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The Lamb waves in nematic elastomer plates are investigated by adopting the viscoelasticity theory in the hydro-dynamic (low frequency) limit. The Legendre polynomial series approach is employed to obtain the complex wave number solutions to characterize the wave propagation and attenuation. Some unique Lamb wave characteristics are revealed. Results show that the cutoff frequencies of all Lamb modes vanish due to the high viscoelasticity. Except for A0 mode, each mode has a minimal attenuation frequency. Besides, the attenuation of nematic phase is thousands of times greater than the isotropic phase, which would be significant in designing damping applications. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of Lamb waves in an orthotropic elastic sandwich plate is investigated. The surface layers and the core layer may be compressible or incompressible. The main aim of the paper is to derive explicit dispersion equations. First, the dispersion equations of symmetric modes and asymmetric modes are derived for compressible sandwich plates by using the effective boundary condition method along with the transfer matrices for orthotropic elastic layers. These dispersion equations recover the dispersion equations of Lamb waves propagating in compressible isotropic sandwich plates. The dispersion equations for incompressible sandwich plates are obtained by using the incompressible limit method. It is shown numerically that the thickness ratio and the stiff contrast affect strongly higher modes and the incompressibility has strong influence on symmetric modes. Remarkably, the obtained dispersion equations can be used to analyze the dispersion characteristic of Lamb waves propagating in sandwich plates with honeycomb core layers because the honeycomb core layers can be replaced effectively by transversely isotropic elastic layers by mean of homogenization. [ABSTRACT FROM AUTHOR]

Multimodal is the prominent characteristic of Lamb waves, which means a variety of Lamb wave modes propagate in the structure and each of them has unique propagation behaviour. For a wideband multimodal Lamb wave signal, it is possible that many different modes share the same group velocity at some frequency points, while their dispersion behaviours change differently to thickness variation. In this study, the diversity and difference of the interaction between the corrosion and Lamb wave modes are investigated. On this basis, a corrosion index (CI) is established to evaluate the time gap between two modes at their identical group velocity points. The simulation results show that the CI value of a corroded path is obviously larger than that of a healthy path, indicating the presence of the damage, which is independent of any base-line signal. Furthermore, the new reconstruction algorithm for the probabilistic inspection of damage (RAPID) was proposed, where the signal difference coefficient was replaced by the CI to visualise damage location. The experimental results demonstrate the effectiveness of the proposed multimodal Lamb wave baseline-free damage detection method. [ABSTRACT FROM AUTHOR]

With the wide application of carbon fibre reinforced plastic (CFRP) structure, a structural health monitoring (SHM) system that can easily detect damages in CFRP structures is urgently needed. Since it is possible to detect damages effectively in a large area in CFRP by using the scattering of Lamb waves, in this research, we investigated the scattering of Lamb waves at an impact damaged area in quasi-isotropic (QI) CFRP laminate. By modelling the impact damage as a cylinder area with a uniform stiffness degradation, the scattering waves are calculated based on Mindlin plate theory, which is more precise than Kirchhoff plate theory. It is shown that in the low-frequency region, the calculation results based on Kirchhoff and Mindlin plate theory was similar, but in a higher frequency range, the results differed. The calculation results were compared with the simulation results, suggesting the validity of Mindlin plate theory within a practical frequency range. Moreover, we validated the analytical and simulation results experimentally using a QI CFRP laminate with a hole. We also conducted some parameter study based on the analytical calculation to clarify influential stiffness components. Since scattering behaviour of Lamb waves can be calculated in a fast and easy way using this method, this work is useful for the successful development of a scattering-based SHM system. [ABSTRACT FROM AUTHOR]

The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance. [ABSTRACT FROM AUTHOR]

In this paper, Lamb mode identification method based on small-sample dictionary algorithm is proposed and applied for the separation of specific Lamb modes, the reconstruction of Lamb waves upon propagating a certain distance and damage identification. This approach includes the creation of small-sample dictionary and querying procession in a dictionary. Firstly, Lamb wave signals upon propagating at a series of distances are simulated, and signal features, {mode, distance, time of flight (Tof), wavelet energy}, are extracted to create a dictionary; secondly, Tof of the received signal is extracted, and then Lamb modes are identified by searching the dictionary; finally, energy parameters are estimated to reconstruct wavepackets. The feasibility of this algorithm is validated in AAA laminate, and the results are presented. In a 2D-simulation model of a pitch-catch configuration, A0 and S0 modes can be identified and reconstructed effectively when the direct waves and the reflected waves are synchronously received, with the propagation distance of 0.3 m and 0.5 m, respectively. In addition, a Lamb-wave-based delamination location is conducted in three-dimensional AAA laminate. The experimental results show that the delamination can be located relatively by combining the identified damage-scattered S0 waves and the probability-based diagnostic imaging. [ABSTRACT FROM AUTHOR]

During production or service life, lightweight components made of fibre-reinforced polymers (FRP) may suffer from different types of defects such as cracks or delamination, which may be detected, amongst others, with the help of ultrasonic lamb waves (LW). The study intends to illustrate the potentials of numerical models to assist the design of LW-based non-destructive testing (NDT) processes. For that, the complete NDT chain of an LW driven inspection system was supported by a Finite Element Analysis (FEA) using stringer-stiffened C FRP panels as an exemplary component. The study was divided in two publications: The first part focused on the description of the numerical model, illustration of its functionalities and – most importantly – the determination of LW related effects that were needed to design the inspection system (dispersion characteristics, excitation frequency, propagating modes etc.). In this part, the FEA driven design approach was first validated with self measured experimental data as well as experiments provided in literature. In the second step, the numerical model was applied for the performance of parameter studies in order to identify component specific aspects that proved important for the NDT process. Finally, general advices and FEA related working steps were derived from all findings to assist practitioners in the implementation of the technique. [ABSTRACT FROM AUTHOR]

