Antisymmetric A0 Research Articles

Numerical simulation of laser-generated ultrasound by the finite element method

The results obtained from the finite element model of laser-generated ultrasound are presented in terms of temperature and displacement. According to thermoelastic theory, considering the temperature dependence of the thermophysical parameters of the material, the transient temperature field can be precisely calculated by using the finite element method; then, laser-generated surface acoustic wave forms are calculated in Al plates of various thicknesses. The elastic waves excited by a pulsed laser in a thin plate are typical Lamb waves, and the numerical results demonstrate that the surface vibration is mainly determined by the lower frequency components of the symmetric mode s0 and antisymmetric mode a0 of the lowest order in very thin plate materials. It is also indicated that, when the sample thickness increases, both the higher frequency components of the lower Lamb wave modes and the higher order Lamb wave modes should be considered. In a relatively thicker plate, the numerical model can still capture the significant details of the transient features taking place in the plates. The surface skimming longitudinal and shear waves are relatively stronger in the near field, distorting the observed wave form of the Rayleigh wave. These effects must be considered when the quantitative near field is applied to determining elastic parameters or residual stresses.

Propagation of ultrasonic guided waves in lap-shear adhesive joints: case of incident a0 Lamb wave.

This paper deals with the propagation of ultrasonic guided waves in adhesively bonded lap-shear joints. The topic is relevant to bond inspection by ultrasonic testing. Specifically, the propagation of the lowest-order, antisymmetric a0 mode through the joint is examined. An important aspect is the mode conversion at the boundaries between the single-plate adherents and the multilayer overlap. The a0 strength of transmission is studied for three different bond states in aluminum joints, namely a fully cured adhesive bond, a poorly cured adhesive bond, and a slip bond. Theoretical predictions indicate that the dispersive behavior of the guided waves in the multilayer overlap is highly dependent on bond state. Experimental tests are conducted in lap-shear joints by a hybrid, broadband laser/air-coupled ultrasonic setup in a through-transmission configuration. The Gabor wavelet transform is employed to extract energy transmission coefficients in the 100 kHz 1.4 MHz range for the three different bond states examined. The cross-sectional mode shapes of the guided waves are shown to have a substantial role in the energy transfer through the joint.

Lamb Wave Interaction with Impact-induced Damage in Aircraft Composite: Use of the A0 Mode Excited by Air-coupled Transducer

A novel technique has been experimented involving the use of an air-coupled transducer to excite Lamb mode in composite material, a pinducer to pick-up local response and a turn-table set-up to reveal impact damage-induced anisotropy. So, a fundamental antisymmetric A0 Lamb mode has been excited under unusual conditions. Its efficiency for detecting impact-induced damage in a multilayered thin quasi-isotropic carbon–epoxy composite laminate has been demonstrated and the knowledge on the A0 Lamb mode interaction with the damage has been improved using an original mapping. Some material characteristics have been obtained. Intrinsic material attenuation of this guided mode at a frequency of 370 kHz and a frequency-thickness product of 740 kHz mm has been assessed and in-plane energy distribution of the A0 mode has been mapped, revealing a relatively directive acoustic field. However, the composite material exhibits slightly anisotropic acoustic behaviour due to a lack of fibres in certain directions. Interactions between the A0 mode and multidelamination of the critical area were also investigated. In-plane mappings of the ultrasonic field have revealed two main phenomena: attenuation and scattering due to damage. Splitting of the ultrasonic wave was observed, creating a region of geometric shadow where attenuation occurs. It is shown on the mappings that the energy lost in this direction of propagation appears in other directions. An increase in the received energy was detected in certain directions, showing that the damage can be considered as a soft scattering centre.

Modal decomposition method for modeling the interaction of Lamb waves with cracks.

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.

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

Detection of Multiple Damages by Prestack Reverse-Time Migration

An approach to detect and image multiple damages in a platelike structure is presented. A structural health monitoring system (SHMS) with a linear array of actuators/sensors is proposed. The integrated actuators/sensors are used to activate/receive lowest-order antisymmetric A0 mode Lamb waves. A migration technique used in geophysical exploration and seismic prospecting is adopted to interpret the backscattering wave e eld and to image thee awsinthestructure.Theproposed approachismodeledbya two-dimensional explicite nitedifferencemethod both in simulating the ree ection waves and in implementing the prestack migration. An analytical solution based on Mindlin plate theory (Mindlin, R. D., “ Ine uence of Rotary Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” Journal of Applied Mechanics , Vol. 18, No. 1, 1951, pp. 31 ‐38) is derived to verify the accuracy of the numerical algorithm. An excitation-time imaging condition specie cally for the migration of waves in a plate is introduced based on a ray tracing concept, and prestack reverse-time migration is proceeded to propagate the ree ection energy back to the damages. The plate is imaged in terms of the velocity of transverse deformation after migration,thus, thelocations, dimensions, and seriousness of thee awscan bevisually displayed. Numerical results show that multiple damages can be successfully detected and the image of the damages correlate well with the target damages. The conclusion is that prestack migration can be a prospective technique in SHMS applications.

