Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave.

A hybrid elastic wave method is applied to determine the anisotropic constants of Olive wood specimen considered as an orthotropic solid. The method is based on the measurements of the Lamb wave velocities as well as the bulk ultrasonic wave velocities. Electrostatic, air-coupled, ultrasonic transducers are used to generate and receive Lamb waves which are sensitive to material properties. The variation of phase velocity with frequency is measured for several modes propagating parallel and normal to the fiber direction along a thin Olivier wood plates. A numerical model based mainly on an optimization method is developed; it permits to recover seven out of nine elastic constants with an uncertainty of about 15%. The remaining two elastic constants are then obtained from bulk wave measurements. The experimental Lamb phase velocities are in good agreement with the calculated dispersion curves. The evaluation of Olive wood elastic properties has been performed in the low frequency range where the Lamb length wave is large in comparison with the heterogeneity extent. Within the interval errors, the obtained elastic tensor doesn't reveal a large deviation from a uniaxial symmetry.

Finite element simulation of the generation and detection by air-coupled transducers of guided waves in viscoelastic and anisotropic materials.

The measured characteristics (efficiency and sensitivity) of two air-coupled transducers allow for the prediction of the absolute values of the pressure of the bulk waves generated in air and for the measurement of the pressure of the field radiated in air by guided waves propagating in a structure. With finite element software, the pressure field generated by an air-coupled transducer is simulated by introducing a right-hand side member in the Helmholtz equation, which is used for computing the propagation from the transducer to a plate. The simulated source is rotated in order to impose an angle of incidence with respect to the normal of the plate and generate the corresponding guided mode. Inside the plate, the propagation is simulated with the dynamic equations of equilibrium and a complex stiffness tensor to take into account the viscoelastic anisotropy of the material. For modeling the three-dimensional fields of the guided modes propagating in a two-dimensional non-symmetry plane, a 2.5 dimensional model is introduced. The model computes the value of the pressure field radiated in air by the plates for any guided modes and can predict the detectability of the system for a known defect in a structure. A test bed incorporating two air-coupled transducers is used to generate and receive various guided modes. Two plates made of Perspex and carbon-epoxy composite are tested. The pressure measured by the receiver at various positions is compared to the results of the model to validate it.

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates.

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.

Wave propagation along transversely periodic structures.

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

Comparison of laser interferometry and radiation force method of measuring ultrasonic power.

The aim of this paper is to compare two different methods for the calculation of the ultrasonic output power of underwater transducers: the radiation force balance, which is the standard method, and the laser heterodyne interferometry, which is rather used to depict displacement or velocity distributions of the acoustic field. Here it is shown that the latter can also be used to calculate the acoustic time-average power with an uncertainty of about 22%, the radiation force balance giving an uncertainty of 12% (with 95% confidence). The interferometry experiments performed with two transducers working at 2.25 MHz and 8.25 MHz showed that they produce different acoustic fields (respectively Gaussian and Lorentz-sigmoidal distributions). Taking into account the acoustic field profiles, the acoustic time-average power from interferometry was calculated. It was found very similar to the time-average power measured with the radiation force balance in the plane-wave assumption.

Surface impedance matrices to model the propagation in multilayered media.

The surface impedance matrices in stratified plates made of fluid layers and/or anisotropic absorbing solid layers link the particle velocity field to the stress field at any interface. A surface impedance matrix represents the impedance at a given interface of all the layers located between that interface and one boundary of the medium. For each interface, there are two surface impedance matrices, each one corresponding to one boundary. This notion simplifies the computations of the modal solutions. The number of elements in the matrices involved in the computations is divided by a factor of four in comparison to usual matrix methods. This paper describes the method and presents examples to illustrate its interests and its efficiency where other techniques fail, for instance in the case of modes possessing energy in layers embedded in the structure.

The measurement of A0 and S0 lamb wave attenuation to determine the normal and shear stiffnesses of a compressively loaded interface.

Guided waves in an elastic plate surrounded by air propagate with very low attenuation. This paper describes the effect on this propagation of compressively loading an elastomer with high internal damping against one surface of the elastic plate. The propagation of both A0 and S0 Lamb modes is considered. The principal effect is shown to be increased attenuation of the guided waves. This attenuation is caused by leakage of energy from the plate into the elastomer, where it is dissipated due to high viscoelastic damping. It is shown that the increase in attenuation is strongly dependent on the compressive load applied across the solid-solid interface. This interface is represented as a spring layer in a continuum model of the system. Both normal and shear stiffnesses of the interface are quantified from the attenuation of A0 and S0 Lamb waves measured at each step of the compressive loading. The normal stiffness is also measured independently by normal incidence, bulk longitudinal wave ultrasound. The resulting predictions of wave propagation behavior, such as attenuation, obtained by the model are in excellent agreement with those measured experimentally.

