Farid Chati

Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section

A modal theory is developed for investigating the acoustic scattering by elastic cylinders of arbitrary cross section immersed in a fluid. Numerical results are presented for a plane wave incidence normal to the axis of an elliptical cylinder but arbitrary with respect to the noncircular cross section. Experimental results are obtained for an aluminum elliptical cylinder with the use of an impulse method. Comparisons between theoretical and experimental data are performed in the broad frequency range 8.5⩽ka⩽30 (k is the wave number in the fluid and a the major axis radius of the elliptic cylinder). The experimental observations are in good agreement with the theoretical predictions.

Acoustic scattering by a metallic tube with a concentric solid polymer cylinder coupled by a thin water layer. Influence of the thickness of the water layer on the two Scholte–Stoneley waves

The problem of a plane acoustic wave scattered by a layered cylinder submerged in water is considered. This cylinder consists of a tube made of aluminum with a solid Lucite cylinder concentrically fitt inside it. These two components are coupled by a thin layer of water. A particular investigation is made on the influence of the thickness of the water layer on the presence of the bending wave A on the tube and the Scholte–Stoneley wave on the cylinder. The presence of these waves is examined in the function of the varying water layer thickness: two special cases are discussed. First, for a layer thickness greater than the tube thickness, it is shown that both the A wave on the aluminum tube and the Scholte–Stoneley wave on the Lucite cylinder are generated. Second, for a thickness much smaller than the tube thickness, a different wave is generated, which is a combination of both waves. These two cases are experimentally verified in a setup that employs a short pulse method.

Application of orthogonality-relation for the separation of Lamb modes at a plate edge: numerical and experimental predictions.

In this study the orthogonality relation-based method for post-processing finite element (FE) predictions and experimental measurements is applied in order to separate Lamb modes at a plate edge at normal incidence. The scattered wave field from the free edge is assumed to be a superposition of all the eigenmodes of an infinite plate. The eigenmode amplitudes of the reflected wave field are determined by implementing the orthogonality-based method on the measured plate edge displacements. Overlapping wavepackets of Lamb modes at a plate edge are simulated by using the FE model and the experiment in the case of an incident S0 mode in a plate with a notch. In the experiment a 3D Scanning Laser Doppler Vibrometer (3D SLDV) (Johansmann and Sauer, 2005) is used to measure 3 dimensional vibrations and thus the edge two-dimensional displacement components simultaneously. It is demonstrated that it is possible to extract signals of various propagating and non-propagating modes in time-domain. The influences of the errors in practical measurements on the extraction procedure have also been studied.

Acoustic radiation of a submerged cylindrical shell in low frequency

The evaluation of sound pressure levels produced by submerged structures is a part of regulations on underwater noise pollution. The purpose of this work is the study of the underwater acoustic radiation of a stainless steel tube subjected to vibrations generated by a shock obtained by using a hammer. The vibrations of the tube, placed successively in air and in water, are measured by using accelerometers. In water, the acoustic radiation measurements are performed by using a hydrophone. Results are presented as frequency spectra and are confronted with results of the elastic theory.

Edge resonance in semi-infinite thick pipe: Numerical predictions and measurements

This paper presents theoretical and experimental studies of axisymmetric longitudinal guided wave L(0,2) interaction with the free edge of the pipe. A numerical method based on normal mode superposition is applied to predict the edge resonance by an analysis of dispersion relations of separate modes. In parallel, the finite element analysis and experimental measurements prove the existence of edge resonance in the pipe in case of L(0,2) wave incidence. It is shown that the edge resonance is mainly caused by the first pair of complex modes. Additionally the behavior of edge resonance phenomenon as a function of the curvature of the pipe is studied. The displacement amplitudes measured at the edge demonstrate that the edge resonance is affected by the frequency and thickness to midradius ratio of the pipe, and it is losing its strength in thicker pipes, as the growing difference between the outer and inner radii destroys symmetry. The reflected energy amplitudes show that at the resonance frequencies the incident wave is strongly converted to L(0,1) and L(0,3) modes, depending also on the curvature parameter of the pipe.