Hybrid acoustic waves in thin potassium niobate plates

The present article seeks to theoretically predict an effect and namely, the resonant interaction between fundamental acoustic modes propagating in a thin piezoelectric plate. It has been theoretically shown that for certain crystallographic cuts and propagation directions the electrical shorting of one of the strong piezoelectric plate sides may result in a coupling between fundamental acoustic modes. For example, the hybrid mode is generated for a frequency of about 10 MHz by an antisymmetric wave A0 and a shear-horizontal wave SH0, which propagate along the X+15° direction in a metallized Y-cut 100-μm-thick potassium niobate plate.

The behavior of Lamb waves in stressed polymer foils

The influence of externally applied unidirectional stress on the lowest-order Lamb modes of a 12-μm poly(ethylene terephthalate) (PET) film has been investigated both theoretically and experimentally. The Lamb wave dispersion was determined in a fully contactless way by using optical generation and detection of ultrasound. The elastic parameters of the film material were obtained by fitting the angle dependence of the low-frequency limit of the velocity of the fundamental Lamb modes. Whereas the dispersion of the symmetric mode S0 is only slightly influenced by an external stress, the antisymmetric mode A0 shows a transition from dispersion behavior determined by the elastic constants at small stresses to a behavior dominated by the applied stress at large stresses.

Analysis of optical interferometric measurements of guided acoustic waves in transparent solid media

Guided acoustic waves propagating in transparent and isotropic solids are studied by optical interferometry via the photoelastic effect. Unlike the photoelastic technique, the interferometric method permits the measurement of the phase shift rather than the polarization change of the light passing through an acoustic field. By analyzing the acoustically induced change in the index ellipsoid of refraction, it is demonstrated that the optical phase shift is proportional to the dilatation or the relative change in volume of the material. The dilatation fields of the symmetric and antisymmetric Lamb modes S0 and A0, as well as that of the Rayleigh wave, were calculated. Experiments performed in fused quartz by the interferometric method are in good agreement with theoretical predictions. Compared to the conventional photoelastic technique, the interferometric measurement of acoustic wave is phase sensitive and quantitative.

ラム波によるＣＦＲＰ板の非破壊検査

In order to improve the reliability and safety of composite materials, it is necessary to have non-destractive testing (NDT) available to detect defects in materials. Although conventional ultrasonic methods have, in principle, been used for NDT, they are inefficient and difficult to inspect large structures, such as ship hulls, because of the high attenuation of ultrasonic waves. In these cases, low frequency waves have an advantage over ultrasonic waves. Therefore, by using low frequency Lamb waves generated by tapping as a means of NDT in composite laminates, the following examinations were made; (1) predicting the thickness of plates, (2) detecting the delamination, (3) predicting the fiber contents in the composite laminates, and (4) measuring the wave velocities depending on propagating directions.(1) and (2) were carried out by using antisymmetric A0 mode waves. The results showed that it was possible to predict the thickness and to detect the delamination based on the relationship between the phase velocities of Lamb waves, which has dispersion characteristics, and the product of frequency and plate thickness. (3) was examined by the resonant method of symmetric S0 mode waves, and (4) was done by S0 waves. The results showed that the fiber content could be predicted from the stationary waves and the wave velocity propagating at an angle to the fiber direction could be calculated from the Young's modulus.

Analysis and synthesis of backscattering from a circular cylindrical shell

The farfield backscattered form function is examined for the problem of plane acoustic pressure wave scattering by an empty elastic circular cylindrical shell. The analysis of the exactly computed total form function has been carried out. The approach of finding the contribution introduced by two peripheral Lamb-type waves—the zero-order symmetric S0 and the zero-order antisymmetric A0—is outlined. An approximate description of these contributions is used to synthesize the backscattered form function. The presentation is developed using the case of an Armco iron shell with moderate thickness, immersed in water.