Wide band gaps with the propagation of elastic waves at low-frequency are desirable for phononic crystals in many traditional and novel applications. Inspired by the natural helix, we designed a microstructure in a metamaterial plate with an antisymmetric dual helix as the basic local resonant cell. The band structure and displacement transmission curve of metamaterial plates with dual helix cells were calculated by using the finite element method at first, then the band gap characteristics with and without consideration of the mass in the center of the dual helix were compared. The results show that the band gap in the band structure and displacement transmission curves have excellent consistency. Besides, the effects of the parameters including the number of turns of the helix, the plate thickness, and the radius of the attached mass sphere on the band gaps of flexural waves for the metamaterial plate were examined for further evaluation of the potential vibration prohibition application. It is found that the lower frequency of the band gap can be significantly tuned by adding a mass element in the metamaterial plates with dual helix elements, which provides a new method to tune the width of the band gap of a metamaterial plate. [ABSTRACT FROM AUTHOR]

Components made of fibre-reinforced polymers (FRP) may suffer from various types of damages, such as cracks or delamination. In order to monitor the structures' material condition, non destructive testing (NDT) methods have emerged – among them, the use of ultrasonic waves. Inter alia, research focused on Lamb waves (LW), which offer promising conditions for NDT processes. However, prior implementation in a specific production environment, practitioners are faced with many open questions such as excitation frequencies to be used or which mode to select for defect identification. Therefore, the study aimed at demonstrating how a finite element analysis (FEA) can assist the experimental design of an LW driven NDT process. For that, a numerical model was developed, capable of computing LW propagations in an exemplary component: Stringer-stiffened C-FRP panels. The study was divided into two parts: In this part, all information regarding the model building is presented and principal functionality demonstrated. In the second part, the FEA is validated and then used to perform parameter studies, highlighting important conditions for practical application. The results of the present paper showed that stiffeners provoke varying interactions with LW modes – effects that increase wave field complexity but do not limit defect identification within or behind the stringer. [ABSTRACT FROM AUTHOR]

Delamination is unavoidable during the fabrication or utilisation of carbon fibre reinforced polymer (CFRP) components. Due to the high sensitivity of the A0 mode for detecting delamination, nonlinear frequency mixing of counter-propagating A0-S0 mode Lamb waves was numerically and experimentally investigated in the CFRP composite plate. Considering the nonlinear effect caused by the heterogeneous structure of CFRP composite, the counter-propagation of primary Lamb waves can minimise the nonlinear interaction induced by material nonlinearity compared to the one-way propagation. Numerically, the nonlinear interaction between primary Lamb waves and delamination was investigated. Moreover, delaminations with different sizes, depths, and interface gaps were explored. It was found that the acoustic nonlinear parameter grows with expanding delamination size and diminishes with increasing delamination depth and interface gap. Furthermore, the nonlinear frequency mixing of counter-propagating A0-S0 mode Lamb wave was experimentally performed. The nonlinear frequency mixing effect induced by the delamination can be maximally isolated from the material nonlinearity. Consequently, the technique based on the nonlinear frequency mixing of counter-propagating A0-S0 mode Lamb waves provides a potential and effective method to detect defects in the composite plate with heterogeneous structures. [ABSTRACT FROM AUTHOR]

The nonlinear Lamb waves are sensitive to closed micro cracks and have a great potential for the detection of damage to prevent the catastrophic failure of entire structure. A five-stage closed micro crack localisation method based on time of flight (ToF) of the second harmonic Lamb waves is proposed in this research. The first step is frequency analysis of the received signals to ensure the generation of second harmonic wave. The second step is to extract second harmonic wave component in frequency range. The third step is to obtain wave signals in time domain. The fourth step is to extract ToF of second harmonic wave. The fifth step is to locate damage with ToFs. The method provides an effective strategy based on wavelet transform to extract the second harmonic Lamb waves from the dynamic response signals for the detection of closed micro crack. The numerical and experimental results indicate that the proposed method can accurately locate the closed micro crack in plate-like metallic and composite structures. [ABSTRACT FROM AUTHOR]

Lamb and Rayleigh waves-based dispersion analysis has been carried out for non-destructive surface wave testing of different slab-like structures involving a concrete roof slab, a concrete floor, a concrete pavement, and an asphaltic pavement. An impact was generated by gently striking the slab's free surface with a hammer. A method has also been given to generate the governing (predominant) dispersion mode in the case of Rayleigh wave propagation considering the complex nature of the dispersion function $\vert {{ D}\lpar {c\comma \; \kappa } \rpar } \vert$ | D (c , κ) | ; $c$ c and $\kappa$ κ refer to phase velocity and wavenumber, respectively. The theoretical dispersion plots generated from the inversion analysis by varying the values of different input parameters were subsequently closely matched with the corresponding obtained field dispersion images for different cases in order to back compute the elastic profile of the slab/pavement. For developing the dispersion images, the Park's wavefield transformation method was employed. For checking the thicknesses of the different layers, cylindrical cores were also extracted. The study is expected to be useful for evaluating different slab-like structures, including pavements, by using surface wave-based non-destructive tests. [ABSTRACT FROM AUTHOR]

