Higher-order Lamb Waves Research Articles

Focusing higher-order Lamb waves based on the Luneburg lens

In order to improve the spatial resolution and the signal-to-noise ratio of Lamb waves in structural health monitoring systems or non-destructive testing techniques, this study presents the construction of Luneburg lenses for focusing higher-order Lamb waves based on the thickness variation. The dispersion curves of Lamb waves are calculated firstly, from which the relation between the phase velocity of a specific mode and the plate thickness is quantified. After that, the plate thickness is determined via the refractive index variation. To demonstrate the generality of this design scheme, two lenses, i.e., the A1-wave-based Luneburg lens and the S2-wave-based Luneburg lens are constructed, and their focusing abilities are examined via numerical simulations in both the time domain and frequency domain. It is revealed that the A1 wave and S2 wave can be focused with a focusing size smaller than one wavelength. The design methodology is easy to realize and can be used to control higher-order Lamb waves efficiently, which also provides potential application values in wave detections and energy collections.

Local Stress Measurement in Thin Aluminum Plates based on Zero-Group-Velocity Lamb mode

The stress state is critical to the reliability of structures, but existing ultrasonic methods are challenging to measure local stress. In this paper, zero-group-velocity (ZGV) Lamb mode was proposed to measure the local stress field in thin aluminum plates. The Lamb wave’s dispersive characteristics under initial stress were analyzed based on the Floquet-Bloch theory with Murnaghan hyperelastic material model. The obtained dispersion curves show that higher-order Lamb wave modes near the cut-off frequencies are sensitive to applied stress across the plate, indicating that the S1-ZGV mode has a rather high sensitivity to stress. Similar to conventional ultrasonic stress measurement, it is found that the frequency of the S1-ZGV mode changes near-linearly with the amplitude of applied stress. Numerical experiments were conducted to illustrate the feasibility of local stress measurement in a thin aluminum plate based on the S1-ZGV mode. Single and multiple localized stress fields were evaluated with the S1-ZGV method, and reconstructed results matched well with actual stress fields, proving that the ZGV Lamb wave method is a sensitive stress measurement technique in thin plates.

Machined phononic crystals to block high-order Lamb waves and crosstalk in through-metal ultrasonic communication systems

For systems that require complete metallic enclosures (e.g., containment buildings for nuclear reactors), it is impossible to access interior sensors and equipment using standard electromagnetic techniques. A viable way to communicate and supply power through metallic barriers is the use of elastic waves and ultrasonic transducers, introducing several design challenges that must be addressed. Specifically, the use of multiple communication channels on the same enclosure introduces an additional mechanism for signal crosstalk between channels: guided waves propagating in the barrier between channels. This work numerically and experimentally investigates a machined phononic crystal to block MHz Lamb wave propagation between ultrasonic communication channels, greatly reducing wave propagation and the resulting crosstalk voltage. Blind grooves are machined into one or both sides of a metallic barrier to introduce a periodic unit cell, greatly altering the guided wave dispersion in the barrier. Numerical simulations are used to determine a set of groove geometries for testing, and experiments were performed to characterize the wave-blocking performance of each design. The best-performing design was tested using piezoelectric transducers bonded to the barrier, showing a 14.4 dB reduction in crosstalk voltage. The proposed periodic grooving method is a promising technique for completely isolating ultrasonic power/data transfer systems operating in a narrow frequency range.

An Advanced Magnetoacoustic Compound Inspection Method of High-Order Mode EMAT

In this study, an advanced magnetoacoustic compound inspection method for a high-order Lamb waves mode electromagnetic acoustic transducer (EMAT) was proposed. The proposed EMAT can achieve the excitation and reception of the A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode which is the first-order Lamb waves mode. According to the characteristics of the A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode EMAT testing signal, a signal processing method for obtaining the pulsed eddy current signal by curve fitting was developed to extract the information for the pulsed eddy current. The voltage of the ultrasonic waves was carried on the pulsed eddy current voltage, and it was obtained by removing the pulsed eddy current voltage and extracting the time-domain testing signal of the A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode EMAT. Through A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode EMAT single detection that was used to obtain the pulsed eddy current and A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode, the multi-parameter from the magnetoacoustic compound testing signal of the A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode EMAT could be used to characterize the aluminum plate performance degradation. The detection accuracy of aluminum plate performance degradation was improved by the magnetoacoustic compound inspection compared with a single detection method.

