Excitations of thermoelastic waves in plates by a pulsed laser

The method of the eigenfunction expansion, also known as the expansion in normal modes, is employed to study numerically the axisymmetric excitation of the thermoelastic waves in plates by a pulsed laser. This method gives a systematic treatment and allows one to investigate not only the quasistatic and dynamic thermoelastic responses of pulsed photothermal deformation on the time scale of 1 s, but also the thermoelastic generation of longitudinal, transverse, and surface acoustic waves in thick materials, as well as the excitations of the Rayleigh-Lamb wave modes in thin plates. The formalism is particularly suitable for waveform analyses of the excitations of transient Lamb waves in thin plates because one needs only to calculate the contributions of several lower eigenmodes. The numerical technique provides a quantitative tool for the experimental determination of material properties, especially the mechanical and elastic properties of free-standing films and thicker sheet materials by thermoelastic detection.     

High frequency shear horizontal plate acoustic wave devices

It has been shown recently that shear horizontal acoustic waves propagating in piezoelectric plates whose thickness h is much less than the acoustic wavelength λ possess a number of attractive properties for use in sensor and signal processing applications. In order to exploit the potential benefits of these waves, however, one needs to fabricate devices on very thin plates. We have developed a suitable fabrication method which can be used to realize devices on such thin plates. In this method, the device is first fabricated on a plate of normal thickness (approximately 500 μm) and the substrate is then lapped from the back side to reduce the thickness. The technique has been utilized to realize devices on plates of thickness less than 70 μm. A shear horizontal plate acoustic wave (SH-PAW) delay line of fundamental resonant frequency greater than 25 MHz and insertion loss less than 7 dB has been realized on a 60 μm thick Y – cut, X – propagation lithium niobate substrate. The device also shows strong response near the third harmonic frequency of 75 MHz.     

A useful analytical description of the coefficients in an inhomogeneous wave decomposition of a symmetrical bounded beam

If a bounded beam is described using a superposition of infinite inhomogeneous waves, the values of the coefficients attributed to each inhomogeneous wave are found using a classical optimization procedure, whence it is impossible to describe the obtained values analytically. In this paper, we develop a new and easy to apply straightforward analytical method to find the appropriate values of the sought coefficients. Supplementary to its analytical and straightforward nature, the method proves to reduce the inherent instabilities found in the inhomogeneous wave decomposition.     

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.     

The use of an orthogonality relation for reducing the size of finite element models for 3D guided waves scattering problems

The scattering of guided waves by complex shaped defects in three-dimensional (3D) waveguides is considered. For such problems, analytical solutions do not exist, and modal decomposition techniques based on the establishment of the displacement and stress fields in the vicinity of the scatterer are quite heavy and complicated to perform. On the other hand, finite elements (FE)-based methods constitute a powerful way to obtain solutions, but they are known to be very memory consuming. This paper proposes a post-processing technique, based on a 3D orthogonality relation, to decompose a complex acoustic field produced by a scatterer and predicted by a 3D FE model, into plane waves, the amplitudes of which are quantified in the far field. This technique allows important reductions in the size of the FE models to be made. Two applications are presented to demonstrate the potential of this method. The first one concerns the scattering of the S₀ Lamb wave incident on a flat bottom circular hole. In this example, the amplitude of each mode is calculated via the orthogonality relation-based method, and compared to that obtained by simply monitoring the displacements at appropriate through-thickness positions. In the second application, the incident S₀ Lamb mode is converted into five modes scattered by a defect of complex geometry.     

Resonant ultrasound spectroscopy and homogeneity in polycrystals

Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample’s smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity.     

Optimal Acoustic Attenuation of Weakly Compressible Media Permeated with Air Bubbles

Based on fuzzy logic （FL） and genetic algorithm （GA）, we present an optimization method to obtain the optimal acoustic attenuation of a longitudinal acoustic wave propagating in a weakly compressible medium permeated with air bubbles. In the optimization, the parameters of the size distribution of bubbles in the medium are optimized for providing uniformly high acoustic attenuation in the frequency band of interest. Compared with other traditional optimization methods, the unique advantage of the present method is that it can locate the global optimum quickly and effectively in need of knowing the mathematical model precisely. As illustrated by a numerical simulation, the method is effective and essential in enhancing the acoustic attenuation of such a medium in an optimal manner. The bubbly medium with optimized structural parameters can effectively attenuate longitudinal waves at intermediate frequencies with an acoustic attenuation approximating a constant value of lO（dB/cm）. Such bubbly media with optimal acoustic attenuations may be applied to design acoustic absorbent by controlling broader attenuation band and higher efficiency.     

