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The ultrasound stimulated thermography method is usually used to detect the temperature rise at a defect position. The temperature rise can be due to the friction between the edges of the defect and/or the plastic deformation around the defect. This paper presents another aspect of the method when the ultrasounds are propagating in a viscoelastic anisotropic material, such as polymers or fiber-reinforced polymers. The attenuation of the waves produces a distributed temperature field. Therefore, even a defect that does not produce some heat can be detected, the ultrasonic field is modified. A finite element model is used for computing the temperature field and for predicting the possibility for an infrared camera of detecting the temperature rise and its modification due to a defect. The model computes the stress and displacement fields associated with the propagation and the loss of energy. Then the heat equation is solved with this loss as a source of heating. An experiment is done with a sonotrode that excites a PVC plate. The ultrasonic displacement at the top of the plate is measured with a laser velocimeter and introduced in the model. Finally, the model result is compared to the image produced by the camera. [ABSTRACT FROM AUTHOR]

In this paper we propose an efficient way to post-process output data predicted by Finite Element (FE) or Boundary Element (BE) codes, when the scattering of Lamb modes by defects in plate-like structures is considered. The use of a general orthogonality relation is compared to classical post-processing made with spatial FFT. To get the amplitudes of incident or scattered modes, this orthogonality relation requires the numerical prediction of the through-thickness displacements, and stress-fields distributions, on each side of the scatterer. The distance between the location where these fields are predicted and the scatterer can be very small, thus allowing huge reductions in the size of the mesh. Through two examples, this orthogonality relation is used to calculate the reflection and transmission coefficients of a pure Lamb mode incident on a notch-like defect, in either an elastic or a viscoelastic plate. Thanks to efficient absorbing regions, the FE meshed domains are reduced to the vicinity of the defects, thus allowing several advantages of the method to be demonstrated in comparison to some weaknesses of the classical post-processing based on spatial FFT. [ABSTRACT FROM AUTHOR]

The absorption of microwaves by material induces a temperature rise that generates a mechanical deformation in the irradiated structure by thermoelastic effect. As a continuous development of this recent generation technique, the present study investigates the in-plane mechanical vibration of disks and rings submitted to pulsed microwaves in order to develop a contactless evaluation method. The vibration of a disk submitted to microwave irradiations depends on the distribution of the electromagnetic field in the sample. If the irradiation is axisymmetric, the purely radial eigenmode is generated. On the contrary, if the irradiation field is not axisymmetric, the vibration is angular dependent. Consequently, one can choose to use various eigenfrequencies for determining the geometrical properties of a circular plate and the mechanical properties of the material. A semi-analytic model is presented to predict the in-plane vibration eigenfrequencies of thin rings and disks. Wave equations are solved by taking into account the angular dependence in order to estimate the maximum number of disk or ring eigenfrequencies. The model is validated by comparison between the theoretical and the experimental results and applied for the evaluation of rings and disks geometries and their constitutive material properties using the microwave excitation technique. [ABSTRACT FROM AUTHOR]

As an application of ultrasound generation by microwave excitation, a study of piezoelectric material behavior is presented. Piezoelectric bars excited electrically or by microwave irradiation give different resonance frequencies. Piezoelectric materials are subject to a stiffening phenomenon (variation of the apparent Young’s modulus) when the electrical boundary conditions change and, as a result, when the material is dynamically excited, a modification of the natural resonance frequencies occurs. A one-dimensional model, to predict the acoustic waves generated in piezoelectric materials by an unspecified excitation source, is presented and compared to experimental results. This model is used as a nondestructive evaluation method to characterize piezoelectric samples and to highlight the thermoelastic origin of the acoustic generation when the piezoelectric materials are excited by pulsed microwaves. [ABSTRACT FROM AUTHOR]