Higher-order Lamb waves with quasi-zero surface displacement components on a GaAs piezoelectric plate

Higher-order Lamb waves with quasi-zero surface displacement components are reported on (100)-cut GaAs propagating along the <110> direction where the total displacement at the surface of the plate is less than 10% of the maximum total displacement. The dispersion curves and the displacement component profiles show the reduction of total displacement at the surface of the plate starting when the phase velocities of the higher-order modes are crossing the shear bulk acoustic wave velocity to the value as low as 5%. Due to the concentration of acoustic energy inside the plate, the reported quasi-zero plate acoustic waves (QZ-PAW) further reduce the radiation of acoustic energy when the plate surface is in contact with liquid. The experimental results validate the occurrence of QZ-PAW with a reduction of viscous damping insertion loss compared to previously reported quasi-longitudinal Lamb waves. The results demonstrate the potential QZ-PAW mode for emerging applications such as dual-mode PAW sensors, PAW devices with integrated sensor and actuator, thin-film and ultra-high frequency PAW sensors in highly viscous liquid media.

Experimental identification of high order Lamb waves and estimation of the mechanical properties of a dry human skull

We experimentally investigate and characterize high order Lamb wave modes in a dry human skull. Specifically, we show that the diploë supports distinct wave modes in the sub-1.0 MHz frequency regime, and we employ these modes for the estimation of equivalent mechanical properties of cortical and trabecular bones. These modes are efficiently generated in a parietal region by direct contact excitation with a wedge beam transducer, and are recorded via infrared laser vibrometry. Frequency/wavenumber data are estimated using a matrix pencil method applied to wavefield measurements recorded on the outer cortical surface. The semi-analytical finite element model of an equivalent three-layered plate provides the platform for the identification of wave modes based on their through-the-thickness profiles, and supports the estimation of equivalent mechanical properties in conjunction with an optimization algorithm developed for this purpose. The results presented herein illustrate how high order Lamb waves can be used to gain understanding of the wave properties of a human skull and to estimate the orthotropic and equivalent isotropic mechanical properties of cortical and trabecular bones.

Experimental and Computational Investigation of Guided Waves in a Human Skull

We investigate guided (Lamb) waves in a human cadaver skull through experiments and computational simulations. Ultrasonic wedge transducers and scanning laser Doppler vibrometry are used respectively to excite and measure Lamb waves propagating in the cranial bone of a degassed skull. Measurements are performed over a section of the parietal bone and temporal bone spanning the squamous suture. The experimental data are analyzed for the identification of wave modes and the characterization of dispersion properties. In the parietal bone, for instance, the A0 wave mode is excited between 200 and 600 kHz, and higher-order Lamb waves are excited from 1 to 1.8 MHz. From the experimental dispersion curves and average thickness extracted from the skull computed tomography scan, we estimate average isotropic material properties that capture the essential dispersion characteristics using a semi-analytical finite-element model. We also explore the leaky and non-leaky wave behavior of the degassed skull with water loading in the cranial cavity. Successful excitation of leaky Lamb waves is confirmed (for higher-order wave modes with phase velocity faster than the speed of sound in water) from 500 kHz to 1.5 MHz, which may find applications in imaging and therapeutics at the brain periphery or skull–brain interface (e.g., for metastases). The non-leaky A0 Lamb wave mode propagates between 200 and 600 kHz, with or without fluid loading, for potential use in skull-related diagnostics and imaging (e.g., for sutures).

