Antisymmetric Wave Modes Research Articles

DISPERSION OF LAMB WAVES IN MULTILAYER STRUCTURES

Low cost, the possibility of online monitoring and high sensitivity distinguish the method of structural monitoring using Lamb waves from other available methods. Structural analysis based on Lamb waves in heterogeneous materials requires fundamental knowledge of the behavior of Lamb waves in such materials. This basic knowledge is critical for signal processing in determining possible damage that can be detected by the propagating wave. Recently, Lamb wave methods have been used to simultaneously survey large areas of composite structures. However, such methods are more complex than traditional ultrasonic testing because Lamb waves have dispersive characteristics, namely, the wave speed varies depending on the frequency, modes and thickness of the plates. Experimentally measured group velocities of Lamb waves in composite materials with anisotropic characteristics do not coincide with theoretical group velocities, which are calculated using the dispersion equation of Lamb waves. This discrepancy arises because in anisotropic materials there is an angle between the direction of the group velocity and the direction of the phase velocity. This work investigates the propagation characteristics of Lamb waves in composites, focusing on group velocity and characteristic wave curves. For symmetric laminates, a robust method is proposed by imposing boundary conditions on the mid-plane and top surface to separate symmetric and antisymmetric wave modes. The dispersive and anisotropic behavior of Lamb waves in two different types of symmetrical laminates is theoretically studied in detail. The dispersion of Lamb waves was studied for 10 symmetric and asymmetric modes. It is shown that only fundamental modes are not characterized by a cutoff frequency, which indicates the interaction of fundamental modes with composite layers in the low-frequency range. A high level of group velocity dispersion was discovered for the SH0 and S0 modes. It is concluded that in isotropic laminates, dispersion is characteristic of symmetric modes. It is shown that the frequency dependence of the group velocity of Lamb waves of laminar composites can be represented in polynomial form.

A multiresolution layerwise method with intrinsic damage detection capabilities for the simulation of guided waves in composite strips

A high-order layerwise multiresolution method that utilizes Daubechies wavelet and scaling functions for the approximation of state variables is presented for the enhanced simulation of guided waves in composite strips. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, and finer components can be added on the coarse one, forming improved predictions until the desired precision is accomplished. The multiresolution approach is combined with a high-order layerwise laminate theory, enabling the accurate prediction of both symmetric and antisymmetric wave modes, the modeling of surface traction, and localized intra-ply and delamination damage types. Numerical results for the simulation of guided waves in laminated composite strips are presented, exhibiting significant reduction in computing times and remarkable convergence rates compared to single-resolution approaches and traditional finite element methods. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing unique inherent capabilities to localize and isolate coexisting wave modes and detect converted and reflected waves, induced by degraded material regions and delaminations.

Highly efficient acousto-optic modulation using nonsuspended thin-film lithium niobate-chalcogenide hybrid waveguides

A highly efficient on-chip acousto-optic modulator is as a key component and occupies an exceptional position in microwave-to-optical conversion. Homogeneous thin-film lithium niobate is preferentially employed to build the suspended configuration for the acoustic resonant cavity, with the aim of improving the modulation efficiency of the device. However, the limited cavity length and complex fabrication recipe of the suspended prototype restrain further breakthroughs in modulation efficiency and impose challenges for waveguide fabrication. In this work, based on a nonsuspended thin-film lithium niobate-chalcogenide glass hybrid Mach–Zehnder interferometer waveguide platform, we propose and demonstrate a built-in push-pull acousto-optic modulator with a half-wave-voltage-length product VπL as low as 0.03 V cm that presents a modulation efficiency comparable to that of a state-of-the-art suspended counterpart. A microwave modulation link is demonstrated using our developed built-in push-pull acousto-optic modulator, which has the advantage of low power consumption. The nontrivial acousto-optic modulation performance benefits from the superior photoelastic property of the chalcogenide membrane and the completely bidirectional participation of the antisymmetric Rayleigh surface acoustic wave mode excited by the impedance-matched interdigital transducer, overcoming the issue of low modulation efficiency induced by the incoordinate energy attenuation of acoustic waves applied to the Mach–Zehnder interferometer with two arms in traditional push-pull acousto-optic modulators.

