Fundamental Symmetric Lamb Mode Research Articles

Propagation of the Fundamental Lamb Modes in Strain Stiffened Hard-Magnetic Soft Plates

Abstract This study focuses on investigating hard-magnetic soft materials, characterized by magnetoactive polymers containing magnetically polarized particles as fillers. The research utilizes the Gent model of hyperelasticity to analyze the propagation of Lamb waves in a magnetically induced deformed compressible plate. In this investigation, we explore both finite deformations and incremental wave propagation in nonlinear hard-magnetic soft materials. The main objective is to formulate the elastic tensor and relevant wave equations within the framework of Lagrangian space. To assess the dispersion characteristics of the guided wave, the study introduces and discusses an extension of the semi-analytical finite element (SAFE) method. Using this numerical approach, the research further examines the effects of magnetic flux densities and its orientation with respect to wave propagation direction on the dispersion characteristics of the fundamental Lamb modes. The study starts by examining the limiting case of the neo-Hookean material model to explain such inherent dependencies. These dependencies are then further emphasized by including the strain-stiffening effect that the Gent material model describes. The research findings reveal the presence of a threshold applied magnetic flux, beyond which the Gent-type material may undergo a snap-through instability, resulting in changes in the dispersion characteristics of the fundamental symmetric Lamb mode.

Propagation of fundamental Lamb modes along the non-principal axes of strain-stiffened soft compressible plates: A numerical investigation.

This paper numerically investigates the propagation of elastic plate waves along the non-principal directions in a prestretched compressible material described by the Gent model of hyperelasticity. We formulate the elastic tensor and the underlying wave equations in the Lagrangian space by employing the theory of nonlinear elasticity together with the linearized incremental equations. An extension of the Semi-Analytical Finite Element (SAFE) method is discussed for computing the dispersion characteristics of the two fundamental guided wave modes. The predictive capabilities of the numerical framework are established using the previously published data for a weakly nonlinear as well as hyperelastic material models. Using the numerical framework, we then bring out the effects of applied prestretch, orientation of the propagation direction, and material parameters on the dispersion characteristics of the fundamental Lamb modes. A limiting case of the neo-Hookean material model is first considered for elucidating such implicit dependencies, which are further highlighted by considering the strain-stiffening effect captured through the Gent material model. Our results indicate the existence of a threshold prestretch for which the Gent-type material can encounter a snap-through instability; leading to the change in the dispersion characteristics of the fundamental symmetric Lamb mode.

S0 Lamb Mode Scattering Studies in Laminated Composite Plate Structures with Surface Breaking Cracks: Insights into Crack Opening Behavior

Ultrasonic-guided waves are attractive for rapid inspection of laminated composite structures, where cracks developed transverse to the loading direction are the severe type of damage. This paper presents studies of the interaction of fundamental symmetric S0 Lamb mode with vertical surface-breaking cracks in laminated composite plate structures. Finite element simulations and experimental investigations are used to study the effect of crack depth on S0 wave reflection behavior. Results show a monotonic rise of the reflection coefficient for different crack depths in a manner that is strongly dependent on the orientation of the plies and transverse ply location in the vicinity of the crack. Scattered wave packets in the reflection regime are captured using an in-plane laser. The S0 Lamb mode's sensitivity is numerically presented for the different crack depths in the long wavelength limit. We also observed that the reflected wave mode depicts the information of the corresponding broken interfaces. An attempt was made to show that this behavior relates to the crack-opening behavior in response to in-plane excitation. The reflection coefficient as a characteristic polynomial is proposed for various orientations. It was observed that the dispersion at receiver nodes makes the analysis challenging for distinguishing the signal from crack faces due to the smaller dimension. The study outcomes show its prospect as a promising NDE tool for crack damage detection in thin laminated plate structures.

Micromachined Heterostructured Lamb Mode Waveguides for Acoustoelectric Signal Processing

This work explores micromachined heterostructured waveguides that leverage strong interactions between acoustic phonons and electrons to enable radio frequency (RF) signal amplification or attenuation. A thin-film piezoelectric-on-semiconductor stack is tailored to generate high electromechanical coupling Lamb waves that are impacted by high mobility electrons within a microacoustic waveguide. Lamb waves are generated by RF signal via interdigital electrodes on the piezoelectric layer; by applying a voltage to the semiconductor layer so that the electrons lead mechanical waves, the RF signal is amplified through the acoustoelectric (AE) effect. Conversely, the signals propagating faster or in the opposite direction of the electron flow undergo attenuation, rendering the waveguide nonreciprocal. Research on the AE effect dates to the mid-20th century and until now has been mostly focused on surface acoustic waves (SAWs). In this work, enabled by high-quality bonded thin films of lithium niobate (LN) and silicon (Si), it is shown that fundamental symmetric ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S0$ </tex-math></inline-formula> ) Lamb mode waveguides at 100 s of MHz can achieve more than 40 dB of AE gain and strong nonreciprocal transmission with less than 10 mW of bias power consumption. This could enable implementation of switches, delay lines, isolators, and circulators, which are critical for interference cancellation and full-duplex radio. The AE effect is observed to be stronger in some higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S0$ </tex-math></inline-formula> harmonics, allowing for scaling to higher frequencies with optimized electrodes that have more relaxed critical dimensions. In addition, up to 5.5-dB sustained terminal gain measured in this work implies the potential for transistor-less amplifiers that could be implemented in concert with more traditional acoustic devices in a single-chip manner.

