Flexural Lamb Waves Research Articles

Transverse cracking signal characterization in CFRP laminates using modal acoustic emission and digital image correlation techniques

The process of formation and subsequent propagation of transverse cracks in 90° plies of carbon-fiber laminated composites was studied using modal acoustic emission approach and digital image correlation techniques. The results from modal acoustic emission approach, which included a newly developed processing tool for acoustic emission waveforms, provided information for identification and subsequent characterization or localization of signals originating from transverse cracking by analysis of the separated flexural and extensional Lamb wave modes in terms of their modal parameters. The digital image correlation method served as a verification tool of the acoustic emission data outputs in the terms of activity of significant localized events originating from the formation of the transverse crack in the 90oply. This made it possible to specify more locally the accompanying activity belonging to the formation or propagation of the magistral transverse crack. The manuscript also presents results related to the evolution of flexural/extensional wave modal parameters as the function of loading force for both [0/0/0/90]S and [90/0/0/0]S panels. It can be concluded that the detection of transverse cracks requires the need for applying a more complex acoustic emission data analysis methodology, while the standard parametric analysis, including the waveform peak frequency, is not sufficient. The presented methodology may serve as a basis for development of robust analysis tool capable of detecting the investigated phenomena.

Elliptic pillars based metasurface for elastic waves focusing in a plate

In this paper, the ability of a metasurface made of resonant elliptical pillars to focus flexural Lamb waves in the sub-wavelength regime is investigated. We report on the influence of the ellipticity parameter on the local resonances of the pillars, in particular the monopolar compressional and dipolar bending modes that are responsible for the desired focusing effect. We also discuss how the transmission through a line of pillars reveals these modes when the orientation of the pillars is changed with respect to the incident wave. Both the resonances can be superimposed for a particular choice of the ellipticity parameter, allowing a phase shift of 2π in the transmission coefficient for an incident antisymmetric Lamb wave, which is a necessary condition for the design of the metasurface. Finally, a gradient design for the pillar ellipticity is investigated, and its capacity to choose the focusing directionality of the transmitted wave at different targeted points is demonstrated.

Broadband acoustic black hole for wave focusing and weak signal sensing

In this work, we investigate wave focusing and weak signal sensing in the circular acoustic black holes (ABHs) with varying plate thickness. We magnify the subwavelength yet strong focusing of the lowest-order flexural Lamb (A0) wave in ABHs with different sizes. Both the experimental and numerical results show the focal position in good agreement with the analytical solution of ray trajectories. In particular, we investigate the weak signal sensing at the focal zone of ABH, and we find that the weak signals with low signal to noise ratio are extremely amplified by ABH. Lastly, we show the broadband feature of A0 wave focusing and we attribute the upper frequency limit to the simultaneous generation of multiple Lamb waves. The broadband wave focusing and weak signal sensing effect can be extended to ABH embed in other complex plates and find potential applications in structural health evaluations.

The holographic algorithm and design for propagation of flexural Lamb waves and particles manipulation using elastic metasurfaces

Controlling propagation of flexural waves is fundamental for energy and information transportation. In recent years, the acoustic holographic method has been developed in air and water for controlling arbitrary wavefronts. Nevertheless, it has not been applied to flexural Lamb waves. Considering the similar form of wave equation, here we develop the Weighted Gerchberg–Saxton(GSW) holographic algorithm for propagation of flexural Lamb waves. The labyrinth-type metasurfaces are used to modulate the amplitudes and phases by the holographic algorithm. Different kinds of wavefronts for the flexural Lamb waves, such as acoustic focusing, are achieved both numerically and experimentally, which can match well with each other. The holographic algorithm for the multi-frequency range is further developed, which is suitable for tuning the flexural Lamb waves. Additionally, we realize the acoustic cloaking by the holographic flexural waves bottle. The flexural waves can be designed to circumvent the obstacle. Finally, the particles are trapped to the nodal lines, which is utilized for visualizing the flexural waves. The splitting of particles pile is further realized by the focusing of flexural waves. This work paves the way for controlling propagation of flexural Lamb waves, thereby opening up the realm of energy transportation, acoustic cloaking, and nondestructive testing.

