Jean Duclos

Numerical description of the edge mode at the beveled extremity of a plate

This paper deals with the reflection of a two-dimensional harmonic Lamb wave at the beveled end of a plate. The existence of a resonant edge mode is described by a numerical model. It is proved that the edge mode is the resonance of different complex modes. The behavior of this mode as a function of the bevel angle is studied. Its amplitude decreases and its resonance frequency shifts as the bevel angle decreases from 90 to 85 deg. An unexpected strong variation of the repartition of the reflected energy is linked to this phenomenon.

Coupling of Lamb waves at a tee junction

Lamb wave propagation in an infinite plate is well known. In this experimental study, propagation in a limited plate and a rib-stiffened plate are investigated. Conversion phenomena, distribution of energy among converted Lamb wave and energy conservation are evaluated.

Aspects of a damped surface wave in the Fourier diamond spaces. New surface wave analysis method (SWAM)

A damped surface wave (complex wave number K=K′+jK″) is described by its space‐frequency representation S(x,ω)=exp(jK(ω)x). The wave‐number‐frequency representation Ksi(k,ω) is the spatial Fourier transform of S(x,ω). A Ksi‐cut versus k is a k‐Breit Wigner form (square modulus maximum for k=K′,K″ half‐width). A Ksi‐cut versus ω is then shown to be an ω‐Breit Wigner form (square modulus maximum for ω=Ω′, with an Ω″ half‐width). New interesting properties are found: the phase velocity is Cp=Ω′/K′ and the group velocity is Cg=Ω″/K″. The wave‐number‐time representation N(k,t) is the inverse frequency Fourier transform of Ksi(k,ω). N(k,t) is then shown to be N(k,t)=exp(jΩ(k)t). The space‐time representation s(x,t) is obtained by inverse frequency (respectively, wave number) Fourier transform of S(x,ω) [respectively of N(k,t)]. The four spaces s, S, Ksi, and N are the four Fourier diamond spaces. Used on s(x,t) experimental datas, the two cuts properties are the basis of the surface wave analysis methods (SWAM)...

5K-1 F.E.M. Simulation of Lamb Wave Propagation: Application to the Thermo-Oxidative Ageing of Carbon-Epoxy Plates

Thermo-oxidative ageing of carbon-epoxy plates has been done for up to 9000 hours at two temperatures (160 and 180degC). Non-destructive evaluation by means of non contact ultrasonic methods has been tested to characterize the aged plates. It is shown that the phase velocity of the A0 and S0 Lamb modes is decreasing when ageing duration increases. Micrographs reveal the presence of oxidation cracks propagating from the free surfaces of the plate. The plates thus become inhomogeneous in the thickness. The propagation of the Lamb waves, in the aged plates, is simulated using a finite element model of an inhomogeneous and anisotropic plate. The excitation of several modes in a frequency range (chirp excitation) or a single mode at a chosen frequency (burst windowed excitation) is applied. To simulate the ageing of carbon-epoxy composite plates (8 plies), the elastic parameters are decreased in the two external plies. The results are then compared with experiments. Using this FE model, we demonstrate that this phenomenon is related to an important decrease of the C55 elastic parameter of the plate

Immersed narrow plate study. Lamb wave identification

An experimental investigation of the interaction of an acoustic plane wave with a limited elastic plate is presented. This study shows that it is possible to observe Lamb waves on a duraluminium limited plate when the wavelengths of the generated Lamb waves are in the same order of magnitude as the target dimension. Impulsional experiments are performed and a laser vibrometer is used to measure the normal displacements on the plate, An experimental image of the vibrations is obtained by scanning the limited plate along a segment in the direction of the Lamb waves.

Space‐wave number representation of transient waves. Experimental determination of the space location origin of Lamb waves on cylindrical shells

A new space‐frequency‐wave number representation is introduced. This representation is obtained by space‐sliding window FFT of the space‐frequency representation. This new method is used to experimentally define the space origin of the pulse‐generated Lamb wave on an air‐filled cylindrical shell immersed in water (relative thickness is equal to 0.03). The space‐wave number slices also allow the measurement of the Lamb‐wave complex wave numbers and their propagation direction (reduced frequencies range from 20 to 1000). The reflected field is experimentally separated from multiple propagating Lamb waves. This efficient method is complementary to the surface wave analysis method (S.W.A.M.) [Martinez et al., 16th ICA and 135th ASA Congress, II, 1359–1360 (1998)]. In particular, the space‐wave number representations are not limited by space windowing. The experimental results confirm the theoretical computations performed on waves propagating on a plane plate.

Scholte wave propagation and diffraction on a fluid-solid periodic rough surface

Experimental results concerning propagation and diffraction of a Scholte wave on periodic liquid-elastic solid interface are presented. We describe the behaviour of the Scholte wave when it meets the grating. Thus, to give a complete description of the phenomena observed, one must account for three effects: (1) Scholte conversion into Rayleigh waves, (2) diffraction along the grating in the liquid and in the solid, and (3) restoration of the Scholte wave at the end of the grating

Experimental determination of plate parameters with an air coupled instrument

The present work deals with an experimental determination of acoustical properties of a viscoelastic homogeneous plate using an air coupled equipment. Usually, these properties are determined separately through several measurements, while our paper provides a quick inverse method which permits to measure them simultaneously and requires only the knowledge of the sound velocity in air and its density. The experimental transmission through a face parallel plate, at normal incidence, is investigated and compared with the theoretically predicted one. Measurements are conducted using a chirp signal having 1.2 MHz central frequency with 800 kHz bandwidth and 100 μs duration. Two signals are being exploited : one only through air path and another one through the sample inserted between the transducers. The FFTs of these signals provide the complex transmission coefficient as a function of frequency. The identification of parameters is carried out using the real and imaginary parts of the transmission coefficient. Then, assuming the wave velocity and density of air are known, we deduce the four properties of the plate (thickness, density, longitudinal velocity and attenuation coefficient) as well as the attenuation coefficient of air. A variety of viscoelastic materials, whose impedances have weak values, has been studied such as Polyethylene, Plexiglas and carbon/epoxy composite. The physical properties for each plate are obtained with a good accuracy in the frequency range of investigation.

Simultaneous determination of physical and acoustical properties of a homogeneous plate in air

This work is concerned with measurements of transmission through an elastic homogenous plate using air-coupled transducers. An experimental technique for investigating the transmission is presented. This method permits to determine simultaneously the velocity and attenuation of ultrasonic waves in the material, its mass density and the thickness of the plate, through a comparison between theory and experiment in the frequency range of investigation.

Scholte Wave Diffraction by a Periodically Rough Surface

Bulk wave reflection and diffraction in an infinite medium or plate have been studied for a long time. In a liquid medium, a bulk wave impinging on a plate, with velocity Cf, may generate Rayleigh or Lamb waves. A wave with phase velocity c may be generated, under an angle β (with the normal to the interface) only if the equation (1) Cf = c·sin(β) is satisfied; so the Scholte-Stoneley wave whose velocity is slightly less then Cf for usual solid mediums, may not be generated. However if engraved by a periodical grating a solid substrate may generate waves not satisfying equation (1); on thick substrates [1] and plates [2] part of the incident wave energy is considered to be converted in a Scholte-Stoneley wave, though such a wave has never been observed.