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.

Ultra-fast tuning of refractive index in Lithium Niobate slab by GHz acoustic wave

Refractive index modulation in optical materials facilitates dynamic control on electromagnetic waves. Ultra fast tuning of both refractive index and its spatial distribution in Y−Z Lithium Niobate slab via strain employed through GHz acoustic perturbation has been simulated and studied. To create acoustic disturbance in taken 500 nm thick slab, the fundamental symmetric Lamb mode at 5 GHz acoustic frequency is excited. Displacement field patterns generated by longitudinal and transverse disturbances of perturbing fundamental symmetric Lamb mode are analyzed under reinstate limits of optical material to create elastic strain. Modification in optical index of Lithium Niobate due to strain generated by longitudinal and transverse acoustic disturbance is then examined. The sinusoidal modulation in refractive index with maximum change of 0.070 along nz and 0.036 along ny is observed. The modulated refractive index has a periodic distribution over space with period equals to wavelength of acoustic disturbance created by fundamental Lamb mode. This acoustically induced ultra-fast change in refractive index and in its spatial distribution depends on perturbing acoustic frequency and thickness of slab. Thus, the slab can optimize dynamically, to control electromagnetic wave for various optical applications.

Acoustically tunable photonic band gap generation in MgO doped Lithium Niobate micro-dimension plate

Refractive index contrast generation in MgO doped LiNbO3 plate via Lamb wave perturbation for induction of acoustically tunable photonic band gap is theoretically studied. Fundamental symmetric Lamb mode is excited in micro dimension thin plate structure to produce symmetric disturbance for periodic contraction and rarefaction along the length of plate. Effect of contraction and rarefaction on production of refractive index contrast is studied using photo–elastic effect. The generated quasi static low–high optical index region in plate modifies electromagnetic wave propagation and provides photonic band gaps, which are investigated using Bloch's theorem and transfer matrix method. The induced photonic band gap shows great dependency on optical contrast and unit cell dimension created by acoustic frequencies. These acoustically tunable photonic band gaps have rewarding applications in acousto optical devices, laser and sophisticated sensing.

A Boundary Element Model for Structural Health Monitoring Based on the S0 Lamb Wave Mode

The aim of this paper was to carry out numerical simulations of structural health monitoring applications for plate structures using the boundary element method (BEM). The fundamental symmetric Lamb mode (S0) is chosen for the SHM applications. The propagation, reflection and diffraction of the S0 mode Lamb wave are modelled using a boundary element formulation based on the plane stress theory. Piezoelectric (PZT) actuators are mounted on plate surfaces to excite the S0 mode wave. A semi-analytical method is adopted to couple the PZT actuators and the host plate. Numerical results show that BEM is a very efficient simulation method for the structural health monitoring of plates.

Effect of ply orientation and through-thickness position of delamination on the reflection of fundamental symmetric S0 Lamb mode in GFRP composite plate structures

This paper studies the interaction of the fundamental symmetric Lamb wave mode S0 with delaminations in 8-layered glass fibre reinforced polymer (GFRP) laminated composites, using numerical models validated against experiments. The validation is performed using experiments on the eight layer quasi-isotropic GFRP composite laminate [0/90/45/−45]S. Further numerical studies were performed on the laminates [0/45/−45/90]S, [0/45/90/−45]S, [90/45/−45/0]S, [90/−45/0/45]S, [45/−45/0/90]S, and [45/90/−45/0]S to study the effect of ply layups on the reflection of S0 Lamb waves. The reflection coefficients calculated for these laminates followed a similar trend as the laminate [0/90/45/−45]S. Physical insight was obtained into the reflection behaviour, based on an analysis of wave dispersion in the sub-laminates. It was difficult to detect the delamination situated at the mid plane of the laminate, where the shear stress was found to be zero for all ply layups. The delaminations present at a depth greater than DL12 (>0.42 mm) from the source of excitation, were found to be accessible for the laminates [0/90/45/−45]S, [0/45/−45/90]S and [0/45/90/−45]S. The sensitivity of the S0 mode reflection depends upon the position of the delamination along the thickness direction and ply layup orientation of the composite laminate. The S0 mode showed higher sensitivity to DL23 and DL34 (0.42 mm to 1.26 mm) in all the laminates that were inspected.

