Thickness Shear Mode Research Articles

An Energy Approach to the Modal Identification of a Variable Thickness Quartz Crystal Plate

The primary objective of modal identification for variable thickness quartz plates is to ascertain their dominant operating mode, which is essential for examining the vibration of beveled quartz resonators. These beveled resonators are plate structures with varying thicknesses. While the beveling process mitigates some spurious modes, it still presents challenges for modal identification. In this work, we introduce a modal identification technique based on the energy method. When a plate with variable thickness is in a resonant state of thickness–shear vibration, the proportions of strain energy and kinetic energy associated with the thickness–shear mode in the total energy reach their peak values. Near this frequency, their proportions are the highest, aiding in identifying the dominant mode. Our research was based on the Mindlin plate theory, and appropriate modal truncation were conducted by retaining three modes for the coupled vibration analysis. The governing equation of the coupled vibration was solved for eigenvalue problem, and the modal energy proportions were calculated based on the determined modal displacement and frequency. Finally, we computed the eigenvalue problems at different beveling time, as well as the modal energies associated with each mode. By calculating the energy proportions, we could clearly identify the dominant mode at each frequency. Our proposed method can effectively assist engineers in identifying vibration modes, facilitating the design and optimization of variable thickness quartz resonators for sensing applications.

Smart structural health monitoring (SHM) system for on-board localization of defects in pipes using torsional ultrasonic guided waves

Most reported research for monitoring health of pipelines using ultrasonic guided waves (GW) typically utilize bulky piezoelectric transducer rings and laboratory-grade ultrasonic non-destructive testing (NDT) equipment. Consequently, the translation of these approaches from laboratory settings to field-deployable systems for real-time structural health monitoring (SHM) becomes challenging. In this work, we present an innovative algorithm for damage identification and localization in pipes, implemented on a compact FPGA-based smart GW-SHM system. The custom-designed board, featuring a Xilinx Artix-7 FPGA and front-end electronics, is capable of actuating the PZT thickness shear mode transducers, data acquisition and recording from PZT sensors and generating a damage index (DI) map for localizing the damage on the structure. The algorithm is a variation of the common source method adapted for cylindrical geometry. The utility of the algorithm is demonstrated for detection and localization of defects such as notch and mass loading on a steel pipe, through extensive finite element (FE) method simulations. Experimental results obtained using a C-clamp for applying mass loading on the pipe show good agreement with the FE simulations. The localization error values for experimental data analysed using C code on a processor implemented on the FPGA are consistent with algorithm results generated on a computer running Python code. The system presented in this study is suitable for a wide range of GW-SHM applications, especially in cost-sensitive scenarios that benefit from on-node signal processing over cloud-based solutions.

Finite element simulations of quartz crystal microbalances (QCM): from Sauerbrey to fractional viscoelasticity under water

2D finite element simulations are performed on QCM working in the thickness-shear mode and loaded with different homogeneous films. They include a purely elastic film, a viscoelastic Maxwellian liquid, viscoelastic-Voigt solid, and the fractional viscoelastic (power-law) version of each case. Unlike single-relaxation kind models, fractional viscoelasticity considers the relaxation-time spectrum often found in polymeric materials. The films are tested in air or covered with liquids of different viscosities. Two substrate thicknesses are tested: 100 nm and 500 nm, the latter being close to the condition that promotes the resonance of the adsorbed film. In all cases the simulations are compared with small-load approximation theory (SLA). The 100 nm films follow the theory closely, although significant deviations of the SLA are observed as the overtone number n increases, even in purely elastic films. We also show that it is possible to identify the viscoelastic ‘fingerprint’ of the 100 nm films in air using raw data and Sauerbrey’s equivalent thickness obtained with the QCM in the 3 < n < 13 range. These numerical data are validated by experimental measurements of crosslinked polydimethylsiloxane films with thicknesses ∼150 nm. In contrast, the 500 nm films deviate notoriously from the SLA, for all viscoelastic models and overtones, with the largest deviation observed in the elastic film. When a liquid layer covers the QCM without an adsorbed film, the only overtone that numerically reproduces the theoretical value is the fundamental, n = 1. For n > 1, strong coupling between the solid and liquid is detected, and the original vibration modes of the crystal are altered by the presence of the liquid. Finally, the numerical simulations suggest that it is possible to detect whether a viscoelastic film is formed under a liquid layer using only the information from n = 1. In these film/liquid systems we also observe the so-called missing-mass effect, although the theory and simulations exhibit different levels of impact of such effect when the liquid viscosity is high.