Debonding regions can occur at the interface of aluminium/rigid polyurethane foam composite plates (ARCP) during manufacturing. To help improve the technological process of manufacture, it is essential to precisely locate these debonding regions. This paper proposed a method to image the debonding regions in the ARCP based on the A0 mode Lamb waves. To study the influence of overlap between the debonding region and the coil of the electromagnetic acoustic transducer (EMAT) on Lamb wave propagation, a three-dimensional finite element simulation model was developed. A positive linear relationship was obtained between the amplitude of the A0 mode and the overlap rate between the debonding region and the coil of the EMAT, which was verified through experiments. Based on such relationship, an imaging method was proposed. The imaging method consisted a horizontal scanning for the entire sample and vertical scanning for possible debonding regions determined from the horizontal scanning. The result of the imaging experiments can precisely reveal the size and position of the debonding regions, the maximum relative error of the centre position of the defect is 7.5% and the maximum relative deviation of the dimensions is 16.0%. This imaging method can serve as a reference for debonding imaging in composite plates. [ABSTRACT FROM AUTHOR]

Lamb and Rayleigh waves-based dispersion analysis has been carried out for non-destructive surface wave testing of different slab-like structures involving a concrete roof slab, a concrete floor, a concrete pavement, and an asphaltic pavement. An impact was generated by gently striking the slab's free surface with a hammer. A method has also been given to generate the governing (predominant) dispersion mode in the case of Rayleigh wave propagation considering the complex nature of the dispersion function $\vert {{ D}\lpar {c\comma \; \kappa } \rpar } \vert$ | D (c , κ) | ; $c$ c and $\kappa$ κ refer to phase velocity and wavenumber, respectively. The theoretical dispersion plots generated from the inversion analysis by varying the values of different input parameters were subsequently closely matched with the corresponding obtained field dispersion images for different cases in order to back compute the elastic profile of the slab/pavement. For developing the dispersion images, the Park's wavefield transformation method was employed. For checking the thicknesses of the different layers, cylindrical cores were also extracted. The study is expected to be useful for evaluating different slab-like structures, including pavements, by using surface wave-based non-destructive tests. [ABSTRACT FROM AUTHOR]

Lamb wave propagation must be understood comprehensively for simply evaluating delamination during ultrasonic testing. However, the difference between wave propagation, visualized using laser Doppler vibrometer and pulsed-laser scanners, has not been sufficiently investigated, and knowledge of optimal conditions for evaluating delamination is limited. Thus, in this study, the mode conversion and multiple reflections of Lamb waves propagating in a delaminated cross-ply laminate were visualized using different laser scanners, delamination depths, and wave incident angles. Delamination was characterized using maximum-amplitude map postprocessing under specific conditions. Further numerical analysis revealed that owing to multiple reflections of the antisymmetric mode in incident and mode-converted waves, standing waves were generated in the delaminated sublaminate. Dispersion curve and flexural stiffness calculations confirmed the conditions required for high-amplitude standing waves, thereby providing guidelines for simply and reliably evaluating delamination during inspections. [ABSTRACT FROM AUTHOR]

Optical security films have gained a lot of attention due to its potential application in authentication services. Electrode-free optical devices are in demand along with electrode devices due to its secure access to the decryption key and ability to hide information from public access. Our concern in this study is the examination of electrode-free optical security film. In such devices, hidden information can be viewed in black/white contrast or controlled birefringent colours, which are produced by patterned phase plate and polariser. In particular, we develop the model of stratified anisotropic media for theoretical description of reflective characteristics of optical security films. Our theoretical results are compared with experimental observations. Blue and yellow birefringent colours of supertwisted nematic liquid crystal cell are achieved by using theory of optical characteristics in anisotropic media and partial coherence. This theoretical analysis suggests new openings in the optimisation of liquid crystal security films. [ABSTRACT FROM AUTHOR]

Electronic circuits must address electromagnetic interference due to high-speed transmissions and simultaneous switching actions. This paper proposes a design of novel planar EBG structure L Bridge with embedded slit type with 3 × 3 array fashion, which can be used in a plane layer of a printed circuit board to reduce simultaneous switching noise (SSN). Two sets of pattern such as alternate structure and entire embedded pattern are considered and measured the cut-off frequencies. The performance of the structure is simulated, experimentally verified using R&S®ZVH Vector Network Analyser for the frequency range 0.1 to 10 GHz and compared the outcomes. It is observed that for the −50 dB of noise depth, proposed structure is achieved 1.6 GHz to 10 GHz as lower and upper cut-off frequency. In addition, this concluded the noise suppression using equivalent circuit model and parallel plate wave guide theory. Signal integrity on this structure is also analysed with single-ended and differential mode signal transition. Eye pattern is generated and compared for measuring and validating the signal quality while using this EBG structure. [ABSTRACT FROM AUTHOR]