Effect of lay-up of sub-waveguide on transmission of So mode from main waveguide to sub-waveguides

This paper focuses on transmission characteristics of fundamental symmetric Lamb mode (So) at the junction of a main waveguide and sub-waveguides in composite laminates. Numerical simulations on transmission of So from the main to sub-waveguide revealed that transmission factors of the modes depend on stacking sequence of plies in the waveguides. Experiments were carried out to verify the observations made in numerical simulations. This work gives an insight on the transmission characteristics of So mode while it propagates from a healthy to a delaminated region in a composite laminate.

Analytical study of the propagation of fast longitudinal modes along wz-BN/AlN thin acoustic waveguides.

The propagation of the fundamental symmetric Lamb mode S0 along wz-BN/AlN thin composite plates suitable for telecommunication and sensing applications is studied. The investigation of the acoustic field profile across the plate thickness revealed the presence of modes having longitudinal polarization, the Anisimkin Jr. plate modes (AMs), travelling at a phase velocity close to that of the wz-BN longitudinal bulk acoustic wave propagating in the same direction. The study of the S0 mode phase velocity and coupling coefficient (K2) dispersion curves, for different electrical boundary conditions, has shown that eight different coupling configurations are allowable that exhibit a K2 as high as about 4% and very high phase velocity (up to about 16,700 m/s). The effect of the thickness and material type of the metal floating electrode on the K2 dispersion curves has also been investigated, specifically addressing the design of an enhanced coupling device. The gravimetric sensitivity of the BN/AlN-based acoustic waveguides was then calculated for both the AMs and elliptically polarized S0 modes; the AM-based sensor velocity and attenuation shifts due to the viscosity of a surrounding liquid was theoretically predicted. The performed investigation suggests that wz-BN/AlN is a very promising substrate material suitable for developing GHz band devices with enhanced electroacoustic coupling efficiency and suitable for application in telecommunications and sensing fields.

Symmetric low-frequency feature-guided ultrasonic waves in thin plates with transverse bends

Recent research by the authors shows that bends in plates can act as features that can concentrate and guide ultrasonic energy along their axis. At low frequencies, two feature-guided modes are identified when the bent plate is subjected to ‘in-plane’ or axial excitation applied uniformly along a through-thickness line bisecting the bent edge. Of these, the slower mode has properties similar to the A0 (fundamental antisymmetric) Lamb mode in flat plates. This paper focuses on the faster bend-guided mode that is similar to the S0 (fundamental symmetric) Lamb mode in flat plates. Using 3D finite element (FE) simulation validated with experiments, this mode is shown to be more strongly generated in smaller angle bends. Features of the mode including velocity, attenuation and modal structure are considered in detailed studies. Results are discussed in light of simple modal studies using the Semi Analytical Finite Element (SAFE) method, suggesting a relationship of bend-guided waves to modes of curved bars.

Experimental Studies on Amplitude Characteristics of So Mode in Composite Laminates Due to Misalignment in Air-Coupled Transducers

This paper presents systematic experiments carried out to study the variation in amplitude of the fundamental symmetric Lamb mode (So) due to misalignments in air-coupled transducers. In this work three misalignments—linear, orientation and synchronized orientation were intentionally introduced in the air-coupled transducers, and experiments were carried out on two glass fiber reinforced plastic laminates of different ply stacking. A-scans were captured positioning the air-coupled probes in several configurations over the laminates. In each misalignment case, variation in amplitude of So mode with respect to misalignment variable was plotted. Curves were fitted in those misalignment cases where there was sufficient experimental data. Interestingly, it was observed that Gaussian curves accurately characterize the variation in amplitude with respect to the misalignment variable.

Antisymmetric feature-guided ultrasonic waves in thin plates with small radius transverse bends from low-frequency symmetric axial excitation

The influence of bends constituting annular polygonal structures on ultrasonic guided waves propagating along their axis is investigated. Considering a single bend as a bent plate connects this problem to the better-understood physics of guided waves in straight plates. Using a three-dimensional finite element simulation validated with experiments, bends in plates are shown to act as features that can concentrate and guide ultrasonic energy along their length. Two interesting feature-guided modes are identified when the bent plate is subjected to "in-plane" or axial excitation applied uniformly along a through-thickness line bisecting the bent edge. Of these, the faster traveling mode has properties similar to, but travels at group velocities lower than, the S0 (fundamental symmetric) Lamb mode in flat plates. This paper however focuses on the slower bend-guided mode that is similar to the A0 (fundamental anti-symmetric) Lamb mode in flat plates. This mode is shown to be more strongly generated in smaller angle bends where it has a low attenuation. The results are discussed in light of simple modal studies performed using the Semi-Analytical Finite Element method.