3D intra-cellular wave dynamics in a phononic plate with ultra-wide bandgap: attenuation, resonance and mode conversion

The intra-cellular wave dynamics of a water jetted phononic plate are experimentally investigated by means of high-resolution three-dimensional (3D) scanning laser Doppler vibrometry. The study is focused on the vibrational behavior around the ultra-wide bandgap of the plate (with a relative bandgap width of 0.89), as the critical frequency range of its phononic functionality. Broadband vibrational excitations are applied using a piezoelectric transducer and both in-plane and out-of-plane operational deflection shapes of the unit-cells are analyzed with respect to mode shapes calculated by finite element (FE) simulation. Attenuation and resonance of both symmetric and antisymmetric wave modes are validated, and it is shown that despite the absence of in-plane wave energy actuation, the symmetric modes are effectively excited in the phononic lattice, due to mode conversion from co-existing antisymmetric modes. Supported by FE modal analysis, this mode conversion observation is explained by the slight through-the-thickness asymmetry introduced during manufacturing of the phononic plate which leads to coupling of modes with different symmetry. The results confirm the potential of such detailed 3D inspection of phononic crystals (and in general acoustic metamaterials) in gaining full insight about their intracellular dynamics, which can also illuminate discrepancies with respect to idealized numerical models that might be due to manufacturing imperfections.

High-Frequency Guided Wave Propagation and Scattering in Silicon Wafers

Abstract Thin monocrystalline silicon wafers are employed for the manufacturing of solar cells with high conversion efficiency. Micro-cracks can be induced by the wafer cutting process, leading to breakage of the fragile wafers. High-frequency guided waves allow for the monitoring of wafers and detection and characterization of surface defects. The material anisotropy of the monocrystalline silicon leads to variations of the guided wave characteristics, depending on the guided wave mode and propagation direction relative to the crystal orientation. Selective excitation of the first antisymmetric A0 wave mode at 5 MHz center frequency was achieved experimentally using a custom-made wedge transducer. Strong wave pulses with limited beam skewing and widening were measured using noncontact laser interferometer measurements. This allowed the accurate characterization of the Lamb wave propagation and scattering at small artificial surface defects with a size of less than 100 µm. The surface extent of the defects of varying size was characterized using an optical microscope. The scattered guided wave field was evaluated, and characteristic parameters were extracted and correlated with the defect size, allowing in principle detection of small defects. Further investigations are required to explain the systematic asymmetry of the guided wave field in the vicinity of the indents.

Ultrasonic Structural Health Monitoring Approach to Predict Delamination in a Laminated Beam Using d15 Piezoelectric Sensors

Abstract Ultrasonic structural health monitoring (SHM), employing embedded piezoelectric elements to actuate and sense ultrasonic waves, has greatly advanced in recent years. This paper presents a novel approach to address the prevailing challenges in the inspection of laminated structures for delamination using shear-mode (d15) piezoelectric transducers, composed of lead zirconate titanate (PZT). To experimentally evaluate the effectiveness of the proposed approach, a beam-like laminated specimen consisting of internally embedded d15 square PZTs was fabricated with simulated delamination at the interface of an adhesive joint. The evaluation of the results showed that the location of shear-mode actuators is a critical factor to detect delamination and to predict the propagation path of delamination. Delamination initiated close to actuators is more likely to be detected owing to their remarkable sensitivity of structural stiffness surrounding their region. The antisymmetric A0 wave mode generated by these actuators exhibits high interaction with damage, suggesting internally embedded d15 PZTs are a viable approach that can potentially advance the inspection tools of ultrasonic SHM.

Manipulation of the guided wave propagation in multilayered phononic plates by introducing interface delaminations

In this paper, the manipulation of the guided elastic waves in periodically multilayered elastic plates (PMEPs) by introducing interfacial delaminations is explored. A periodic array of interfacial delaminations (PAIDs) distributed along the direction of wave propagation is considered. The spectral element method (SEM) is adopted and applied to accurately and efficiently calculate the transmission spectra and the band structures of the symmetric and antisymmetric guided elastic waves. The central and side periodic interfacial delaminations are considered separately in this paper. Through the comparison of the band structures for the perfect PMEP and the PMEP with PAIDs, we find that not only the total frequency ranges of the band-gaps are increased significantly, but also all of the band-gaps are moved to the relatively low-frequency ranges when PAIDs exist in a PMEP. Extra band-gaps will be generated, especially some of them are in the low-frequency ranges. In addition, the presence of PAIDs in a PMEP can widen the frequency ranges where the guided waves can only propagate with a single wave mode, i.e. the symmetric wave mode or the antisymmetric wave mode. Thus, the capacity of a PMEP to block or filter the guided waves can be strengthened significantly by just intentionally introducing the interfacial delaminations or cracks, which may provide a new way for the design of novel phononic crystals.