Influence of transparent coating thickness on thermoelastic force source and laser-generated ultrasound waves

A numerical model is established to investigate the influence of transparent coating thickness on the laser-generated thermoelastic force source and ultrasound waves in the coating-substrate system by using the finite element method (FEM). Taking into account the effects of thermal diffusion, the finite width and duration of the laser source, as well as the temperature dependence of material properties, the transient temperature distributions are obtained firstly. Applying this temperature field to structure analyses as thermal loading, the thermoelastic stress field and laser-generated ultrasound wave in the specimen are obtained. The generation and propagation of the laser thermoelastically induced stress field and ultrasonic waves in coating-substrate system are presented in detail. The influence of transparent coating thickness on the transient temperature distribution, thermoelastic force source and the laser-generated ultrasound waveforms is investigated. The numerical results indicate that the thermoelastic force source and laser-generated ultrasound waveform are strongly affected by the coating thickness due to the constraint of coating. This method can provide insight into the generation and propagation of the laser-generated stress field in coating-substrate system consisting of a transparent coating and an opaque metallic substrate. It provides theoretical basics to optimize ultrasonic signal generation in particular applications and invert the physical and geometrical parameter of the coating-substrate system more accurately in the experiment.     

A semi-analytical model for predicting multiple propagating axially symmetric modes in cylindrical waveguides

A semi-analytical model for multiple mode axially symmetric wave propagation in finite solid cylindrical waveguides is presented. The model is designed as a tool for predicting and interpreting experimental signals. The model is based on a common experimental configuration and considers the excitation, propagation and reception of the ultrasonic signal in the waveguide. The Pochhammer-Chree solution for an infinite cylinder is the basis for the model. Extensions are made to enable comparison to experimental results. Comparisons with experiment are performed in the time, frequency and joint-time frequency domain for both narrow band and broad band excitation of the piezo-electric transducer.     

Minimization of finite beam effects in the determination of reflection and transmission coefficients of an elastic layer

A special data acquisition technique was applied to determine the acoustic plane-wave reflection and transmission properties of a plane-parallel aluminum plate. In this technique, the reflected and transmitted wavefield along a plane or line normal to the reflected or transmitted wave vector is recorded at equidistant receiver positions. The obtained traces are subsequently added up in the temporal domain to satisfy plane-wave conditions, thus effectively removing the effect of the limited beam of commonly used transducers. The agreement between plane-wave theory and experiment was found to be excellent, both in the temporal and in the frequency domain.     

Air-coupled ultrasonic assessment of wood veneer

Air-coupled ultrasound (ACU) provides a tool to evaluate wood samples of small or moderate thickness (<30 mm) thereby avoiding direct contact or liquid coupling. Results of through-transmission ACU measurements on wood veneer samples and related products are reported with respect to a wide variety of quality aspects. Fluctuations in the averaged received signal levels appear to be correlated to the presence of natural or machine-induced thickness and density variations, flaws and grain damage, errors produced by the manufacturing process, insufficient bonding on a substrate, etc. In addition it is seen that the variability of the signal levels enables to distinguish between quarter and crown areas.     

A computer simulation study of imaging flexural inhomogeneities using plate-wave diffraction tomography

This paper investigates the feasibility of plate-wave diffraction tomography for the reconstruction of flexural inhomogeneities in plates using the results of computer simulation studies. The numerical implementation of the fundamental reconstruction algorithm, which has recently been developed by Wang and Rose [C.H. Wang, L.R.F. Rose, Plate-wave diffraction tomography for structural health monitoring, Rev. Quant. Nondestr. Eval. 22 (2003) 1615-1622] is investigated addressing the essential effects of applying the discrete form of the Fourier diffraction theorem for solving the inverse problem as discussed by Kak and Slaney [A.C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, 1988] for the acoustic case, viz. diffraction limited sensitivity, influence of weak scatterer assumption, damage location and scatter field data processing in time and Fourier space as well as experimental limitations such as finite receiver length and limited views. The feasibility of the imaging technique is investigated for cylindrical inhomogeneities of various severities and relative position within the interrogation space and a normal incident interrogation configuration. The results show that plate-wave diffraction tomography enables the quantitative reconstruction of location, size and severity of plate damage with excellent sensitivity and offers the potential for detecting corrosion thinning, disbonds and delamination damage in structural integrity management applications.     

