Lamb Modes Research Articles

Modeling lamb wave propagation in visco-elastic composite plates using a fifth-order plate theory

A new extension of the shear deformation theory to fifth order in order to calculate the spectrum of Lamb waves in orthotropic media over a wide frequency range is developed and analyzed. The aspiration of the proposed method is to create an alternative framework to exhaustive 3D elasticity based solutions by increasing computational efficiency without losing accuracy, nor robustness. A new computational framework is introduced which allows to estimate the dispersion curves for the first nine symmetric and nine anti-symmetric Lamb modes. Analytically calculated dispersion curves using 5-SDT for different propagation directions and polar plots for selected frequency of different materials are compared with the results from both the semi analytical finite element method, and lower order shear deformation theories. Careful analysis for individual laminae and for symmetric composite laminates exhibits a good agreement between the new higher order plate theory and the semi analytical finite element method over an extensive frequency range. In addition, attenuation plots show that the proposed method can also be used for visco-elastic materials (or highly damped materials). The advantage of the new higher order plate theory and its numerical implementation is that it is much more computationally efficient compared to comprehensive methods as Lamb wave polar plots of composite plates as function of incidence angle, polar angle and frequency can be calculated in less than a second on a standard laptop. Consequently, the use of this framework in inversion routines opens up the possibility of quasi real-time Structural Health Monitoring for visco-elastic composites covering a sufficiently wide frequency range.

Radiation Characteristics of Cranial Leaky Lamb Waves.

We numerically and experimentally investigate the dispersion properties of leaky Lamb waves in the cranial bone. Cranial Lamb waves leak energy from the skull into the brain when propagating at speeds higher than the speed of sound in the surrounding fluid. The understanding of their radiation mechanism is significantly complicated by the geometric and mechanical characteristics of the cortical tables and the trabecular bone (diploë). Toward such understanding, we here analyze the sub-1.0 MHz radiation angle dispersion spectrum of porous bone phantoms and parietal bone geometries obtained from μ CT scans. Our numerical results show that, when diploic pores are physically modeled, leakage angles computed from time transient finite-element analyses correspond to those predicted by an equivalent three-layered fluid-loaded waveguide model. For the bone geometries analyzed, two main leaky branches are observed in the near-field dispersion spectrum: a fast wave radiated at small angles, which is related to the fastest fundamental Lamb mode supported by the cranial bone, and a slower wave radiated at larger angles. This observation is also confirmed by experimental tests carried out on an immersed parietal bone.

Random versus regular square lattice experimental comparison for a subwavelength resonant metasurface

An experimental comparison is reported here between two equivalent resonant subwavelength metasurfaces made of long aluminum beams glued closely together on a thin aluminum plate. One metasurface has a random distribution of the resonator beams, and the other has a regular square lattice of pitch 1.5 cm. The random lattice shows the "resonant" behavior of a typical metasurface, with a wide full bandgap for the first A0 Lamb mode. Instead, the regular square lattice combines Fano resonance with Bragg scattering at the edges of the passband, thus creating anisotropy and a pseudo bandgap. Comparisons with numerical simulations are performed, with good agreement with the experimental data. The multimodal response of the beams is also responsible for double negativity in a narrow frequency band, and the event of a pseudo bandgap around this same flexural resonance. In addition, the scattering regimes for both the random and regular metasurfaces are characterized using coherent and incoherent signal analysis.

Switchable Transducers in GaN MEMS Resonators: Performance Comparison and Analysis.

This work presents a comprehensive comparison of switchable electromechanical transducers in an AlN/GaN heterostructure toward the goal of reconfigurable RF building blocks in next-generation ad hoc radios. The transducers’ inherent switching was achieved by depleting a 2D electron gas (2DEG) channel, allowing an RF signal launched by interdigital transducers (IDTs) to effectively excite the symmetric (So) Lamb mode of vibration in the piezoelectric membrane. Different configurations for applying DC bias to the channel for electromechanical actuation in the piezoelectric are discussed. Complete suppression of the mechanical mode was achieved with the transducers in the OFF state. Equivalent circuit models were developed to extract parameters from measurements by fitting in both ON and OFF states. This is the first time that an extensive comparative study of the performance of different switchable transducers in their ON/OFF state is presented along with frequency scaling of the resonant mode. The switchable transducer with Ohmic IDTs and a Schottky control gate showed superior performance among the designs under consideration.