Study on the Propagation of Stress Waves in Natural Fiber Composite Strips

The propagation of Lamb waves within the structure of natural fiber reinforced composite strips is investigated using a semi-analytical solution and a time domain spectral finite element numerical method. The need to monitor the structural health of natural fiber reinforced composites is becoming greater, as these sustainable composites are being increasingly used in various industrial applications in automotive and marine structures. Three different types of flax fiber composites were studied and the fundamental wave modes were excited on the structure. Both methods under consideration were able to capture the symmetric and antisymmetric wave modes for all the material configurations. Especially the complex nature of a hybrid flax/glass fiber composite was studied and results were very promising for future damage investigation. Further to this, an attempt was made to excite the hybrid strip at higher frequency and the study revealed the potential to capture all the existing wave modes.

Dispersion curves and identification of elastic wave modes for fiber metal laminates

The current work is devoted to the problem of the validation of dispersion curves and numerical simulations of fundamental Lamb wave and shear horizontal elastic wave modes for fiber metal laminates (FML). In the present study, two types of FM laminates are considered. In the first case, the studied composite material consists of 7 layers: one layer is made of aluminum alloy AW-6060 while the rest of the layers are made of carbon/epoxy resin. In the second case, the FML is constructed of one layer of aluminum alloy and the rest six layers are made of glass/epoxy. In order to extract the dispersion curves for the fundamental S0, SH0, and A0 modes, as well as higher modes from the range 5 up to 1000 [kHz], the stiffness matrix method, is employed. In the first case the computations are performed for the following cross-ply stacking sequences: [Al, ±5°6], [Al, ±15°6], [Al, ±25°6], … , [Al, ±85°6]. Next, the FEM simulations of elastic wave propagation are performed in the case of plates, which are made of analyzed FML composites. In the first studied FML material, the fundamental symmetric mode S0 is generated while in the second case the fundamental antisymmetric mode A0 is excited. It occurred that in the case of aluminum alloy/carbon fibers the generation of the pure fundamental symmetric mode S0 is very difficult. In addition, the fundamental symmetric mode S0, the shear horizontal SH0, and the antisymmetric A0 wave modes are also present. In the case of aluminum alloy and carbon/epoxy, the pure antisymmetric mode A0 can be relatively easily generated. However, a significant dispersion phenomenon is visible. For the aluminum alloy and glass/epoxy, the obtained results are experimentally verified.

Selective actuation and sensing of antisymmetric ultrasonic waves using shear-deforming piezoelectric transducers

Structural health monitoring of thin plate and beam structures using ultrasonic guided wave techniques has been widely studied and demonstrated advanced capabilities dependent on detailed analysis of specific guided wave modes. A common setup employs the d31 electromechanical coupling of piezoelectric wafer active sensors mounted on the surface of a beam or plate. Analysis of output signals from these basic systems is complicated because they represent multiple superposed ultrasonic wave modes that propagate at different velocities, are dispersive, and undergo reflection, refraction, and mode conversion. Multiple techniques have been pursued to overcome this complication. This article presents recent research into the use of shear-deforming lead zirconate titanate piezoelectric transducers, employing the d15 electromechanical coupling property, embedded within beam-like structures to selectively actuate and sense specific ultrasonic wave modes. The internally located transducers actuated and sensed transverse shear, coupled to bending and antisymmetric waves. A combination of results from finite element simulations and experiments found that d15 transducers located at the neutral axis of a beam exclusively coupled to antisymmetric wave modes and did neither directly actuate nor sense symmetric wave modes. Further study was performed to evaluate the effects of off-neutral-axis location on the mode selectivity and found that off axis location of the d15 transducer did not diminish the coupling to antisymmetric wave modes, but introduced coupling to symmetric wave modes. Additional study was performed to assess the ability of structural health monitoring systems employing shear-deforming d15 lead zirconate titanates located at the neutral axis to detect common forms of damage in laminate structures. The combination of selective actuation and selective sensing provides a powerful tool for signal analysis in ultrasonic structural health monitoring of thin plates and beams.