Flexible and bendable acoustofluidics for particle and cell patterning

Surface Acoustic Wave (SAW) based microfluidic devices provide active techniques to manipulate fluid and particles, which can be used for precise and controllable patterning of microparticles and biological cells, with a high efficiency in a non-invasive and contact-free manner. This paper investigates flexible and bendable SAW microfluidic devices and explores the effects of bending and twisting of SAW devices on microparticle and cell patterning, using both experimental and numerical modelling. We showed that bending flexible SAW devices changes the distribution of particle pattern lines significantly. In devices with concave bending the particle pattern lines converge towards the centre of the curvature, whereas for devices with convex bending, they diverge away from it. Comparing the particle patterning using Lamb and Rayleigh wave devices with concave bending, we found that particle alignment is more efficient in the flexural mode Lamb wave device, whereas for the devices with convex bending, the particle patterning is more clear and regular when Rayleigh waves are used. We further investigated the effects of twisting the flexible SAW devices and observed that the particles are patterned into lines parallel to the deformed interdigital transducers (IDTs). We finally patterned yeast cells using our flexible SAW devices, and demonstrated the possibility of using our flexible acoustofluidic device for biomechanical systems such as body conforming technologies, wearable bio-sensors, and flexible point-of-care devices for personalized health monitoring.

Development of PZT fiber rosette to locate acoustic source

Because of their electro-mechanical coupling property, Lead-Zirconate-Titanate (PZT) materials have been widely used for ultrasonic wave sensing and actuation in structural health monitoring applications. In this paper, a PZT rosette concept is proposed to conduct Lamb wave-based damage detection in panel-like structures by exploring its best directional sensing capability. First, a directivity study was conducted to investigate sensing of flexural Lamb wave propagation using a PZT fiber having d33 effects. Then, commercial off-the-shelf PZT fibers were polarized in-house in order to construct the PZT rosette configuration, in which three PZT fibers are oriented at 0°, 45°, 90°, respectively. Since Lamb wave responses are directly related to measured PZT fiber voltage signals, a simple interrogation scheme was developed to calculate principal strain direction in order to locate an acoustic source. Comprehensive tests were conducted to evaluate the performance of the proposed PZT rosette using an aluminum plate. It is shown that the PZT rosette is able to sense Lamb wave responses and accurately locate an acoustic source. We expect to further evaluate the PZT rosette performance when damages are introduced.

Abnormal dispersion of flexural Lamb waves in functionally graded plates

A closed-form dispersion equation for Lamb waves is obtained for analyzing dispersion in functionally graded (FG) plates with arbitrary anisotropy and arbitrary transverse inhomogeneity. The dispersion equation is derived and analyzed by a variant of the sextic formalism, previously developed for Lamb waves propagating in anisotropic layered plates with homogeneous layers. For the case of FG plates with transverse asymmetric inhomogeneity, some peculiarities in dispersion of the fundamental flexural Lamb mode are observed, revealing discrepancy in asymptotic behavior at high frequencies between homogeneous and FG isotropic plates.

Lamb Wave Directional Sensing with Piezoelectric Fiber Rosette in Structure Health Monitoring

Directional piezoelectric sensors can detect the Lamb wave propagation direction to locate damage in structural health monitoring (SHM). The directivity of the round piezoelectric fiber is exploited with a 0°/45°/90° rosette configuration to acquire flexural Lamb wave signals. The directional response of the piezoelectric fiber under narrowband tone‐burst excitation is theoretically deduced. Experimental tests are conducted to demonstrate the directivity and the frequency response property of the piezoelectric fiber under different excitation central frequencies in comparison with the MFC, rectangular piezoelectric sheet, and circular piezoelectric disc. Continuous wavelet transform (CWT) is applied to extract the maximum response amplitude information of the acquired Lamb wave signal at a central frequency. Experimental test results indicate that the piezoelectric fiber is capable to be used as a Lamb wave directional sensor than other piezoelectric sensors. A numerical estimation method for the Lamb wave propagation direction is proposed by defining an error function between the theoretical and experimental normalized response amplitude. The proposed method is generally applicable for different rosette configurations. Experimental results validate the accuracy of the proposed estimation method. The research results are significant to design or select the piezoelectric sensor to measure Lamb wave signals.