This article explores the effects of two temperatures on the combined problem of wave propagation and thermomechanical loading in a homogeneous isotropic plate. The governing equations are converted to non-dimensional form, and the potential functions are introduced to simplify the problem. The plate's surfaces are assumed to be traction-free, rigidly fixed, thermally insulated and isothermal to study the wave propagation phenomenon. Secular equations in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation are derived. The phase velocity and attenuation coefficient are examined for the first problem. The results for uncoupled, coupled, Lord-Shulman (LS) and Green-Lindsay (GL) theories of thermoelasticity have been attained as special cases and agree with that in literature for one temperature theory. In the second part, thermo-mechanical loading has been considered to obtain the expressions of stress and displacement components, conductive and thermodynamic temperatures. The obtained analytical results are computed numerically as well as displayed graphically for copper material to demonstrate the impacts of two temperature theory and compared theoretically as well as numerically with one temperature Lord and Shulman theory. [ABSTRACT FROM AUTHOR]

The current research is concerned with the study of Lamb waves propagating in a traction-free plate with cubic anisotropy along the crystallographic axes. Splitting all cubic crystals into two non-intersecting classes revealed either the appearance or disappearance of the crossing points of the fundamental branches. The spectral analysis of the resolvent matrix in the vicinity of the crossing points showed existence of a two-fold degeneracy with two distinct kernel eigenvectors and absence of the non-semisimple degeneracy, meaning stability of the flexural and symmetric fundamental branches passing through the crossing point. [ABSTRACT FROM AUTHOR]

In nonlinear ultrasonic damage detection, the appropriate Lamb wave mode to accurately characterise the nonlinearity attributed to the material damage should be selected important. However, an effective mode is more difficult to select practically as impacted by the dispersion and multi-mode characteristic of the Lamb wave. In this study, based on the dispersion curve of Lamb waves, the modes meeting the second harmonics and third harmonics phase velocity matching were given, and the nonlinear cumulative effects exerted by different modes on fatigue cracks were compared. In addition, an investigation was conducted on the amplitude change of the second and third harmonics signal of the identical fatigue damage. The results show that the harmonic amplitude decreases with the increase of the fatigue crack length. The third harmonics under the two modes are more sensitive to fatigue damage than the second harmonics. Moreover, the amplitude of the third harmonic excited by S1 mode exceeds that of the other mode. As the fatigue crack length increases, the relative second- and third-order nonlinear coefficients generated by S1 mode have approximately the same trend, first increasing and then decreasing. The results reveal that the third harmonic under S1 mode could more effectively characterise fatigue damage. [ABSTRACT FROM AUTHOR]

Piezoelectric Transducer(PZT) plays a significant role for intelligent materials and structures for its better coupling compatibility with structures. The amplitude imaging is easily influenced by the grating and side lobes, while the phase imaging is disturbed by several random single-pixel highlighted spots. Considering that the combination of the amplitude and phase information, which can be acquired simultaneously by Hilbert transform, could introduce higher robustness and accurateness of damage detection, the array focused Hilbert holographic imaging method for Lamb wave is proposed. A0 mode and S0 mode are also combined to detect surface and inner defects through the logical operation. [ABSTRACT FROM AUTHOR]

Appearance of multiple Sezawa (M2,2) modes and the related interfacial Stoneley waves at propagation of Lamb wave in a stratified medium containing several layers obeying Wiechert condition is observed. Possible appearance of the multiple high frequency Stoneley and Sezawa modes may have importance in various applications starting from micro and nanomechanics to geophysics along with developing the nondestructive acoustic methods for qualitative and quantitative assessment of the high frequency asymptotics. The analysis is based on Cauchy sextic formalism. [ABSTRACT FROM AUTHOR]

The constructed closed form solutions for the long-wave limits for guided waves propagating in anisotropic crystals reveal a principal ability for existence of several long-wave limiting velocities exhibiting dependence on the wave normal. Numerical examples for guided waves propagating on the (1,0,0)-plane of several cubic crystals indicate existence of two distinct long-wave limiting velocities for all directions of the wave normal, except a possible discrete number of directions where two long-wave limiting velocities may coincide. [ABSTRACT FROM AUTHOR]

In this work, ultrasonic guided waves and a dual-branch version of convolutional neural networks are used to solve two different but related inverse problems, i.e., finding layup sequence type and identifying material properties. In the forward problem, polar group velocity representations are obtained for two fundamental Lamb wave modes using the stiffness matrix method. For the inverse problems, a supervised classification-based network is implemented to classify the polar representations into different layup sequence types (inverse problem − 1) and a regression-based network is utilized to identify the material properties (inverse problem − 2). [ABSTRACT FROM AUTHOR]

The closed form expressions for the low frequency velocity limits of Lamb waves propagating in anisotropic homogeneous, stratified and functionally graded (FG) plates with arbitrary elastic anisotropy and arbitrary (continuous) transverse variation of physical properties are constructed. The applied method is based on Cauchy sextic formalism coupled with the stratification convergence theorem for FG plates. The constructed solutions are obtained in the form of vanishing auxiliary determinants related to derivatives of the closed form solutions of dispersion equations. [ABSTRACT FROM AUTHOR]

Rayleigh – Lamb wave propagation in a heterogeneous medium containing an upper sandy layer in a perfect contact with isotropic elastic substrate is analyzed by applying the modified Cauchy sextic formalism. It is also proved that sandy material is essentially anisotropic and should be modeled as an anisotropic material with the cubic symmetry. The performed numerical analysis revealed essential peculiarities with respect to dispersion of Rayleigh – Lamb waves. The observed discrepancy in dispersion portraits of media with sandy layer and with isotropic layer, may be important for the nondestructive evaluation of presence sandy layers in the upper Earth crust. [ABSTRACT FROM AUTHOR]