In this paper, constitutive relations are solved in the Fourier domain using a finite-element-based commercial software. The dynamic responses of viscoelastic bars or plates to either thermal or mechanical loads are predicted by considering complex moduli (Young, Poisson, stiffness moduli) as input data. These moduli are measured in the same frequency domain as that which is chosen for modeling the wave propagation. This approach is simpler since it suppresses the necessity of establishing a rheological model. Specific output processing then allows the numerical predictions to be compared to analytical solutions, in the absence of scatterers. The performances of this technique and its potential for simulating more complicated problems like diffraction of waves or for solving inverse problems are finally discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article develops a method for investigating some anisotropic media, such as composites, by the use of ultrasonic waves transmitted through a plate-shaped sample immersed in water. The discussion begins with Christoffel's equations for plane linear anelastic waves under the assumptions that for small angles of incidence the wave modes are plane and inhomogeneous and that the anisotropy is representable by hexagonal symmetry. The water-sample interface is treated using the law of Snell-Descartes for nonabsorbing media and takes into account mode conversion and the generation of acoustic surface waves. The method produces viscoelastic constants and relative attenuation coefficients as a function of the angle of refraction. The experimental measurement apparatus is described and data are given for the 25-layer unidirectional Gr/epoxy composite. Results are presented in terms of slowness, damping vector, and attenuation curves. The results are significant in that they demonstrate the anisotropy both for the elastic stiffness and the attenuation. The method appears to hold promise for characterizing some classes of anisotropic media, including 2-D composites, in terms of their anelastic behavior. [ABSTRACT FROM AUTHOR]

The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear-type (T) plate vibrations which are coupled due to the boundary conditions. Without such coupling, their phase-velocity dispersion curves would form two intersecting families, which at high frequency, tend toward the elastic-wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L⇆T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid-borne (Stoneley-Scholte-type) wave which is known from the studies of Grabowska and Talmant to be present in this case, and of the usual A0 Lamb wave exhibit a similar repulsion phenomenon. [ABSTRACT FROM AUTHOR]

The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear type (T) plate vibrations that are coupled due to the boundary conditions. Without such coupling, their phase-velocity dispersion curves would form two intersecting families, which at high frequency tend towards the elastic-wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves, similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L↔T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid-borne (Stoneley-Scholte type) wave, which is known from the studies of Grabovska and Talmant to be present in this case, and of the usual A0 Lamb wave exhibit a similar repulsion phenomenon. [ABSTRACT FROM AUTHOR]

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.

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.

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.

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.

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.

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.

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.

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.

The acoustic wave generation in a specimen irradiated by a pulsed microwave is predicted theoretically. The specimen is a viscoelastic rod inserted into a wave guide. The model is based on Maxwell's equations, heat equation and thermoviscoelasticity theory. Computations show the presence of temperature oscillations due to the electromagnetic interferences in the irradiated rod if its electromagnetic absorption is low. An experimental method to infer indirectly the detailed behavior of microwave-generated acoustic waves in polymer rods, including the influence of electromagnetic wave reflection at the rod ends, is presented. The method consists of measuring the oscillations in the particle acceleration detected at the end of the rod that are induced by variations in the polymer rod length. The oscillations are caused by changing electromagnetic standing-wave conditions within the rod. It is found that these oscillations are in agreement in period, amplitude, and phase, with independent values of the complex dielectric constant and complex acoustic slowness of the polyvinyl chloride samples used in the study.

In this paper both theoretical and experimental investigations on the reflection and transmission of an incident plane wave by immersed viscoelastic orthotropic plates are presented. Taking the anisotropy of the layer into account the reflection and transmission coefficients are expressed in terms of nine complex elastic constants. In agreement with the Snell's laws, any waves generated in the layer are bulk heterogeneous plane waves. Using a method already described in the isotropic case, the reflection and transmission coefficients are obtained as a function of the reflection and refraction coefficients of bulk heterogeneous plane waves at the two single solid/liquid interfaces, which limit the plate. In this way, these coefficients can be easily expanded in Debye's series. In addition, for many incident and azimuthal angles, the calculations are compared with trial results on a composite made of unidirectional carbon fibers and epoxy matrix. Finally, by the measurement of the variation of attenuation versus the frequency, a linear model permits the computations in a large frequency range. Conclusions are carried out regarding the use of the LLW method in the inverse problem to recover elastic constants of composite materials.