Guided waves propagating in sandwich structures made of anisotropic, viscoelastic, composite materials.

The propagation of Lamb-like waves in sandwich plates made of anisotropic and viscoelastic material layers is studied. A semi-analytical model is described and used for predicting the dispersion curves (phase velocity, energy velocity, and complex wave-number) and the through-thickness distribution fields (displacement, stress, and energy flow). Guided modes propagating along a test-sandwich plate are shown to be quite different than classical Lamb modes, because this structure does not have the mirror symmetry, contrary to most of composite material plates. Moreover, the viscoelastic material properties imply complex roots of the dispersion equation to be found that lead to connections between some of the dispersion curves, meaning that some of the modes get coupled together. Gradual variation from zero to nominal values of the imaginary parts of the viscoelastic moduli shows that the mode coupling depends on the level of material viscoelasticity, except for one particular case where this phenomenon exists whether the medium is viscoelastic or not. The model is used to quantify the sensitivity of both the dispersion curves and the through-thickness mode shapes to the level of material viscoelasticity, and to physically explain the mode-coupling phenomenon. Finite element software is also used to confirm results obtained for the purely elastic structure. Finally, experiments are made using ultrasonic, air-coupled transducers for generating and detecting guided modes in the test-sandwich structure. The mode-coupling phenomenon is then confirmed, and the potential of the air-coupled system for developing single-sided, contactless, NDT applications of such structures is discussed.

Microwave excitation of ultrasound in graphite-fiber reinforced composite plates.

In this paper is demonstrated the effect of microwave beam polarization on the thermal generation of acoustic waves in continuous fiber-reinforced composite laminates. It is found that beam polarization strongly influences the dielectric interaction that leads to thermal losses, bulk expansion, and acoustic wave generation. The oriented graphite fibers in the composite laminate effectively short the microwave fields and reduce the generation efficiency nearly to zero. Ultrasonic waves at several hundred kHz generated in the composite are detected by air-coupled acoustic transducers located on the opposite side of the plate specimen from the 9.41 GHz incident microwave beam. With some averaging signal-to-noise ratios of better than 26 dB are obtained. Applying a conventional model of electromagnetic wave scattering in anisotropic media to this experiment yields good agreement between calculations and measured data. Implications for microwave-acoustic testing of graphite-reinforced composites are also discussed.

Numerical predictions and experiments on the free-plate edge mode.

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.

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 wave generation by microwaves and applications to nondestructive evaluation.

Although acoustic wave generation by electromagnetic waves has been widely studied in the case of laser-generated ultrasounds, the literature on acoustic wave generation by thermal effects due to electromagnetic microwaves is very sparse. Several mechanisms have been suggested to explain the phenomenon of microwave generation, i.e. radiation pressure, electrostriction or thermal expansion. Now it is known that the main cause is the thermal expansion due to the microwave absorption. This paper will review the recent advances in the theory and experiments that introduce a new way to generate ultrasonic waves without contact for the purpose of nondestructive evaluation and control. The unidirectional theory based on Maxwell's equations, heat equation and thermoviscoelasticity predicts the generation of acoustic waves at interfaces and inside stratified materials. Acoustic waves are generated by a pulsed electromagnetic wave or a burst at a chosen frequency such that materials can be excited with a broad or narrow frequency range. Experiments show the generation of acoustic waves in water, viscoelastic polymers and composite materials shaped as rod and plates. From the computed and measured accelerations at interfaces, the viscoelastic and electromagnetic properties of materials such as polymers and composites can be evaluated (NDE). Preliminary examples of non-destructive testing applications are presented.

Prediction of the generation of acoustic waves due to the penetration of pulsed microwaves in multilayer media.

The acoustic wave generation in a body irradiated by a pulsed microwave is predicted theoretically. The irradiated body is a viscoelastic multilayer rod inserted into a waveguide or an uniformly irradiated viscoelastic plate. The model is based on Maxwell's equations, the heat equation, and thermoviscoelasticity theory. It is validated experimentally by means of four tests performed on three different specimens. The two first specimens are homogeneous rods used to evaluate and verify the mechanical and electromagnetic characteristics of two different materials. The third specimen is a composite rod made up of these materials. Two tests are performed with this specimen. The comparison between the experimental results and the theoretical computations leads to the validation of the theoretical model.

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.