Lamb-wave-based structural health monitoring technique for inaccessible regions in complex composite structures

This work investigated feasibility of Lamb wave based SHM technique for in-situ monitoring of hidden (inaccessible) web region, for delamination type of defect, in a typical stiffened composite (I-joint) section of an aircraft structure. Finite element model was proposed to understand and compare the wave propagation of fundamental symmetric Lamb mode (S0) through a healthy and center delaminated web of the I-joint. In simulations, S0 mode was excited at the center of web, which then, travels along the web and propagates into skin regions of the I-joint. Turning modes were also observed. From the S0 mode captured at two locations on the skin, one for the direct mode and another for the turning mode, it was seen that amplitude of the captured mode can used as a feature for delamination detection. Experiments were carried out on the I-joint with bonded piezoelectric wafer active sensor patch on the web and skin regions. In order to reduce the weight of the SHM instrumentation, an attempt was made to develop a low footprint, portable instrumentation for actuation, and reception of Lamb waves and wireless live transmission of the ultrasonic data. Experimental measurements showed a similar trend of significant decrease in the amplitude of S0 modes when propagating through the web delamination when compared to simulation. Copyright © 2013 John Wiley & Sons, Ltd.

Asymmetric Lamb wave propagation in phononic crystal slabs with graded grating

Asymmetric Lamb wave propagation is important for control and manipulation of the Lamb wave signals in various devices. Through numerical simulation of the Lamb wave propagation in phononic crystal slabs with graded grating, we proposed and studied a linear phononic device that shows asymmetric Lamb wave transmission in low-frequency domains. This exotic phenomenon stems from the threshold frequency of the fundamental antisymmetric Lamb mode conversion to the fundamental symmetric Lamb mode is different at the different locations of the acoustic diode. Remarkably, a bi-directional asymmetric Lamb wave propagation is achieved by tuning the grade of the grating depths. The back propagating acoustic waves of the second band of hybridized Lamb modes plays the essential role in the phenomena for relatively high-frequency regions. This should be potentially significant in helping design chip-scale integrated phononic devices.

Numerical Modelling of Propagation of the Fundamental Symmetric Lamb Mode through a Metal Composite Adhesive Joint

The interaction of the fundamental S0Lamb mode with adhesive joint considered between GFRP composite laminate and aluminium was studied through numerical modelling carried out using FEM. The numerical simulations were carried out by exciting the fundamental A0 Lamb mode at metal end in the frequency range of 150-225kHz by varying the adhesive orientation in the range of 1 in 20 to 900.When S0 Lamb mode interacts with adhesive, reflection, transmission and generation of A0 takes place. The incident S0 and generated A0 modes propagate in the model as S0S0 and S0A0 modes. The ToF of reflected and transmitted S0S0 and S0A0 modes at receiving points were calculated analytically and compared with those obtained from numerical simulations.Further, RF and TF of Lamb modes S0S0 and S0A0 propagating through the sample were estimated. It is observed that, RF and TF values are depending on the adhesive orientation and the excitation frequency. The detailed study on variation of RF and TF was made by exciting at metal and composite end with excitation frequency in the above range. Further, It was found that, scattered (transmitted and reflected) S0S0 and S0A0 Lamb modes are sensitive to the adhesive and hence, it can be used for detection of disband in metal-composite adhesive joint

Propagation of the Fundamental Symmetric Lamb Mode in a Symmetrically Delaminated Composite Laminate

In this paper, a study on the propagation of the fundamental symmetric Lamb mode (So) in a symmetrically delaminated glass/epoxy composite laminate is presented. It was found that when So mode is incident at the front and rear edges of a symmetric delamination, it generates Ao mode. This mode is exclusively confined to the sub-laminates. It was also observed that, during the interaction of the generated Ao mode with the edges of delamination, it, in turn generates So mode. Thus, So mode and mode converted Lamb modes undergo multiple mode conversions in the sub-laminates. The only mode that propagates in the main laminate is So. A signal-processing scheme based on the time-frequency spectrographic analysis was utilized to identify the wave groups propagating in the main and sub-laminates.

Damage localization in plate-like structure using built-in PZT sensor network

In this study, a Lamb-wave based damage detection approach is proposed for damage localization in plate. A sensor network consisting of three PZT wafer type actuators/sensors is used to generate and detect Lamb waves. To minimize the complication resulted from the multimode and dispersive characteristics of Lamb waves, the fundamental symmetric Lamb mode, S0 is selectively generated through designing the excitation frequency of the narrowband input signal. A damage localization algorithm based upon the configuration of the PZT sensor network is developed. Time-frequency analysis method is applied to purify the raw signal and extract damage features. Experimental result obtained from aluminum plate verified the proposed damage localization approach.