Selective guided wave mode transmission enabled by elastic metamaterials

This article presents the selective guided wave mode transmission enabled by elastic metamaterials. The metamaterial unit cells are comprised of Locally Resonant (LR) cylinders arranged in a periodic pattern bonded on an aluminum plate. Via a careful design, the band structure of the metamaterial system displays a complete bandgap for either symmetric wave modes or antisymmetric wave modes within different frequency ranges. A numerical-based effective medium approach is adopted to calculate the effective dynamic mass densities for in-plane and out-of-plane wave motions under the subwavelength requirement. The finite element harmonic analysis of a chain model further substantiates the selective mode transmission capability via the frequency spectrum of the transmitted wave modes. Finally, a coupled-field transient dynamic finite element simulation is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis of the transmitted wave field illuminates the successful achievement of the selective mode transmission behavior. Experimental demonstrations are also presented to validate the numerical predictions. The proposed selective wave mode transmission control capability may possess great application potential in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM). The paper finishes with summary, concluding remarks, and suggestions for future work.

Estimating dispersion curves from Frequency Response Functions via Vector-Fitting

Driven by the need for describing and understanding wave propagation in structural materials and components, several analytical, numerical, and experimental techniques have been developed to obtain dispersion curves. Accurate characterization of the structure (waveguide) under test is needed for analytical and numerical approaches. Experimental approaches, on the other hand, rely on analyzing waveforms as they propagate along the structure. Material inhomogeneity, reflections from boundaries, and the physical dimensions of the structure under test limit the frequency range over which dispersion curves can be measured. In this work, a new data-driven modeling approach for estimating dispersion curves is developed. This approach utilizes the relatively easy-to-measure, steady-state Frequency Response Functions (FRFs) to develop a state-space dynamical model of the structure under test. The developed model is then used to study the transient response of the structure and estimate its dispersion curves. This paper lays down the foundation of this approach and demonstrates its capabilities on a one-dimensional homogeneous beam using numerically calculated FRFs. Both in-plane and out-of-plane FRFs corresponding, respectively, to longitudinal (the first symmetric) and flexural (the first anti-symmetric) wave modes are analyzed. The effects of boundary conditions on the performance of this approach are also addressed.

Spectral finite element method for wave propagation analysis in smart composite beams containing delamination

PurposeThe purpose of the study is to present a frequency domain spectral finite element model (SFEM) based on fast Fourier transform (FFT) for wave propagation analysis of smart laminated composite beams with embedded delamination. For generating and sensing high-frequency elastic waves in composite beams, piezoelectric materials such as lead zirconate titanate (PZT) are used because they can act as both actuators and sensors. The present model is used to investigate the effects of parametric variation of delamination configuration on the propagation of fundamental anti-symmetric wave mode in piezoelectric composite beams.Design/methodology/approachThe spectral element is derived from the exact solution of the governing equation of motion in frequency domain, obtained through fast Fourier transformation of the time domain equation. The beam is divided into two sublaminates (delamination region) and two base laminates (integral regions). The delamination region is modeled by assuming constant and continuous cross-sectional rotation at the interfaces between the base laminate and sublaminates. The governing differential equation of motion for delaminated composite beam with piezoelectric lamina is obtained using Hamilton’s principle by introducing an electrical potential function.FindingsA detailed study of the wave response at the sensor shows that the A0 mode can be used for delamination detection in a wide region and is more suitable for detecting small delamination. It is observed that the amplitude and time of arrival of the reflected A0 wave from a delamination are strongly dependent on the size, position of the delamination and the stacking sequence. The degraded material properties because of the loss of stiffness and density in damaged area differently alter the S0 and A0 wave response and the group speed. The present method provides a potential technique for researchers to accurately model delaminations in piezoelectric composite beam structures. The delamination position can be identified if the time of flight of a reflected wave from delamination and the wave propagation speed of A0 (or S0) mode is known.Originality/valueSpectral finite element modeling of delaminated composite beams with piezoelectric layers has not been reported in the literature yet. The spectral element developed is validated by comparing the present results with those available in the literature. The spectral element developed is then used to investigate the wave propagation characteristics and interaction with delamination in the piezoelectric composite beam.

Controlled interconversion of quantized spin wave modes via local magnetic fields

In the emerging field of magnonics, spin waves are considered for information processing and transmission at high frequencies. Towards this end, the manipulation of propagating spin waves in nanostructured waveguides for novel functionality has recently been attracting increasing focus of research. Excitations with uniform magnetic fields in such waveguides favors symmetric spin wave modes with odd quantization numbers. Interference between multiple odd spin wave modes leads to a periodic self-focusing effect of the propagating spin waves. Here we demonstrate, how antisymmetric spin wave modes with even quantization numbers can be induced by local magnetic fields in a well-controlled fashion. The resulting interference patterns are discussed within an analytical model and experimentally demonstrated using microfocused Brillouin light scattering ({\mu}-BLS).

