructive testing (NDT) and utilizes the so-called diffraction coefficients obtained by solving canonical problems, such as diffraction from a half-plane or an infinite wedge. Consequently, applying GTD as a ray method leads to several limitations notably when the scatterer contour cannot be locally approximated by a straight infinite line: when the contour has a singularity (for instance, at a corner of a rectangular scatterer), the GTD field is, therefore, spatially nonuniform. In particular, defects encountered in ultrasonic NDT have contours of complex shape and finite length. Incremental models represent an alternative to standard GTD in the view of overcoming its limitations. Two elastodynamic incremental models have been developed to better take into consideration the finite length and shape of the defect contour and provide a more physical representation of the edge diffracted field: the first one is an extension to elastodynamics of the incremental theory of diffraction (ITD) previously developed in electromagnetism, while the second one relies on the Huygens principle. These two methods have been tested numerically, showing that they predict a spatially continuous scattered field and their experimental validation is presented in a 3-D configuration.

Multi-modal leaky Lamb waves in two parallel and immersed plates: Theoretical considerations, simulations, and measurements.

Leaky Lamb waves have the potential to be used to perform non-destructive testing on a set of several parallel and immersed plates. Short-time Fourier transform and two-dimensional Fourier transform have both been successfully used to measure the propagation properties: phase and group velocity, and leaky attenuation. Experimental measurements were validated by comparison between theory, experimentation and finite-element simulations (using comsol multiphysics® software) in the case of one immersed plate in water. These signal processing techniques proved to be efficient in the case of multi-modal propagation. They were applied to two immersed plates to identify the leaky Lamb mode generated in the second plate. Dispersion curves of the system composed by two immersed and parallel plates are computed. When plates have the same thickness, leaky Lamb modes propagate from the first to the second plate without any mode change, with the apparent attenuation being weaker in the second plate. Considering that the second plate is continuously supplied in energy by the first one, an energy-based model is proposed herein to estimate the apparent attenuation in the second plate. Despite our extremely simplifying assumption, this model proved to be in good agreement with both finite-element modelling and experimentation.

Effects of the interface roughness in metal-adhesive-metal structure on the propagation of shear horizontal waves.

The influence of the interface roughness in a three-layer metal-adhesive-metal structure on the propagation of shear horizontal waves and more particularly on the transmission coefficient versus the frequency is studied in the particular case of a periodic grating of triangular grooves. For given phonon frequencies, the interaction of an incident shear horizontal mode with the periodical grating gives rise to a retro-converted mode. A numerical finite element simulation permits us to predict the existence of the phonon mode in the three-layer structure and to obtain the evolution of the transmission coefficient around the phonon frequency. An experimental study, based on a generation of waves by a piezocomposite contact transducer and a reception by a laser vibrometer, then confirms these predictions. Finally, a parametric numerical study is performed: the influence of the depth of the roughness and of the number of spatial periods of the grooves on the transmission coefficient is studied.

The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane.

Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.

Interaction of a monochromatic ultrasonic beam with a finite length defect at the interface between two anisotropic layers: Kirchhoff approximation and Fourier representation.

This paper presents a fast computation method to simulate the interaction between a bounded acoustic beam and a 2-layered anisotropic structure with a finite defect on the internal interface. The method uses the classical Fourier decomposition of the fields into plane waves, and the Kirchhoff approximation is introduced to calculate the diffusion by the defect. The validity of the approximation is estimated by comparison with the Keller Geometrical Theory of Diffraction and with results obtained by boundary element methods. The quickness of the method allows testing several geometrical configurations (varying incident angle, thickness of the layers or the physical nature of the defect). These studies may be used to foresee what experimental configurations would be adequate to have a chance to detect the defect.

Deviation of a monochromatic Lamb wave beam in anisotropic multilayered media: asymptotic analysis, numerical and experimental results.

The aim of this paper is threefold: to describe the physical phenomenon of the excitation of modal waves such as Lamb waves, in anisotropic multilayered media, by a monochromatic incident beam, using an asymptotic approach; to present a three-dimensional model using the decomposition of the incident beam into monochromatic plane waves (the formalism is applied to the particle displacement vector); to illustrate the phenomenon both numerically and experimentally. Numerical and experimental maps of the reflected field of pressure are presented, and the reradiation of the Lamb wave beam in an oblique plane is theoretically and numerically illustrated.

A stationary phase argument for the modal wave beam deviation in the time-space domain for anisotropic multilayered media.

The aim of the paper is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic multilayered media by a monochromatic incident beam and then by a time depending signal. A modal beam is generated in the structure and, due to the anisotropy of the media constituting the structure, is deviated with respect to the sagittal plane of the incident bounded beam. Using a stationary phase approach, it is possible to determine the deviation direction of the modal beam in the far field at a given frequency. This direction is normal to the modal curve, at the point corresponding to the main modal wave vector. Using Lagrange multipliers, it is possible to obtain the equation of an oblique plane in which the modal beam reradiates in the external fluid. As the modal waves are dispersive, the group velocity and the direction of propagation of the principal modal wave vary with the frequency. So, in the far field, for a time depending signal, the different monochromatic components of the main modal wave are found in different directions. In general, the main crest line of this modal wave packet is not a straight line.