Parametric Analysis of Complex Dispersion Curves for Flexural Lamb Waves in Layered Plates in the Low-Frequency Range

A combined asymptotical and iteration method is used to study dispersion curves for the case of dynamic bending of isotropically layered plates. Based on the explicit limit formulation of dispersion equation, asymptotics of roots are derived in closed form for large values of root moduli. The influence of elastic and geometric parameters of layers are analyzed. The existence of critical values of geometric parameters that correspond to change of the type of asymptotics is demonstrated. The errors of asymptotics are estimated, and an iterative method is proposed for calculating the exact values of roots in statics. A low-frequency long-wave asymptotics of complex dispersion curves is derived; its accuracy is the higher the lower the frequency and the greater the number of the curve are. It is also proved that each complex curve has a long flat segment, the length of which increases simultaneously with the number of curve. The dispersion curves themselves are also calculated by another specific iterative procedure. The fundamental bending mode is analyzed together with its purely imaginary sister. The existence of the additional purely imaginary curve at low frequency is proved. Examples of calculating the static roots and the dispersion curves for subcritical and supercritical values of geometrical parameters are presented, and the efficiency of the algorithm is estimated.

Effect of microannulus on ultrasonic pulse-echo resonance, flexural, and extensional Lamb-wave cement-evaluation measurements

Subterranean wells are usually constructed by cementing steel tubes, called casings, inside the borehole. The cement quality is typically verified through ultrasonic measurements deployed from inside the casing. Environmental effects such as cement shrinkage or changes in static pressure can alter the bonding properties between casing and cement with significant effects on the acoustic measurement response. The cement may detach from the casing, opening a gap, called a microannulus. This microannulus is sized from submicrometer to hundreds of micrometers and filled with either gas or liquid. The subwavelength nature of the microannuli does not allow a direct, unambiguous characterization through an ultrasonic measurement. We studied the measurement signature of ultrasonic-pulse-echo resonance, and flexural and extensional Lamb waves for air- and liquid-filled microannuli for various annulus materials and steel-casing thicknesses. This characterization allows statistically linking measured results to microannulus widths. The highest-precision measurements used in-situ laser interferometry through transparent annulus samples to characterize the microannulus thickness.

The influence of the initial stresses on Lamb wave dispersion in pre-stressed PZT/Metal/PZT sandwich plates

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.

A self-assembled metamaterial for Lamb waves

We report the design and characterization of a self-assembled, locally resonant acoustic metamaterial for Lamb waves, composed of a monolayer of 1.02 μm polystyrene microspheres adhered to a 1.27 μm thick free-standing silicon membrane. A laser-induced transient grating technique is used to generate Lamb waves in the metamaterial and to measure its acoustic response. The measurements reveal a microsphere contact resonance and the lowest frequency spheroidal microsphere resonance. The measured dispersion curves show hybridization of flexural Lamb waves with the microsphere contact resonance. We compare the measured dispersion with an analytical model using the contact resonance frequency as a single fitting parameter, and find that it well describes the observed hybridization. This study may lead to an improved understanding of microscale contact mechanics and to the design of new types of acoustic metamaterials.

Diagnostics of metal plates with residual stresses and defects by nonlinear scanning laser vibrometry

Nonlinear scanning laser vibrometry is used for diagnostics of cylindrical resonators made of polycrystalline aluminum alloy with residual stresses and defects. The diagnostics is performed with flexural Lamb waves. The eigenmode frequency of such a resonator is found to depend on the amplitude of flexural Lamb waves excited in it (the fast dynamics effect), which points to the presence of a nonclassical nonlinear elasticity in the resonator material. Studying the nonlinear interactions between amplitude-modulated flexural Lamb waves in resonators allow the determination of the coordinates of defects and residual strains in them.

Diagnosis of Metal Plates with Defects Using Laser Vibrometer

The method of nonlinear laser scanning vibrometry is used for diagnostics of thin cylindrical resonators of polycrystalline aluminum alloy D16 with latent defects and residual stresses. Flexural Lamb waves are used for diagnosis. The dependence of the frequency of the resonator eigenmode on the amplitude of the flexural Lamb waves in it is detected (the effect of the fast dynamics); it indicates the presence of defects in the material of the resonator. Coordinates of defects were identified by vibromodulation technique in the resonator.

Beam paths of flexural Lamb waves at high frequency in the first band within phononic crystal-based acoustic lenses

This work deals with an analytical and numerical study of the focusing of the lowest order anti-symmetric Lamb wave in gradient index phononic crystals. Computing the ray trajectories of the elastic beam allowed us to analyze the lateral dimensions and shape of the focus, either in the inner or behind the phononic crystal-based acoustic lenses, for frequencies within a broad range in the first band. We analyzed and discussed the focusing behaviors inside the acoustic lenses where the focalization at sub-wavelength scale was achieved. The focalization behind the gradient index phononic crystal is shown to be efficient as well: we report on FMHM = 0.63λ at 11MHz.