Enhanced transduction of MPT for antisymmetric Lamb waves using a detuned resonator

We propose a novel method to boost the power of a magnetostrictive patch transducer (MPT) for generating antisymmetric Lamb wave modes in a plate. Because an MPT installed on a plate mainly exerts in-plane deformation onto a test specimen, it cannot efficiently generate antisymmetric wave modes such as the lowest antisymmetric Lamb wave (A0) mode, unlike the generation of symmetric wave modes. To achieve the high-power generation of antisymmetric modes, we propose an add-on passive boosting element which is referred to here as a detuned resonator. The resulting MPT can serve both as an actuator and a sensor. Here, we present the specific boosting resonator configuration, explain its operating mechanism, and verify its role in increasing the transducer power. A theoretical analysis and experimental validation are carried out.

Large acoustoelastic effect for Lamb waves propagating in an incompressible elastic plate.

In this paper, the effect of a large pre-stress on the propagation of small amplitude Lamb waves in an incompressible elastic plate is investigated. Using the theory of incremental elasticity, the dispersion equations, which give the phase velocity of the symmetric and anti-symmetric wave modes as a function of the wavenumber, plate thickness, and pre-stress state, are derived for a general strain energy function. By considering the fourth-order strain energy function of incompressible isotropic elasticity, the correction to the phase velocity due to the pre-stress is obtained implicitly to the second order in the pre-strain/stress, and depends on the second, third, and fourth-order elastic constants. Numerical results are presented to show the dependence of the phase velocity of the Lamb wave modes upon the applied stress. These are compared to the first-order correction, and agree well with the limiting and asymptotic values obtained previously. It is envisaged that the present results may well find important practical applications in various guided wave based ultrasonic techniques utilising gels and rubber-like materials.

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10–30 mTorr) and frequencies (60–80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

Instabilities of an annulus flow between rotating cylinders in a helical magnetic field.

The stabilities of an annulus flow between the rotating inner and outer cylinders with an external helical magnetic field are studied by using the quasistatic approximation. It is shown numerically that for the spiral base flow with a zero axial pressure gradient, the helical magnetic field yields a helical traveling wave at a critical Reynolds number. This wave mode is revealed to be the most unstable mode by linear stability analysis. At higher Reynolds numbers, the first wave mode is superposed by a second antisymmetric helical wave mode, which travels with a higher phase velocity than the first mode. When the Reynolds number is increased further, the flow becomes turbulent, but the key features of the flow structure are still dominated by the first and the second wave modes. Furthermore, when a finite axial pressure gradient is applied to guarantee a zero axial flow rate, the annulus flow is found to be more unstable than the case with zero axial pressure gradient.

A Hermite Spline Layerwise Time Domain Spectral Finite Element for Guided Wave Prediction in Laminated Composite and Sandwich Plates

A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

Modeling Hypervelocity-Impact-Induced Shock Waves for Characterizing Orbital Debris-Produced Damage

Hypervelocity impact (HVI) is a scenario involving an impacting velocity in excess of 1 km/s. Ubiquitous in outer space, paradigms of HVI are typified by the collision between orbital debris and spacecraft. HVI features transient, localized, and extreme material deformation under which the induced acoustic emission (AE) signals present unique yet complex features. A dedicated modeling and numerical simulation approach, based on the three-dimensional smooth-particle hydrodynamics (SPH), was developed to gain an insight into characteristics of HVI-induced AE propagation. With the approach, both normal and oblique HVI scenarios were interrogated, and material failure in both cases was predicted. The coincidence in results between simulation and HVI experiment, as observed at a qualitative degree, has demonstrated the effectiveness of the modeling. Signal analysis shows that the shock wave converts to Lamb wave quickly as propagation from HVI spot, with the zeroth-order symmetric wave mode (S0) (i.e., the first-arrival wave) dominating wave signal energy. S0 is observed dispersive in a wide frequency range with majority of it below 1 MHz. In comparison, the antisymmetric wave mode distributes in a range below 200 kHz with a peak value at 30 kHz. S0 was employed to pinpoint the location of HVI, using an enhanced delay-and-sum-based diagnostic imaging algorithm, which was validated by locating orbital debris-induced orifice in space structures, showing precise identification results.