Acoustic scattering from a finite plate: Generation of guided Lamb waves S0, A0 and A

In the domain of renewable energies, marine current turbines constitute one of the possibilities of producing electrical energy. Naked-eye inspection, or with the aid of video monitoring systems of these machines to ensure their perfect working order, can be difficult in a turbid environment. Acoustic methods are conceivable. The study focuses on the blades of these machines, by considering rectangular plates. The propagation of Lamb waves in a plate is studied by analyzing experimental time signals obtained from acoustic scattering. These signals are analyzed employing the ray theory. In vacuum, the flexural wave is the A(0) Lamb wave, whilst in water this wave splits in a bifurcation: the A wave with a phase velocity always smaller than the sound speed in water, and the A(0) wave with a phase velocity always higher than the sound speed in water. In the central bandpass of the transducers used in the experiments, mainly the A and S(0) waves exist. However, signals observed in the third harmonic bandpass of the transducers are also analyzed. In order to complement these results, resonance frequencies of the plate studied are calculated taking into account the boundary conditions and compared with the resonance frequencies of the experimental spectra.

Maxima and minima of the displacement components for the Lamb modes

This paper revisits the vanishing of the transverse component of the particle displacement vector in free surfaces of an isotropic homogeneous plate, for both symmetric and antisymmetric Lamb waves. Drawing on well-known analytical expressions from Viktorovs book [(1967) Rayleigh and Lamb Waves: Physical Theory Applications, Chap. II, pp. 67-121], two distinct frequency-thickness product expressions, in cases where this vanishing occurs, are derived: one for the symmetric modes and another for the antisymmetric modes. At these frequency-thickness products, phase and group velocities have appreciable values which are discussed herein. It appears that these velocities depend on the transverse bulk wave velocity only. This is the specific condition of the Lamé modes. Moreover, theoretical and experimental investigations of displacements in the surface of a plate in air have been carried out. The theoretical part shows that the normal and transverse displacements have, respectively, a local maximum and a local minimum in the vicinity of these frequency-thickness products. The experimental part corroborates the presence of the local maximum of the S(0) Lamb mode for various materials.

Acoustic radiation of low frequency flexural vibration modes in a submerged plate

In some submarine structures, the acoustic radiation of vibrations at the neighbourhood of sonar equipment limits their use. So the aim of this study is to understand the process of acoustic radiation of a submerged plate subjected to a vibration. For the low frequency domain, only two types of wave can propagate: the first antisymmetric Lamb wave (A0) and the first symmetric Lamb wave (S0). When the plate is immersed in water the A0 wave is modified and the new wave is named A wave. In this work, experimental and numerical analysis of vibration modes in a plate are carried out. The studied rectangular plate of thickness 10 mm is made of steel. Its length and width are respectively 1.0 m and 0.5 m. The plate is partially immersed in water (90%). Flexural vibrations are generated by a shaker normally connected to the emerging plate part. The applied signal is one sinusoidal period at a frequency which is under the critical frequency. Relations between the admittance of the plate and the radiated pressure in water are highlighted.

Guided wave attenuation due to deposits on the pipe wall

Our interest is taken in the reflection and the attenuation of longitudinal waves caused by a circular shape deposit placed on the pipe wall. The reflection of the S0 mode by the deposit is experimentally shown. The experimental results are compared with the theoretical results obtained from a finite element method (FEM). The attenuation of modes is determined and analyzed for five widths of deposit. In the case of a tube filled with water, only the symmetrical waves, S0 in low frequency and S1 (f=2.56 MHz), are considered because of their strongly axial nature. A viscous deposit (epoxydic resin) characterized by different widths and placed on the surface of a pipe is the defect considered in this article. Our interest is taken in the attenuation of the longitudinal waves at particular frequencies. Theoretically and experimentally, the propagation of guided waves is considered in a stainless steel tube (length L=3 m) with an outer radius a = 19 mm, an inner radius b = 17.5 mm (thickness d = 1.5 mm). The mechanical parameters are CL = 5823 m/s (longitudinal wave speed), CT = 3210 m/s (transverse wave speed), ρ = 8027kg/m 3 (density), filled or not with water (Fig.1).

Forward acoustic scattering analysis from solid objects immersed in the water

Forward acoustic scattering of an immersed solid LINE (cylinder bounded by hemispherical endcaps) in water is investigated in our study. The object is made of stainless steel and its L/2a ratio is equal to 2 (L: Length of the cylinder part and a: the radius is equal to 60 mm). An impulse measurement method is used in the experimentation. Most of results are obtained experimentally, in bistatic configuration. Mobile receiver transducer is located in a distinct position from the emitter. The polar diagram patterns of the scattered pressure shows an important amplitude of pressure in the shadow side of this object. Analysis of this phenomenon is based on theoretical and experimental results obtained for a sphere with the help of elasticity theory. Moreover, this study relies on the grey-level representation of the angular position of the receiver in function of recorded time signals. Thus on forward acoustic time signals, it is possible to identify echoes due to propagation paths of waves on this object.