Enabling Higher Order Lamb Wave Acoustic Devices With Complementarily Oriented Piezoelectric Thin Films

In this work, we present a new paradigm for enabling gigahertz higher-order Lamb wave acoustic devices using complementarily oriented piezoelectric (COP) thin films. Acoustic characteristics are first theoretically explored with COP lithium niobate (LiNbO3) thin films, showing their excellent frequency scalability, low loss, and high electromechanical coupling (k2). Acoustic resonators and delay lines are then designed and implemented, targeting efficient excitation of higher-order Lamb waves with record-breaking low loss. The fabricated resonator shows a 2nd-order symmetric (S2) resonance at 3.05 GHz with a high quality factor (Q) of 657, and a large k2 of 21.5% and a 6th-order symmetric (S6) resonance at 9.05 GHz with a high Q of 636 and a k2 of 3.71%, both among the highest demonstrated for higher-order Lamb wave devices. The delay lines show an average insertion loss (IL) of 7.5 dB and the lowest reported propagation loss of 0.014 dB/μm at 4.4 GHz for S2. Notable acoustic passbands up to 15.1 GHz are identified. Upon further optimizations, the proposed COP platform can lead to gigahertz low-loss wideband acoustic components.

Aluminum Nitride Combined Overtone Resonators for the 5G High Frequency Bands

This work presents a new acoustic MEMS resonator technology, dubbed Aluminum Nitride (AlN) Combined Overtone Resonator (COR), capable of addressing the filter requirements for the 5G high frequency bands in the 6-40GHz range. The COR exploits the multimodal excitation of two higher-order Lamb waves ( $2^{\mathbf {nd}}$ and $3^{\mathbf {rd}}$ order Asymmetrical Lamb Waves) in a suspended thin-film AlN plate to transduce a 2-dimensional vibration mode with high electromechanical coupling coefficient $k_{t}^{2}$ (up to 1.9%) and quality factor $Q>1100 $ at twice the frequency of a fundamental thickness-extensional mode in the same structure. Analytical and finite-element method (FEM) models are developed to describe the working principle of the COR technology and predict the achievable $k_{t}^{2}$ , Q and lithographic frequency tunability. An 8.8 GHz COR prototype was fabricated showing a high $k_{t}^{2}~\sim ~0.3$ % (using a simple top-electrode-only configuration with a 2-mask process) and a groundbreaking $Q\sim {1100}$ which is the highest ever achieved among piezoelectric resonators above 6 GHz. The $f - Q$ product $\sim 1\times 10 ^{\mathbf {13}}$ is the highest among all demonstrated piezoelectric resonators with metallic coverage >50%. Additionally, the capability of the COR technology to deliver contiguous filters with bandwidths between 355 and 592 MHz (aggregated BW >2GHz) in the mmWave spectrum, with relaxed lithographic requirements, is demonstrated by FEM. [2019-0229]

Obliquely incident EMAT for high-order Lamb wave mode generation based on inclined static magnetic field

Lamb waves have the characteristics of long propagation distance, and they can be used to realize rapid and wide-scale nondestructive testing of plates. The detection sensitivity can be improved by using a high-order Lamb wave mode with a short wavelength. However, Lamb waves have multimode characteristics. The number of Lamb wave modes greatly increases at high frequencies, and it is difficult to obtain a pure single high-order Lamb wave mode with electromagnetic acoustic transducers (EMATs); this increases the difficulty of signal processing and analysis. In this study, an obliquely incident EMAT based on the inclined static magnetic field was designed to solve this problem. The mode selectivity of the proposed obliquely incident EMAT is superior to that of the traditional EMAT. A new parameter is proposed to improve the mode selectivity of EMATs: the polarization angle of the permanent magnet. The incident angle of incident ultrasonic waves is controlled by selecting the polarization angle of permanent magnet. A rectangular permanent magnet is obliquely polarized to provide a biased inclined static magnetic field. The obliquely incident Lorentz force is formed through the coupling between the eddy current and the inclined static magnetic field by an obliquely polarized permanent magnet. The obliquely incident Lorentz force is the source of the obliquely incident ultrasonic wave. Simulation and experimental results show that the developed obliquely incident EMAT can reduce the amplitude of the unwanted modes and enhance the mode selectivity. It was also verified that the developed obliquely incident EMAT had better frequency-response characteristics and sound-field directivity.

Detection of high-order Lamb waves using an end-face injection of ultrasonic pulses

Abstract In this work, we report the time-of-flight detection of high-order Lamb waves by using an end-face injection of ultrasonic pulses in plates. We used two piezoelectric transducers attached to the opposite edges of a rectangular plate. We applied the Short Time Fourier Transform (STFT) to determine the time-of-flight. We compare the contours of the STFT on the time-frequency spectrogram with the theoretical time-of-flight. This technique defines a broadband map for multiple Lamb waves on the same experimental run. We have found clear evidence not only of the lowest symmetric and antisymmetric modes ( S 0 and A 0 ) but also of higher order modes ( S 1 , A 1 , and S 2 ).