Phase Transition in Acoustic Localization in a Soft Medium Permeated with Air Bubbles

Propagation of an acoustic wave in a soft medium permeated with air bubbles is theoretically investigated by using a self-consistent approach. The soft medium is assumed to be viscoelastic to estimate the effect of acoustic absorption on the acoustic localization in such a medium. The oscillation phases of bubbles are examined by employing a phase diagram method. A collective oscillation of the bubbles is observed once the acoustic localization occurs, which is known as a phenomenon of ＇phase transition ＇, and such a phenomenon persists as we manually increase the viscosity factor of the soft medium. Therefore it is proven that the phenomenon of phase transition may serve as a unique criterion to effectively identify acoustic localization in a bubbly soft medium even in the presence of viscosity, and the directions of the phase vectors help to determine the extent of localization. This is of practical significance for experimental research studying the acoustic localization in such a medium, for which the presence of viscosity generally causes great ambiguity in distinguishing the effects of localization and acoustic absorption.     

Ultrasonic wave propagation in heterogeneous solid media: theoretical analysis and experimental validation

This research deals with the ultrasonic characterization of thermal damage in concrete. This damage leads to the appearance of microcracks which then evolve in terms of volume rate and size in the material. The scattering of ultrasonic waves from the inclusions is present in this type of medium. The propagation of the longitudinal wave in the heterogeneous media is studied via a homogenization model that integrates the multiple scattering of waves. The model allows us to determine the phase velocity and the attenuation according to the elements which make the medium. Simulations adapted to the concrete are developed in order to test the responses of the model. These behaviors are validated by an experimental study: the measurements of phase velocity and attenuation are performed in immersion, with a comparison method, on a frequency domain which ranges from 160 kHz to 1.3 MHz. The analysis of different theoretical and experimental results obtained on cement-based media leads to the model validation, on the phase velocity behavior, in the case of a damage simulated by expanded polystyrene spheres in granular media. The application to the case of a thermally damaged concrete shows a good qualitative agreement for the changes in velocity and attenuation.     

Synthetic aperture focusing for defect reconstruction in anisotropic media

Ultrasonic inspection plays an important role in numerous industrial fields. One of the prominent tasks with respect to quantitative nondestructive evaluation is the determination of location, shape, size and orientation of defects. In this respect, the synthetic aperture focusing technique (SAFT) has been successfully applied to isotropic materials over the years. In anisotropic media, however, its application suffers from several phenomena, which are the direction dependence of the ultrasonic velocities, the beam skewing effect and the modified transducer radiation characteristics. In this article, a SAFT imaging algorithm is presented which fully accounts for the nature of wave radiation and propagation within anisotropic materials. For three-dimensional defect reconstruction, the spatial dependence of the ultrasonic group velocities as well as the radiation characteristics of the transducer are exploited--respective algorithms have been implemented for orthotropic material symmetry. Tests have been performed on unidirectional composite material.     

The detectability of kissing bonds in adhesive joints using ultrasonic techniques

This paper concerns a study of the detectability of dry contact kissing bonds in adhesive joints using three ultrasonic inspection techniques. Conventional normal incidence longitudinal and shear wave inspection were conducted on dry contact kissing bonds using a standard damped ultrasonic transducer and an electro-magnetic acoustic transducer (EMAT) respectively. The detectability of the dry contact kissing bonds was assessed by calculating the reflection coefficient of the imperfect interface at varying loads for a number of surface roughnesses. A high power ultrasonic method was also employed to determine the non-linear behavior of the adhesive interface. The non-linearity of the interface was determined by the ratio of the amplitudes of the first harmonic and fundamental frequencies of the transmitted waveform. It was found that the high power technique showed the greatest sensitivity to these kissing bonds at low contact pressures, however at high loads conventional longitudinal wave testing was more sensitive. It was also noted that a combination of two or more techniques could provide enhanced information about the kissing bond compared to a single technique alone.     

Impact of localized inhomogeneity on the surface-wave velocity and bulk-wave reflection in solids

The effect of a weak surface, near-surface and interfacial inhomogeneity on the frequency dependence of the surface wave velocity and of the SH (shear horizontal) wave reflectivity in isotropic elastic media is studied analytically and numerically. The inhomogeneity is modeled as an infinite planar layer with continuously varying properties. Weak inhomogeneity may markedly affect the dispersion of the Rayleigh velocity and especially of the reflectivity. It is demonstrated how this effect, particularly pronounced at high frequency, depends on the extent of inhomogeneity. The material data for damaged and ideal concrete and several simple examples of inhomogeneity profiles are utilized for the numerical calculations based on the Peano expansion. The use of explicit low- and high-frequency approximations is also exemplified. Among these, simple WKB asymptotics are shown to be particularly helpful for the Rayleigh velocity in the case of a prominent inhomogeneity attached to the surface and for the reflection on weak interfaces.