Lamb waves in the wavenumber–time domain: Separation of established and non-established regimes

This article deals with the dynamic response of laterally unbounded, horizontally layered plates subjected to dynamic sources applied at arbitrary locations, which is ultimately a classical problem. This response is most often obtained via a modal superposition in terms of the complex Lamb modes by casting the equations in the frequency–space domain, followed by a Fourier inversion into the space–time domain. Then again, a much less often used alternative method relies on formulating the problem directly in the time domain in terms of a modal superposition in the wavenumber domain, which is followed by a Fourier inversion into the space–domain, as considered in further detail herein. This alternative can offer powerful advantages in some cases, such as dealing easily with anisotropy, or with slowly propagating waves even in the absence of damping. At the same time, however, it is beset by difficulties associated with the Fourier inversion into the space–domain. As a matter of fact, during forcing, the truncation of the modal series and of the numerical integrals is hindered by poorly convergent behaviors. Here we overcome both of these difficulties by considering the asymptotic, static behavior of the integrands. We find that by introducing a regularizing term, the response can be effectively separated into near and far fields, despite the fact that these frequency-domain concepts are alien to a wavenumber–time formulation. The so-defined far field is free of sharp variations and can then be computed in a numerical grid that is optimized regarding the propagating wavelengths, which only depend on the time-spectral content of the excitation and not on its space-spectrum. Finally, we also propose a hybrid way to compute the remaining near field by combining with a non-modal formulation, expressed in the wavenumber–Laplace domain.

Experimental and numerical analysis of Lamb wave transmission through the coronal suture of a dry human skull

Cranial Lamb waves have recently gained attention as potential means for ultrasound imaging and diagnostics of the skull. The inherent capability of these waves to travel for long distances across the cranial vault requires the understanding of transmission mechanisms across cranial sutures, which remain mostly unexplored. This work investigates such mechanism in the coronal suture of a dry human skull. The transmission analysis is performed experimentally by recording velocity arrays induced by short tone-bursts along curvilinear paths that intercept the suture at different locations. For each path, the experimental frequency-wavenumber spectrum of the incident wave indicates the presence of fundamental and higher order Lamb modes, with transmission being mainly associated with the fundamental antisymmetric Lamb mode. By calculating the corresponding transmission coefficients and comparing them with those obtained from a semi-analytical multilayered model of the cranial bone, we demonstrate that the coronal suture can be described by a simplified constitutive law defined by distributed shear and compressional stiffness coefficients. The experimental results and the estimated suture constitutive parameters provide the basis for a comparative analysis of the suture mechanical properties at different spatial locations, which may be employed for suture characterization and imaging.

Multiple crossing points of Lamb wave propagating in a magneto-electro-elastic composite plate

This article is concerned with the propagation of guided type-Lamb waves in a magneto-electro-elastic composite plate. As a numerical method, the ordinary differential equation with the Thomson Haskell parameterization of Stroh formalism is employed to determine the wave characteristics in the composite plate by imposing the traction-free boundary condition on the top and bottom surfaces. Multiple crossing appears in the dispersion curves between the symmetric and the antisymmetric Lamb modes, which makes the dispersion curves more complicated and interesting to study. We are trying in this research to find, are these modes really coupled and why? For that, a set of numerical results are presented like the dispersion curves, the non-dimensional frequency, bulk waves slowness curve as well as the mechanical displacement U1 and U3 versus the non-dimensional thickness. These results could be interesting for the analysis and design of new acoustic devices based on magneto-electro-elastic material as well as a good candidate for nondestructive testing technology.