In this paper, we present the dispersion relation of Lamb waves propagating along one-dimensional phononic and along nesting Fibonacci superlattices, using the plane wave expansion and stiffness matrix methods. More band gaps of Lamb wave appear in nesting Fibonacci superlattices plates than in phononic composite plates. Effect of substrate on band gap structures of nesting Fibonacci composite model is analyzed. In addition, the influence of widths of the materials' strips on the band structure is discussed. Finds could be relevant to understand the intrinsic physical properties of quasi-periodic composites piezoelectric and provide flexible choices to meet real engineering applications. [ABSTRACT FROM AUTHOR]

Among many damage imaging methods based on Lamb wave, phased array Delay and Sum (DAS) has attracted much attention because of its high efficiency. However, inherent dispersion effect leads to the inaccurate acquisition of time-domain features, which affects imaging accuracy. The imaging index based on the amplitude of scattering wave ignores the interaction between Lamb wave and damage, which is difficult to reflect the physical characteristics of damage scattering, and further affects imaging accuracy. We use the physical characteristic parameter-reflectivity of the damage surface as the imaging index and establish an inverse scattering model of damage in frequency domain with dispersion relationship. The simulation and experiment results show that the DAS method combined with the frequency-domain inverse scattering model can realise the high-quality imaging of the damage in the isotropic waveguide structure. [ABSTRACT FROM AUTHOR]

Lamb waves propagating in anisotropic functionally graded (FG) plates with an arbitrary continuous transverse inhomogeneity are considered. Along with the FG plates, stratified ones with the homogeneous physical properties inside the individual layers, are considered. Theorem on convergence of dispersion curves in stratified plates to the corresponding dispersion curves in the FG plates is proved, allowing one to analyze dispersion of Lamb waves in FG plates by constructing the less complicated solutions related to stratified plates. Numerical examples for isotropic FG and stratified plates are considered. [ABSTRACT FROM AUTHOR]

This paper presents a detailed study on detecting defects in isotropic plates by studying scattering analysis of first and second harmonics of symmetric Lamb wave (S0) at cracks in aluminium plates induced by Contact Acoustic Nonlinearity (CAN) using experimental and 3D Finite Element (FE) simulation approaches. In this study, a set of models with different crack sizes and orientations are studied. The effects of crack size and crack orientation on scattering behaviour of first and second harmonics of Lamb waves are investigated. The results show that the Scattering Directivity Pattern (SDP) of Lamb wave around the cracks is significantly influenced by crack size and crack orientation. It is also shown that the largest amplitude of scattered S0 wave is acquired from forward scattering waves for linear waves while the largest amplitude of scattered S0 Lamb wave is obtained from backward scattering waves for nonlinear waves. Therefore, it is expected that pulse-echo sensor configuration enhances nonlinear wave damage detection while pitch-catch configuration may suit better when linear wave is used. It is shown that selecting proper propagation direction for incident wave and proper geometry and angle for monitoring points are the key factors to achieve successful damage detection in isotropic plates. [ABSTRACT FROM AUTHOR]

Guided wave propagation and its dispersion phenomenon of infinite solid elastic rods are encountered in several applications including, mechanical and civil engineering fields. In this paper, the elastic stress wave propagation in the axisymmetric circular cross-section of a high strength steel wire with cylindrical waveguide is investigated using a semi-analytical finite element (SAFE) method. The error analyses are carried out on fundamental modes, namely, flexural F (n , m) , longitudinal L (0 , m) , and torsional T (0 , m) modes. The theoretical framework for finite element (FE) discretization is established for the cylindrical waveguide. A three-node triangular linear element is used for solving SAFE dispersion solutions such as the wavenumber-frequency curve, phase velocity, and group velocity curves. The convergence and accuracy of the method are analyzed by comparing it with the calculation results of the transcendental Pochhammer frequency equation, and the meshing criterion is proposed. The use of higher-order (quadratic) elements are proposed for lower computational burden and effective method for solving eigenvalue problems. The effect of using 6-node triangular quadratic elements in the SAFE method for improving frequency accuracy is discussed in a detailed manner by proposing the meshing criterion. The calculation accuracy of a quadratic element semi-analytical discretization exceeds that of a linear element discretization with four times its radial circumference. The statistical histograms are demonstrated to prove the results of the proposed semi-analytical discretization method which can be used for solving cylindrical waveguides. [ABSTRACT FROM AUTHOR]

We have modeled and investigated band structures and the electromagnetic density of modes in one-dimensional photonic crystal whose refractive index is modulated by the excitation of the fundamental symmetric mode of Lamb wave using the Wigner phase time approach and transfer matrix method. The Rayleigh–Lamb dispersion curves are plotted to select the proper thickness of each sub-layer of considered photonic crystal structure which is comprised of silica (SiO2) and rutile (TiO2) layers as sub-layers of unit cell. The propagation of Lamb wave into the considered structures produced phononic band gaps in gigahertz frequency for acoustic waves. Also, the propagation of Lamb wave into the considered structures causes compression in SiO2 and dilation in TiO2 or vice versa, which can further increase or decrease the refractive index of both layers. Thus, there can be three combinations of change in refractive indices: case 1 (both layers have an unperturbed refractive index), case 2 (maximum change of the refractive index in SiO2 and minimum change in the refractive layer of TiO2), and case 3 (minimum change of the refractive index in SiO2 and maximum change in the refractive layer of TiO2). The band gap structures of considered structures are plotted for both polarized electromagnetic waves. [ABSTRACT FROM AUTHOR]

