The interaction of the S0 Lamb mode with vertical cracks in an aluminium plate

This article presents the interaction of the first symmetric Lamb mode S0 with vertical cracks in an aluminium plate placed in vacuum. The cracks are symmetrical regarding to the median plane of the plate and their heights are increasing from 0% to 100% of the plate thickness, by steps of 25%. The frequency-thickness product is chosen to be lower than the S1 frequency cut-off. A modal decomposition method is used to solve the diffraction problem. The variation with the height of the crack of the reflection and transmission coefficients of modes propagating in the far field is predicted. The displacement fields at both sides of the cracks are also calculated, so that it is possible to quantify the crack-opening displacement. These results are compared to numerical predictions obtained using a finite element software. Measurements are also conducted and compared to the predictions.     

Acoustic scattering from a finite plate: generation of guided Lamb waves S(0), A(0) 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.     

Measurement of the scattering of a Lamb wave by a through hole in a plate

Flexural waves propagating in an aluminum plate containing a circular hole are studied. In the experiments the first antisymmetric Lamb wave mode A0 is excited selectively by a piezoelectric transducer. The scattered field around a circular cavity is measured pointwise using a heterodyne laser interferometer. The measurements are compared with theoretical calculations. Different approximate analytical approaches, employing Kirchhoff and Mindlin types of plate theories to describe the scattered field, are used. Good agreement between the experimental data and the analytical solutions is found within the ranges of validity of the different models. Introduction of a small imperfection, like a notch, at the boundary of the cavity changes the measured scattered field     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Short range scattering of the fundamental shear horizontal guided wave mode normally incident at a through-thickness crack in an isotropic plate

Interaction of the fundamental shear horizontal mode with through-thickness cracks in an isotropic plate is studied in the context of low frequency array imaging for ultrasonic guided wave nondestructive evaluation with improved resolution. Circular wave fronts are used and the symmetric case where a line from the wave source bisects the crack face normally is considered. Finite element simulations are employed to obtain trends subject to analytical and experimental validation. The influence of the crack length and of the location of source and measurement positions on the specular reflection from the crack face is first examined. These studies show that low frequency short range scattering is strongly affected by diffraction phenomena, leading to focusing of energy by the crack in the backscatter direction. Study of the diffraction from the crack edges reveals contributions due to a direct diffraction at the edges and multiple reverberations across the crack length. A simple diffraction model is shown to adequately represent cracks up to moderate lengths, providing an easy means of estimating the far field of the waves. The presence of multiple diffraction components is quantitatively established and surface waves on the crack face are identified as equivalent to low frequency symmetric modes of rectangular ridge waveguides.     

A0模态Lamb波聚焦透镜的结构设计及实验研究

基于折射率的弯曲波透镜多在板结构上打孔或挖槽,这种设计破坏了原有的结构,降低了板的刚度和稳定性。鉴于此,通过在板表面镶嵌棱柱的方式设计了A0模态Lamb波的聚焦透镜。首先,详细讨论了棱柱的结构参数对Lamb波带隙的影响机理,获取了波速与结构尺寸的定量关系,并实现了透镜的结构设计;其次,有限元仿真了该聚焦透镜的工作性能,包括聚焦位置、焦点处能量分布、聚焦尺寸、工作带宽等;最后,通过实验验证了该透镜设计的正确性。研究结果表明,设计的透镜能够使弯曲波聚焦在预先设定位置,且在不改变结构参数的情况下具有一定的工作频率带宽。该透镜设计方法具有聚焦性能优越、刚度强、易于加工等优点,为声聚焦透镜在无损检测、能量收集等领域的实际应用提供了参考。     

Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers

This work concerned a technique for a health monitoring system based on the generation and sensing of Lamb waves in composite structures by thin surface-bonded piezoceramic transducers. The objective was to develop transducers that are adapted for the damage detection in orthotropic composites. The key problem with the investigated Lamb waves was to select a mode to be sensitive to the damage. A hybrid modeling technique was therefore used to conceive transducers that were adapted to achieve such a feature. This modeling technique enabled studying the influence of the transducer characteristics on the Lamb waves propagating in orthotropic plates. It was demonstrated that a Lamb mode could be generated dominantly to other modes by using a multi-element transducer. The effectiveness of this technique was successfully verified experimentally on composite plates. It was shown that the dominant Lamb mode, obtained by use of dual-element transducers, was an appropriate mode for successfully detecting a damage in composites.     

Acoustic scattering from complex elastic shells: visualization of S0, A0 and A waves

Acoustic scattering phenomena from complex immersed elastic shells are studied by high-speed Schlieren visualization for spark-generated spherical quasi-Dirac excitations. The situations considered are air-filled cylindrical shells under normal insonification and air-filled cylindrical shells soldered at one end with a hemispherical endcap under axial and non-axial incidences. The results are compared with those provided by the Methode d'Isolement et d'Identification des Resonances (MIIR) method and corresponding analytical theoretical solutions. The combination of these complementary approaches better highlights some of the behaviors of the symmetric S0- and antisymmetric A0-Lamb waves, as well was the Scholte-Stoneley A-wave, on the considered targets. In particular, the influence of the internal solder inhomogeneities on the creation and/or the conversion of these modes is demonstrated.     