Abnormal dispersion of fundamental Lamb modes in FG plates: II—symmetric versus asymmetric variation

A closed-form dispersion equation for Lamb waves propagating in functionally graded (FG) plates with arbitrary varying anisotropic physical properties in transverse direction is constructed by applying Cauchy sextic formalism. Comparative analyses of the dispersion curves related to the fundamental modes of homogeneous and FG plates reveal their substantial and visually detected differences even at sufficiently small transverse inhomogeneity. The observed discrepancy in dispersion curves may serve for developing acoustic nondestructive methods for determination of possible transverse inhomogeneity.

Broadband piston mode operation of solidly mounted resonator employing A1 Lamb mode on lithium niobate

This paper discusses the impact of etched holes given to the solidly mounted resonator (SMR)-supported A1 Lamb mode resonators. The authors pointed out that the etched holes are effective at suppressing the lateral leakage and the transverse mode resonances for free-standing A1 Lamb mode resonators, and the technique was named the broadband piston mode (BPM). First, the SMR structure is designed for an A1 Lamb mode resonator, and it is shown that the release windows are effective in the suppression of transverse mode resonances even when the SMR is added. Detailed analysis is given to spurious responses that newly appeared by applying the SMR. Then, the discussion is extended to the impact of partial etching of the SMR layers underneath the release windows. The result indicates that the etching of the top SMR layer is enough for recovery of the BPM function.

Effects of multiaxial pre-stress on Lamb and shear horizontal guided waves

A theoretical model is derived to extend existing work on the theory of acoustoelasticity in isotropic materials subjected to uniaxial or hydrostatic loadings, up to the case of arbitrary triaxial loading. The model is applied to study guided wave propagation in a plate. The semi-analytical finite element method is adapted to deal with the present theory. Effects of triaxial loading on velocities of Lamb and shear horizontal (SH) modes are studied. They are non-linearly dependent on stress, and this nonlinearity is both frequency-dependent and anisotropic. Velocity changes induced by the effect of stress on the plate thickness are shown to be non-negligible. When a stress is applied, both Lamb and SH modes lose their simple polarization characteristics when they propagate in directions different from the principal directions of stress. The assumption that effects induced by a multiaxial stress equal the sum of effects induced by each of its components independently is tested. Its validity is shown to depend on frequency and propagation direction. Finally, the model is validated by comparing its predictions to theoretical and experimental results of the literature. Its predictions agree very well with measurements and are significantly more accurate than those of existing theories.

A novel damping based feature for rich resin defect detection in a four layer composite plate using S0 Lamb mode

ABSTRACT 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.

Ultralow-frequency tunable acoustic metamaterials through tuning gauge pressure and gas temperature

Acoustic metamaterials possessing subwavelength characteristics can be used for low-frequency noise and vibration control. Acoustic metamaterials with adjustable dynamic properties can further enhance their possible applications. This paper designs a kind of tunable acoustic metamaterials consisting of the frame structure, airbag, and balancing weight. And their dynamic characteristics can be manipulated by tuning gauge pressure and gas temperature in the airbag. The calculation results indicate that the tunable acoustic metamaterials can effectively suppress the wave propagation and vibration in the ultralow-frequency band gap (about 13Hz∼90Hz) during manipulation. The complete band gap is the overlapping frequency range of an out-of- and in-plane band gaps. Numerical analyses indicate that the formation of out-of-plane band gap is due to the coupling between the out-of-plane resonant mode of balancing weight and the anti-symmetric Lamb mode of the frame structure. In contrast, the formation of an in-plane band gap is due to the coupling between the in-plane resonant mode of balancing weight and the symmetric Lamb mode of the frame structure. Meanwhile, the manipulation mechanism of these band gaps stems from the fact that through tuning gauge pressure or gas temperature, the structural stiffness of the airbag (torsional stiffness, in-plane, and out-of-plane stiffness) and frame structure (in-plane and bending stiffness) can be significantly tuned so that the modes related to them can be manipulated. The tunable acoustic metamaterials can be used for active control of low-frequency vibration and noise. It is possible to provide guidelines for designing other acoustic metamaterials to suppress low-frequency vibration and noise.