Dual-resonator Lamb wave strain sensor with temperature compensation and enhanced sensitivity

In this letter, we demonstrate a high-temperature dual-resonator Lamb wave tensile strain sensor which can achieve temperature compensation in a wide temperature range and has high strain sensitivities. This sensor consists of two identical AlN-on-SOI Lamb wave resonators (LWRs) adhered on a uniaxial tensile plate, with the wave propagating directions in the two LWRs parallel and perpendicular to the tensile axis, respectively. The most obvious higher-order Lamb wave modes, i.e., the A4, S4, and S5 modes, in the “parallel” LWR present high strain sensitivities of 0.229 ppm/με (196 Hz/με), 0.480 ppm/με (431 Hz/με), and 0.222 ppm/με (205 Hz/με) all with minus signs, whereas in the “perpendicular” LWR, they demonstrate smaller strain sensitivities all with plus signs. The S4 modes in the two LWRs have almost the same temperature coefficients. Based on the experimental results, a generally applicable beat frequency method with these two LWRs is proposed to realize temperature compensation as well as the high-sensitivity strain measurement.

Absorption Performance of an Anechoic Layer with a Steel Plate Backing at Oblique Incidence

The sound absorption of steel-plate-backed anechoic coatings at oblique incidence is investigated theoretically and numerically. An analytical expression for the absorption coefficient is derived using elasticity theory. A 2D numerical periodic model suitable for inhomogeneous coatings under oblique incidence is built using the finite-element method. To interpret the absorption mechanism, the dispersion curves for guided elastic waves in a uniform coating and a steel plate are calculated using the spectral method. The absorption coefficients are analyzed with respect to the incident angle and frequency using elastic plate resonance theory. The effects of the steel plate backing and the attenuation of the coating are investigated. For the Alberich anechoic coating with a steel plate backing, the absorption coefficients are calculated numerically, and the absorption mechanism is investigated by structural displacement vectors and deformations. The following absorption characteristics can be found. In the frequency-angle spectra for absorption coefficients, the bright areas resulting from low-order Lamb waves in the coating are recognizable at low frequencies. A broad, strong anechoic area appears at large incident angles and low frequencies; under these conditions, the displacements of the steel plate and the 2D cavity are the main components of structural vibration. The resonance moves to low frequency when the thickness of the steel plate is incorporated and the cavity height is increased. At relatively high frequencies, some new absorption areas result from the resonance of periodic cavities and cover the contribution from the high-order Lamb waves in the coating caused by attenuation. The corresponding absorption coefficients decrease with an increasing angle of incidence.

Comparison of acoustoelastic Lamb wave propagation in stressed plates for different measurement orientations.

High order Lamb waves are investigated for the effects of stress on both symmetrical and anti-symmetrical modes in an aluminum plate for wave propagation and load parallel. Data are compared with those for the case of load and measurement axis perpendicular. It is the S1 mode which exhibits significantly higher sensitivity to stress than other Lamb modes. For aluminum the use of the S1 mode for stress measurement is found to be about six times more sensitive, than bulk waves, for the load-measurement axes parallel case and this compares with about ten times for the case of load-measurement axes perpendicular.

Super high sensitive plate acoustic wave humidity sensor based on graphene oxide film

The changes of density and elastic modules due to water vapor adsorption are measured for graphene oxide film at room temperature. Dominant mechanism for acoustic wave humidity sensing by the film is shown to be related with variation of its electric conductivity. Basing on the data, super high sensitive humidity sensor employing high-order Lamb wave with large coupling constant, standard lithium niobate plate, and graphene oxide sorbent film is developed. The minimal detectable level of the sensor is as low 0.03% RH, response times are 60/120s, and reproducibility is ±2.5%. The sensor is completely selective towards H2, CO, CH4, NO, O2.