Prediction and measurement of nonpropagating Lamb modes at the free end of a plate when the fundamental antisymmetric mode A0 is incident

Reflection of Lamb waves when the fundamental mode A0 is incident at the free end of a plate is studied, in order to identify the extent to which the generation of nonpropagating modes influences the field local to the end of the plate. Semi-analytical predictions, finite element simulations, and experimental measurements are presented for frequencies below the A2 cutoff. First it is shown, for frequencies below the A1 cutoff, that reflection of the A0 mode is accompanied by a delay in phase, and that there is significant additional motion due to nonpropagating modes within about five plate thicknesses of the end. The extend of this additional motion in the vicinity of the end of the plate is demonstrated by subtracting the contribution of the propagating modes from the displacement field. The wave field at frequencies above the A1 cutoff is more complex because the A1 as well as the A0 propagating modes are present at the end of the plate. Nevertheless, it has still been possible, using semi-analytical predictions and finite element simulations, to demonstrate the additional motion due to the nonpropagating modes.     

Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions

In a previous paper, Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] obtained two formulas for the effective wavenumber in a dilute random array of circular scatterers. They emerged from a study of the problem of the reflection of a plane wave at oblique incidence to a half-space containing the scatterers. Here, their study is extended to obtain formulas for the reflection and transmission coefficients and to investigate the average fields near the boundary of the half-space. Comparisons with previous work are made.     

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a traveling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T.R. Lin, J. Pan, A closed form solution for the dynamic response of finite ribbed plates, Journal of the Acoustical Society of America 119 (2006) 917–925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

Scattering of S0 Lamb Mode from a Blind Hole in a Plate Using Mindlin/Mindlin Plate Theory

An analytical model of Lamb wave scattering from a circular blind hole in isotropic plates is presented using the Mindlin plate theory for describing in-plane and flexural wave modes simultaneously. The model makes use of the wave function expansion technique and the boundary conditions at the hole edge to evaluate the scattered far fields of three fundamental guided wave modes. Comparisons are made to existing approximate models using Poisson/Kirchhoff theory and Poisson/Mindlin theory and a 3D model using the exact 3D equations. The results reveal that the present model is more consistent with the exact 3D model at higher frequencies than existing approximate models.     

The reflection of the fundamental torsional mode from cracks and notches in pipes

A quantitative study of the reflection of the T(0,1) mode from defects in pipes in the frequency range 10-300 kHz has been carried out, finite element predictions being validated by experiments on selected cases. Both cracklike defects with zero axial extent and notches with varying axial extents have been considered. The results show that the reflection coefficient from axisymmetric cracks increases monotonically with depth at all frequencies and increases with frequency at any given depth. In the frequency range of interest there is no mode conversion at axisymmetric defects. With nonaxisymmetric cracks, the reflection coefficient is a roughly linear function of the circumferential extent of the defect at relatively high frequencies, the reflection coefficient at low circumferential extents falling below the linear prediction at lower frequencies. With nonaxisymmetric defects, mode conversion to the F(1,2) mode is generally seen, and at lower frequencies the F(1,3) mode is also produced. The depth and circumferential extent are the parameters controlling the reflection from cracks; when notches having finite axial extent, rather than cracks, are considered, interference between the reflections from the start and the end of the notch causes a periodic variation of the reflection coefficient as a function of the axial extent of the notch. The results have been explained in terms of the wave-number-defect size product, ka. Low frequency scattering behavior is seen when ka < 0.1, high frequency scattering characteristics being seen when ka > 1.     

The band gaps of Lamb waves in a ribbed plate: A semi-analytical calculation approach

In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell.     

The effect of couple stresses on stress distribution in a thin plate due to the pressure of a rivet on one side of a circular hole

In this paper we shall investigate the effect of couple stresses on stress distribution in an infinite plate with a circular hole subjected to pressure exerted by a rivet.     

An experimental study of transmission,reflection and scattering of sound in a free jet flight simulation facility and comparison with theory

When a free jet (or open jet) is used as a wind tunnel to simulate the effects of flight on model noise sources, it is necessary to calibrate out the effects of the free jet shear layer on the transmitted sound, since the shear layer is absent in the real flight case. In this paper, a theoretical calibration procedure for this purpose is first summarized; following this, the results of an experimental program, designed to test the validity of the various components of the calibration procedure, are described. The experiments are conducted by using a point sound source located at various axial positions within the free jet potential core. By using broadband excitation and cross-correlation methods, the angle changes associated with ray paths across the shear layer are first established. Measurements are then made simultaneously inside and outside the free jet along the proper ray paths to determine the amplitude changes across the shear layer. It is shown that both the angle and amplitude changes can be predicted accurately by theory. It is also found that internal reflection at the shear layer is significant only for large ray angles in the forward quadrant where total internal reflection occurs. Finally, the effects of sound absorption and scattering by the shear layer turbulence are also examined experimentally.