Considering the frequency dispersion and the scale sensitivity in wave propagation, the central frequency and bandwidth should be carefully selected in Lamb wave-based structural health monitoring. These crucial parameters are hardly determined without the prior knowledge. Therefore, massive trials should be conducted before the formal test. A Fourier spectral Frequency Response Function (FRF) method is proposed to address this problem. As the FRF contains wide-band information on the relationship between excitation and output, the Lamb wave responses in a wide frequency range can be estimated by using an arbitrary virtual input within the frame of single FRF test, being free from the massive experimental works. The theoretical FRF can be obtained from the unit impulse response of a linear system, but this path is impracticable due to the difficulty of exciting the ideal impulse. Considering the integral relationship and Fourier differential properties between step excitation and the ideal impulse, a robust approximation of wave signal by FRF is developed. Synthetic data tests and experiments both verified that the present method can accurately extract the response in isotropic and anisotropic materials for the specifically designed excitation signal in a wide parameter range. [ABSTRACT FROM AUTHOR]

In this paper, local damping behaviour of S0 ultrasonic Lamb mode is investigated to determine the reason of amplitude reduction of signals come from a rich resin defect in a composite plate. A four-layer woven glass fibre-epoxy (WGF/epoxy) composite plate, containing a predefined rich resin area as the damage, has been manufactured and inspected with S0 Lamb mode via through transmission and pulse-echo method. Results have shown that there is a considerable amplitude reduction in the transmitted wave while a negligible damage reflected wave has been captured in the related receiver. An experimental based method has been employed in order to extract Rayleigh damping coefficients for the healthy composite plate, followed by a novel methodology to evaluate the damping coefficients at the defected area. Having calculated Rayleigh damping coefficients for both damaged and undamaged areas of the composite plate, several finite element simulations have been carried out, in order to quantify the wave amplitude reduction due to attenuation at the damage. The Amplitude Reduction Ratio (%ARR), obtained from numerical simulation matches closely with experimental ARR, represents that the proposed method for Rayleigh damping coefficients evaluation at the rich resin area can be used for further rich resin defect investigations. [ABSTRACT FROM AUTHOR]

In this research, a thorough experimental and numerical study is conducted to investigate a novel application of the ultrasonic Lamb waves which is its capability to detect the coating disbond in a double-layer waveguide (aluminium-adhesive) and a triple-layer waveguide (aluminium-adhesive-coating). The experimental tests are set up and implemented to evaluate how the attenuation of Lamb waves is affected by the adhesive bonding beside the contribution of the coating layer to the behaviour of Lamb waves. In the presence of additive white Gaussian noise (AWGN), a range of important indices including energy index (EI), amplitude index (AI), pulse width index (PWI), and the time of flight index (ToFI) are worked out in association with the disbond length. It is inferred that a) even in the very noisy environment of 0 dB SNR, the Lamb waves are effectively able to identify debonding defects particularly using the EI, giving sensitivity rates 105% and 30% for triple-layer and double-layer, respectively; b) the contribution of adhesive to the absorption of the guided wave energy is 30%, 40%, and 50% in EI, AI, and PWI, respectively, corroborating the value of the features to distinguish the debonding between each layer of bonded structures. [ABSTRACT FROM AUTHOR]

Dispersion of Lamb waves propagating in stratified and functionally graded (FG) plates is analyzed by a newly developed variant of Cauchy sextic formalism. Comparative analysis of Lamb wave dispersion in stratified, FG, and homogenized plates reveals a substantial discrepancy in dispersion properties of the studied media, making the use of homogenization techniques almost meaningless, with the only exception at the limiting phase velocity that corresponds to vanishing frequency. At the same time, dispersion curves in the stratified plates converge to the corresponding curves in the FG plate at the increasing number of the stratification layers. [ABSTRACT FROM AUTHOR]

This paper presents a review on the use of SAW for thermal conductivity sensing of gases. Uncoated SAW device is used as a sensing element by exploiting its high temperature sensitivity. The device is heated to a high temperature (100–150°C) and is exposed to a flow of gases at ambient temperature. Due to the temperature gradient there is a heat loss from the device resulting in temperature drop. As the quantum of heat loss depends on the thermal conductivity of the gas, the resultant variation in temperature is a measure of heat capacity of the gas. The paper brings out key advantages of SAW device for thermal conductivity-based sensing. Various SAW substrate materials are compared and their suitability for thermal conductivity application is discussed. Design considerations are discussed and validated with actual design and fabrication of SAW device. Experimental results are also presented for different flow rates of N2 and for mixture combinations of N2 and H2 at constant flow. Various limitations, particularly selectivity, are discussed towards the end and their solutions are also explored. The future trends involving Lamb Wave devices and passive sensing are also discussed. [ABSTRACT FROM AUTHOR]