Effect of uniaxial stress on the propagation of higher-order Lamb wave modes

On the basis of the non-linear theory of elasticity and the invariant based formulation developed by Ogden, we analyse the effect of homogeneous stress on the propagation of Lamb waves. Using the theory of incremental deformations superimposed on large deformations, we derive the equations governing the propagation of small amplitude waves in a pre-stressed plate. By enforcing traction-free boundary conditions at the surfaces of the plate, we further obtain the characteristic equations for symmetric and anti-symmetric Lamb wave modes and investigate the effect of stress on the phase velocity, i.e. the acoustoelastic effect. A comparison with experimental data exhibits a better correlation than previously published results. The outcomes of this study can be utilised in the development of new techniques for the measurement of applied stresses based on the acoustoelastic effect. In particular, a strong sensitivity of the phase velocity to the applied stress near the cut-off frequencies of higher-order Lamb wave modes is a very promising option, which seems to have been overlooked in previous studies.

Measurement and analysis of laser generated Rayleigh and Lamb waves considering its pulse duration

In this article, laser generated Rayleigh and Lamb waves are studied by taking into account its pulse duration. The physical model and theoretical solution are presented to predict the corresponding waveforms for aluminum samples under the ablation generation regime. The waveforms of the excited Rayleigh and Lamb waves by laser with selected pulse duration were measured by laser interferometer and analyzed theoretically, and the agreement between measurement and analysis is demonstrated for the validation of the theoretical model and solution. The broadening of the Rayleigh wave and the disappearing of high order Lamb wave modes can be found with the increase of the pulse duration by the laser ultrasonic technique.

Performance optimization of high-order Lamb wave sensors based on silicon carbide substrates

Silicon carbide (SiC), as a new type of material for substrates in micro-electromechanical system (MEMS), was given high consideration in virtue of the properties of high acoustic velocity, low loss, chemical resistance, and etc. In this work, five performance parameters, which are electromechanical coupling coefficients, mass sensitivities, conductivity sensitivities, insert losses and minimum detectable masses, are theoretically investigated in Lamb wave chemical sensors for gas sensing based on SiC substrates. It is presented that higher performance can be achieved based on high-order modes other than fundamental modes, and the abovementioned five parameters can be simultaneously optimized. Then, according to the optimized operating conditions, operating parameters of the SiC-based high-order Lamb wave sensors are designed, which can be easily realized in MEMS technology. Finally, it is demonstrates that the SiC-based sensor exhibits better performance than that of the sensor with a conventional silicon substrate.

Dispersion of Lamb waves under a periodic metal grating in aluminum nitride plates.

Dispersion of Lamb waves propagating in AlN plates with a periodic Al grating on the top surface and an Al electrode on the bottom surface is investigated using the numerical technique SDA-FEM-SDA, which combines finite element modeling (FEM) analysis of the electrode region with spectral-domain analysis (SDA) of the adjacent multi-layered half-spaces. Characteristics of zero-order and higher-order Lamb waves are presented as functions of plate thickness and spectral frequency, which varies in the first Brillouin zone. The structures of typical Lamb waves are examined via visualization of the instantaneous displacement fields in the AlN plate confined between the grating and the bottom electrode. The mechanism of building hybrid modes, which arise from intermode coupling between the counter-propagating Lamb waves of different symmetry and order, is illustrated by two examples of modes propagating with wavelengths λ = 3p and λ = 4p, where p is the pitch of the grating.

Theoretical research on ultrasonic sensors based on high-order Lamb waves

In an ultrasonic sensor, the electromechanical coupling coefficient, sensitivities related to the mass load and conductivity variation, insert loss and minimum detectable mass are important parameters determining the performance of the sensor, while it is challenging to optimize the abovementioned five parameters simultaneously. In this paper, we show that the multi-mode characteristic of Lamb wave provides possibilities to improve the performance of ultrasonic sensors by simultaneously considering the five parameters. According to the simulated results, piezoelectric films, relative thicknesses of films and substrates, structures of interdigital transducers, operating wavelengths and frequencies are optimized based on properly selected operating modes of Lamb wave. Then, high performance of Lamb wave sensors can be realized, in which high electromechanical coupling coefficients, mass sensitivities and conductivity sensitivities in addition to low insert losses and minimum detectable masses are simultaneously achieved.