Beam path and focusing of flexural Lamb waves within phononic crystal-based acoustic lenses

We describe an analytical approach that allows calculating the trajectories of an elastic beam within a two-dimensional phononic crystal-based gradient index medium. The formalism takes into account the anisotropy along the lines of inclusions where the equi-frequency contours may depart from a circle. We then report on a numerical and experimental study of the focusing of flexural Lamb waves in gradient-indexed phononic crystals. The silicon/air heterostructures that we considered for this work features an index that is obtained through the modulation along one axis of either the diameter of the air inclusions or their spacing. In both cases, numerical and experimental results agree very well. The formalism that we have developed explains well the location, shape and size of the focus in either system.

Efficient focalization of antisymmetric Lamb waves in gradient-index phononic crystal plates

The focalization of elastic waves within a two dimensional gradient-index phononic crystal (GRIN PC) is numerically and experimentally investigated. The structure is formed by a square lattice of air holes in a silicon plate with transverse variation of holes’ diameters. The geometry and efficiency of focalization are computed with a finite element method. A non-contact laser-ultrasonic technique is used both to excite flexural Lamb waves and to monitor in situ the displacements field within the GRIN PC. The efficient subwavelength focusing is achieved and analyzed; furthermore, we describe the oscillatory behavior of focusing and show the relationship between the responses of waves in GRIN PC and the source intensity.

Dynamics of confined cavity modes in a phononic crystal slab investigated byin situtime-resolved experiments

The confinement of elastic waves within a single defect in a phononic crystal slab is investigated both experimentally and theoretically. The structure is formed by a honeycomb lattice of air holes in a silicon plate with one hole missing in its center. The frequencies and polarizations of the localized modes in the first band gap are computed with a finite element method. A noncontact laser ultrasonic technique is used both to excite flexural Lamb waves and to monitor in situ the displacement field within the cavity. We report on the time evolution of confinement, which is distinct according to the symmetry of the eigenmode.

Impact localization in composite structures of arbitrary cross section

This article proposes an in situ structural health monitoring method able to locate the impact source and to determine the flexural Lamb mode A0 velocity in composite structures with unknown lay-up and cross section. The algorithm is based on the differences of the stress waves measured by six surface-attached acoustic emission piezoelectric (lead zirconate titanate) sensors and is branched off into two steps. In the first step, the magnitude of the squared modulus of continuous wavelet transform, which guarantees high accuracy in the time–frequency analysis of the acoustic waves, was used to identify the time of arrival of the flexural Lamb wave. Then, the coordinates of the impact location and the group speed values are obtained by solving a set of non-linear equations through a combination of local Newton’s iterative method associated with line search and polynomial backtracking techniques. The proposed method, in contrast to the current impact localization algorithms, does not require a priori knowledge of the anisotropy angular-group velocity pattern of the measured waveforms as well as the mechanical properties of the structure. To validate this method, experimental location testing was conducted on two different composite structures: a quasi-isotropic carbon fibre–reinforced plastic laminate and a sandwich panel. The results showed that source location was achieved with satisfactory accuracy (maximum error in estimation of the impact location was approximately 3 mm for quasi-isotropic carbon fibre–reinforced plastic panel and nearly 2 mm for sandwich plate), requiring little computational time (nearly 1 s). In addition, the values of the fundamental flexural Lamb mode A0 obtained from the optimization algorithm were compared with those determined by a numerical spectral finite element method.

Fragmentation of DNA in a sub-microliter microfluidic sonication device

Fragmentation of DNA is an essential step for many biological applications including the preparation of next-generation sequencing (NGS) libraries. As sequencing technologies push the limits towards single cell and single molecule resolution, it is of great interest to reduce the scale of this upstream fragmentation step. Here we describe a miniaturized DNA shearing device capable of processing sub-microliter samples based on acoustic shearing within a microfluidic chip. A strong acoustic field was generated by a Langevin-type piezo transducer and coupled into the microfluidic channel via the flexural lamb wave mode. Purified genomic DNA, as well as covalently cross-linked chromatin were sheared into various fragment sizes ranging from ∼180 bp to 4 kb. With the use of standard PDMS soft lithography, our approach should facilitate the integration of additional microfluidic modules and ultimately allow miniaturized NGS workflows.