Being the most detrimental mode in laminated structures, delamination initially degrades local structural strength, and lastly causes global structural failure, thus necessitating delamination identification at its incipient stages. For identification purposes, a comprehensive numerical and experimental study on delamination within both the laminated isotropic acrylic-glass and orthotropic epoxy-glass plates is presented. As the first step, frequency variations in the acrylic-glass plate induced by different-sized delamination are examined at varying the in-plane or out-of-plane location as well as boundary conditions of delamination. Tiny delamination is identified by the use of processed signals of Lamb wave simulated by spectral finite element (SFE) technique in the next step when noticing the delamination-induced changes of frequency to be inefficient for detection purposes. While utilising absorbing layers with the obtained mechanical properties along the axis of symmetry, a quarter of the plate in the SFE domain is modelled. The study is concluded with finding the accurate location and shape of small delamination using A0 or S0 modes. The preference of A0 mode for the delamination identification compared to S0 mode is indicated. Finally, for verification purposes of Lamb wave patterns in real-life applications, a composite epoxy-glass plate is experimentally investigated via laser Doppler vibrometer (LDV). [ABSTRACT FROM AUTHOR]

Due to mechanical loads, thermal fields and the limitation of the manufacturing technology, initial stresses in layered cylindrical structures are ineluctable. Accordingly, for the purpose of the guided wave nondestructive testing for the layered cylindrical structure with a sectorial cross-section, an analytical approach, the double-orthogonal polynomial method is utilized to investigate the influence of axial initial stress on wave characteristics. Based on Biot's "Mechanics of Incremental Deformations", the dynamic equations for the sectorial cylindrical structures in terms of displacements and axial initial stress are deduced. By virtual of the Heaviside function, the boundary conditions are automatically incorporated into constitutive equations and then into wave equations. The corresponding dispersion curves and displacement distributions of various sectorial cylindrical structures are calculated. Numerical results indicate that the influence of the initial stress applied on the outer layer is much significant at low frequencies, and the influence of the initial stress applied on the inner layer is much significant at high frequencies; the cut-off frequencies have negative relation with the area of the cross-section; the displacements at high frequencies are mainly distributed in the layer with smaller elasticity modulus, especially the layer simultaneously with bigger initial stress. [ABSTRACT FROM AUTHOR]

The constantly growing demand for cost-intensive lightweight structures is accompanied by an increased demand for reliable non-destructive testing (NDT) methods. Previous investigations have shown that Lamb Waves (LW) are very well suited for the use in Structural Health Monitoring (SHM) due to their relatively undamped propagation over long distances. Therefore the numerical modelling of a non-contact and automated system for non-destructive testing of C-FRP laminates was investigated in the present study. The method is based on the propagation of LW, which are excited by an actuator-driven piezo transducer and interact with defects in the structure. In contrast to classical Structural Health Monitoring, a scanning inspection system is used instead of a sensor permanently integrated into the structure to detect the measurement signals. For the representation of the wave propagation a three-dimensional simulation model with the commercial FEM software PZFlex was modelled. The wave interactions in defective C-FRP coupons are investigated and visualized through different output formats like A-, B- and C-Scans. Additionally the model allows the determination of the dispersion characteristics of the LW in the examined laminate. The validation of the numerical results was successfully carried out at different levels with the help of experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional waving plate as a fish-like body with unequal amplitude traveling wave motion that the maximum amplitude occurring at the tail in the wind is numerically simulated. We analyze the influence of the maximum amplitude, wavelength, and dimensionless wave velocity on the efficiency of energy extraction. Besides, we compare the unequal amplitude traveling wave motion with the equal one. The findings show that: when the wavelength is constant, the efficiency increases first and then decreases at a certain maximum amplitude with the increasing dimensionless wave velocity. When the dimensionless wave velocity is constant, the efficiency increases at a large wavelength with the increasing maximum amplitude while the efficiency increases first and then decreases at a small wavelength with the increasing maximum amplitude. When the maximum amplitude is constant, the efficiency increases first and then decreases at a certain dimensionless wave velocity with the increasing wavelength. In the same motion parameters, the efficiency of the equal amplitude traveling wave motion is higher than that of the unequal one with the maximum amplitude occurring at the tail. [ABSTRACT FROM AUTHOR]

In this study, an interferometric method was proposed for the simultaneous measurement of phase retardation and fast-axis azimuth angle of a wave plate by using a Mach–Zehnder interferometer. The wave plate to be tested is placed in one of the light passages in the interferometer, and two analyzers with transmission axes at horizontal and vertical orientations are arranged at the two output regions. When a linearly polarized laser light beam is passed through the interferometer, two interference light beams are simultaneously generated. Through an analysis of the intensities of the two light beams, the phase retardation and fast-axis azimuth angle of the tested wave plate can be simultaneously determined using specially derived equations. The feasibility of the proposed method was demonstrated using measurements of zero-order half-wave and zero-order quarter-wave plates. The proposed method is easy to operate, enables rapid measurement, and has high stability and accuracy. [ABSTRACT FROM AUTHOR]

Two-dimensional equations for flexural motions of a lithium niobate piezoelectric plate are derived from three-dimensional equations. The plate has a ferroelectric inversion layer where the piezoelectric constants reverse signs. The equations show an unconventional behavior that a uniform electric field along the plate thickness can produce bending. This offers many possibilities for new designs of devices. Waves in unbounded plates are examined for the accuracy of the equations. A piezoelectric energy harvester based on such a plate is analyzed as an example of the application of the equations derived in vibrations of finite plates. [ABSTRACT FROM AUTHOR]