Lamb wave coupled resonance for SAW acoustofluidics

A surface acoustic wave (SAW)-driven acoustofluidic chip of high energy efficiency is proposed through model analysis. The chip supports propagation of Lamb waves in the lid above a fluid-filled channel. Eigenmode resonance in the on-chip channel is then achieved by coupling both the SAWs and the Lamb waves into the fluid. Specifically, the phase velocity of the Lamb mode equals the SAW speed along the substrate, and the leaky angles of both match that required by the expected channel mode. Compared to resonant SAW acoustofluidics (RSA), Lamb wave coupled RSA can make the energy tripled or higher. Meanwhile, the obtained resonance frequency deviates very slightly from the designed value, limiting the error to 0.5, while RSA chips exhibit errors as high as 5.7. The proposed design protocol can help to promote the energy efficiencies and contain the in-channel temperature rise and resonance frequency deviations in SAW acoustofluidics.

Enabling the complete mode conversion of Lamb waves into shear horizontal waves via a resonance-based elastic metamaterial

Manipulating the conversion phenomena among different wave modes is of great interest within the physics and engineering communities. In this Letter, a resonant elastic metamaterial is elaborately designed to achieve complete conversion from Lamb modes (A0 and S0) into the fundamental shear horizontal (SH0) mode. The key to achieving this interesting behavior resides in the design of a pillared perforated metamaterial, providing the strong coupling between the stub modes in shear resonant motion and the plate modes in the substrate medium. Both numerical modeling and experimental verification are conducted to validate the achievement of the mode conversion phenomenon.

Nondestructive characterization of mechanical properties on metallic and polymer plates using hybrid laser-air coupled ultrasonic techniques

Ultrasonic non-destructive techniques have been extensively used in various applications such as material characterization to extract important properties of materials. This work presents a non-contact hybrid system which integrates laser ultrasound and air-coupled transducer for generation and detection of guided waves. Furthermore, by adjusting the air-coupled transducer for an estimated angle, A0 S0 Lamb modes and longitudinal waves was detected in aluminum, stainless steel, and epoxy resin plates. Subsequently, the experimental measurements of dispersion curves are computed and Young’s modulus, thickness were calculated using inversion technique. Results show that the error percentage of Young’s modulus and thickness was about 7.60% and 9.26% for aluminum plate while the steel plate showed with 3.98% and 3.58%. Besides, the error percentage of Young’s modulus and thickness was about 4.05% and 5.88% for epoxy resin plate. The obtained experimental measurements were in good agreement with inversed material properties, which verified that the hybrid laser-air coupled ultrasonic technique can prove that the system is feasible, and the accuracy can be improved in the future to measure the material properties and geometrical character of metallic and polymer plates.

Modulating optical properties of Lithium Niobate through acoustic stress

Optical index modulation in Z-X Lithium Niobate slab through acoustic stress is theoretically studied. To generate acoustic stress, fundamental symmetric Lamb mode is excited in the slab. A periodic disturbance of period 858 nm in 500 nm thick slab is noticed when 5 GHz frequency Lamb wave mode is used. The displacement field pattern caused by 5 GHz acoustic disturbance is then estimated using potential techniques and applied to photo-elastic relations. Theoretical calculation reveals that the disturbance modulates optical index sinusoidally, with alternate decrement and increment in optical index around the unperturbed value. The maximum observed variation was found along the direction of acoustic wave propagation is of order of 1.5 percent.

Scattering of Lamb Waves Near Lamé Point at an Opening Crack

Abstract The scattered fields of Lamb waves resulting from damage have been extensively studied because they carry rich structural information that allow us to identify and evaluate damage. This paper investigates the interaction of the fundamental symmetric Lamb mode (S0) near the first Lamé point with opening cracks of various heights under the plane strain condition. The scattering coefficients obtained by the semi-analytical method indicate a significant non-mode-conversion point, where the mode conversion is very weak. The frequency of this non-mode-conversion point originates in the first Lamé point and increases linearly with the crack height when the normalized height is less than 25%. The finite element simulations validate the calculation results. In addition, similar phenomena are also observed for the scattering at a symmetric internal crack. These interesting scattering characteristics are related to the special mode shapes near the Lamé point, which may provide a candidate to evaluate the height of an opening crack.