Recent advances in the field of physical acoustics, imaging, and images processing, piezoelectric materials and ultrasonic transducer designs have led to the emergence of new methods and equipment for ultrasound diagnostics, therapy and esthetic medicine, as well as the development of traditional and emerging new application fields. One of the promising applications of piezoceramics and composite materials are ultrasonic transducers, in particular, high intensity focused ultrasound (HIFU) transducers for medical therapeutic devices. This paper describes the results of the development of mathematical models, numerical modeling and optimization of acoustic fields and designs of composite HIFU transducers, which were made from porous piezoceramics. [ABSTRACT FROM AUTHOR]

Surface acoustic wave devices have widespread applications in various fields including in communication and wireless sensing devices. However some shortcomings like lower sensitivity and the corrosion of IDT's limit their application as sensing devices. Lamb wave SAW devices have proved to be promising for sensing applications. In the present work effort has been made to find out the optimum etching temperature in order to get the sufficiently fast etch rate and smooth surface for the fabrication of SiO2/Si membrane for Lamb wave acoustic (LWA) devices. Piezoelectric ZnO thin film deposited using rf sputtering technique has been integrated with the SiO2/Si membrane. The bulk etching of Silicon has been carried out from back side of each LWA device using wet etching. The devices are packaged and frequency response is studied using a network analyzer. The antisymmetric and symmetric modes of the Lamb wave devices have been identified. [ABSTRACT FROM AUTHOR]

Experimental results on application of ultrasonic technique utilizing Lamb waves for evaluation mechanical state of AA2024T3 specimens under tensile testing are presented. PZTs used as actuators and sensors were glued onto the specimen surface with epoxy adhesive. The set of static tensile tests with two frequencies of acoustic testing (50 kHz and 335 kHz) were performed. The recorded signals were processed to calculate the informative parameters (maximum envelope and 2nd central moment) in order to evaluate the changes of the stress-strain state of the specimen and its microstructure evolution. The relations between acoustic signal features and damages occurring during the loading allow determining the defectiveness of the structure and predicting its residual lifetime. [ABSTRACT FROM PUBLISHER]

In this study, an optical scheme based on the measurement of light intensity and a proper orientation of the Fresnel Rhomb is successfully developed for simultaneous determination of the phase retardation and fast axis of a wave plate. The theoretical analysis of the principle of measuring the reflection-induced retardance of the Fresnel Rhomb and the phase retardation of a wave plate is given taking Stokes–Mueller Formalism as a mathematical tool. In this method, the fast axis position of the wave plate need not be determined in advance. In addition, the measured result is free of the intensity fluctuation of light source. An application example is also demonstrated. The measured result of the example is verified with an experiment. Some of the merits of the method, such as, a simple optical set-up, high stability and high accuracy, low cost and easier operation, are presented, and the validity of the method is demonstrated. [ABSTRACT FROM PUBLISHER]

Wave-plate separators are widely used to remove fine liquid droplet entrained in gas flow based on the inertia force difference of gas and liquid phase. The CFD method is adopted to simulate the separating process of wave-plate separator, the models and parameters used in the simulation were verified through comparing with the experimental data. It is validated that including the droplet coalescence and breakup model, which take place during the separating process, can depict the separating process better. The results indicate that the separation efficiency of wave-plate separator presents two peaks with the increasing of the separating velocity, the first peak is caused by gravity and the second peak is formed for the inertia separation, whereas with the increasing of the droplet diameter, the two peaks are no longer distinct. In addition, the separation efficiency is changed little with droplet diameter variation if the wave-plate separator is worked on the corresponding velocities of the two peaks, and changed a lot at other velocity. Researching results about droplet breakup also showed that only large diameter droplet will break up at lower flow velocity, and the droplet breakup diameter became smaller and smaller with the increasing of the flowing velocity. [ABSTRACT FROM AUTHOR]

The Lamb wave dispersion in a PZT/Metal/PZT sandwich plate is investigated by employing the exact linear equations of electro-elastic waves in piezoelectric materials within the scope of the plane-strain state. It is assumed that at the interfaces between the piezoelectric face layers and metal core layer, shear-spring and normal-spring type imperfect conditions are satisfied. The degree of this imperfectness is estimated through the corresponding shear-spring and normal-spring type parameters which appear in the contact condition characterizing the transverse and normal displacements’ discontinuity. The corresponding dispersion equation is derived, and as a result of the numerical solution to this equation, the dispersion curves are constructed for the first and second lowest modes in the cases where the material of the face layers is PZT and the material of the middle layer is Steel (St). Consequently, for the PZT/St/PZT sandwich plate, the study of the influence of the problem parameters such as the piezoelectric and dielectric constants, layer thickness ratios, non-dimensional shear-spring, and normal-spring type parameters, is carried out. In particular, it is established that the imperfectness of the contact between the layers of the plate causes a decrease in the values of the wave propagation velocity. [ABSTRACT FROM PUBLISHER]

The disperse curves of lamb waves in glass fibre reinforced aluminium laminate (GLARE laminate) is the basis of GLARE laminate's ultrasonic lamb waves' detection. In this paper, air-coupled ultrasonic transmitter-receiver system and transducers were used to generate and receive lamb waves in the GLARE laminate. Continuous wavelet transform was applied to the lamb waves' signals to obtain the characteristic information in time-frequency domain. Select the points from the contour line and draw the disperse curves. Compare the experimental disperse curves with the theoretical ones. The experimental results of the A0 mode agree well with the theoretical dispersion curve. [ABSTRACT FROM AUTHOR]