Monitoring internal corrosion in steel pipelines: a two-step helical guided wave approach for localization and quantification

This article presents a two-step approach for the assessment of internal corrosion in cylindrical structures using helical guided ultrasonic waves. The approach consists of two steps such as (1) localization and (2) estimation of the size of the corroded area. Localization is performed with the algebraic reconstruction technique where the energy ratio of the two fundamental Lamb modes S0 and A0 is used as input damage coefficient. Using the output of the localization step, the size of the corroded area is estimated by iteratively solving the eikonal equation using a finite-difference approach. The proposed approach is validated by an accelerated corrosion test. Furthermore, numerical simulations are carried out to study the interaction of the energy ratio and the phase velocity travel time with various thickness profiles acquired from the experiment. The proposed approach is validated against the experimental data up to approximately 50% thickness loss.

Influence of a piezoelectric ZnO intermediate layer on Rayleigh waves propagating in Sc43%AlN57%/ZnO/diamond hetero-structures subjected to uniaxial stress

Surface acoustic waves (SAWs) are of practical importance across several fields. Particularly, a wide range of SAW devices is available, which are based on the stacking piezoelectric layered hetero-structures. As such, efficient and stable algorithm of analyzing electromechanical coupling factor (K2) should be of specific interest, inspiring a variety of piezoelectric layered structures. Motivated by the above considerations, this paper exploits the performance of Sc43% AlN57%/ZnO/diamond piezoelectric hetero-structures using matrix and polynomial methods. Consequently, dispersion curves, the electromechanical coupling factor and profiles of Rayleigh waves are calculated, in which the properties of hexagonal intermediate ZnO layer are varied. Here, $$ (0001) - [10\bar{1}0]{\text{ZnO}} $$ or $$ (11\bar{2}0) - [0001]{\text{ZnO}} $$ directions of the middle layer were integrated with Sc43% AlN57%/diamond to be a composite hetero-structure with a larger K2 of SAW. Accordingly, a commercial ZnO specimen was characterized by scanning electron microscopy (SEM) as well as Raman and XRD spectroscopy to determine its available crystallographic directions and the C-axis hexagonal character. Comparing with conventional AlN/diamond hetero-structures, the inclusion of ZnO as the intermediate layer provides with an excellent electromechanical coupling factor which significantly improves the $$ (11\bar{2}0) - [0001] $$ structure. However, comparing with the ZnO/diamond hetero-structure, a high phase velocity (Vph) was observed. Therefore, the development of a well-balanced structure that maximizes the values of Vph and K2 is systematically challenging. Moreover, it was found that initial stresses have a significant effect on the Rayleigh wave velocities. Fundamental A0 Lamb mode can be generated in piezoelectric hetero-structures when the properties of substrate remain very low relative to the film. Numerical results obtained in this paper can provide a deeper insight into the nature of the Rayleigh wave behaviors in piezoelectric hetero-structures, involving a ZnO intermediate layer.

Hybrid laser and air-coupled ultrasonic defect detection of aluminium and CFRP plates by means of Lamb mode

This study presents two non-contact systems – hybrid laser with air-coupled ultrasound and pure air-coupled ultrasonic system for the non-destructive inspection and detection of flaws in CFRP and aluminium plates. B-scans are used to identify the size and location of the defects. The defects are detected through changes in amplitude of the waves passing through them. B-scans, represented as intensity graphs, clearly show the changes in the defect profiles. In addition, there is agreement between the experimental values of the diameter of the defect and the measured values. The two systems and configurations are tested and compared in order to determine their effectiveness in defect identification. The results of this study prove the potential of these non-destructive and non-contact systems for defect detection in aluminium and CFRP composites.