A nonlinear analysis of electrically forced vibrations of piezoelectric plates with viscous damping near the thickness-shear mode

Based on the theory of nonlinear piezoelectricity, an approximate solution for electrically forced nonlinear thickness-shear vibrations of piezoelectric plates is introduced. The model considers an infinite piezoelectric plate subjected to an alternative voltage, incorporating 3rd-order and 4th-order elastic constants and viscous damping under finite deformation. The system's differential equations for steady-state forced vibrations are derived from the nonlinear pure thickness-shear vibration problem, and transformed so that the new electrical boundary conditions are free. After the application of Galerkin's method, the transformed differential equations lead to a cubic equation, capturing the nonlinear current-frequency curves of AT-cut quartz plates without the need of the quality factor Q, due to the introduced viscous damping. When the damping effect is ignored, the frequency response curves of the AT-cut quartz plate under a specific voltage are confirmed with the existing literature. The study emphasizes the presence of the critical voltage and the importance of the fourth-order elastic constant (c6666) in the stability, revealing lower c6666 values correspond to improved stability. Additionally, a proposed algorithm efficiently determines critical voltages for resonator stability.

Magnetoelectric Sensor Operating in d15 Thickness-Shear Mode for High-Frequency Current Detection.

For the application of high-frequency current detection in power systems, such as very fast transient current, lightning current, partial discharge pulse current, etc., current sensors with a quick response are indispensable. Here, we propose a high-frequency magnetoelectric current sensor, which consists of a PZT piezoelectric ceramic and Metglas amorphous alloy. The proposed sensor is designed to work under d15 thickness-shear mode, with the resonant frequency around 1.029 MHz. Furthermore, the proposed sensor is fabricated as a high-frequency magnetoelectric current sensor. A comparative experiment is carried out between the tunnel magnetoresistance sensor and the magnetoelectric sensor, in the aspect of high-frequency current detection up to 3 MHz. Our experimental results demonstrate that the d15 thickness-shear mode magnetoelectric sensor has great potential for high-frequency current detection in smart grids.

Multimodal vibration damping of a three-dimensional circular ring coupled to analogous piezoelectric networks

Analogous piezoelectric networks have been shown to be effective for multimodal vibration attenuation in structures, including beams, plates, and rings. Previous studies for rings have only accounted for in-plane transverse vibration attenuation and disregarded the out-of-plane vibration modes. Furthermore, these previous numerical models and experiments have only been studied on thin rings, which ignore the effects of shear deformation and rotary inertia. As a result, these networks are not suitable for attenuating vibrations in thick rings. This study enhances on the previous electrical networks, considering both shear deformation and rotary inertia for both in-plane and out-of-plane vibrations. A new passive network topology is developed for the out-of-plane dynamics of thick rings, and the existing passive analogous network of in-plane vibration of thin rings is enhanced by considering the effects of shear deformation and rotary inertia. Combined, these new networks are capable of multimodal vibration damping of a thick ring in three-dimensions, encompassing primarily six types of vibration modes: the inextensional bending modes, the extensional modes, the thickness-shear modes, the coupled twist-bending modes, the torsional modes, and the transverse thickness-shear modes. By using piezoelectric elements to couple two separate analogous passive electrical networks derived from both the in-plane and out-of-plane governing equations of a ring and optimizing the internal resistance in each unit cell, it becomes possible to replicate the dynamics and effectively attenuate different types of vibration modes. This study serves as a theoretical foundation for implementations of passive vibration attenuation in ring structures.

Metasubstrate-based SH guided wave piezoelectric transducer for unidirectional beam deflection without time delay

Focusing the energy of a guided wave along a desired direction is of great significance in structural health monitoring (SHM), since it can improve the sensitivity to defects and reduce the complexity of signal interpretations. The phased array method is the most common approach for beam deflection, which requires a high uniformity of each element and the support of expensive and complex electronics. Moreover, the mirrored wave beam cannot be avoided for a linear array, resulting in the difficulty of distinguishing the defects at the symmetric positions. In this work, a metasubstrate-based piezoelectric transducer (MSBPT) is developed for unidirectional SH0 wave (the fundamental shear horizontal wave) beam deflection under a single driving source. The proposed MSBPT is constituted by a metasubstrate and two columns of thickness-shear mode PZT wafers. The metasubstrate is designed to provide the required phase gradient for unidirectional beam deflection, so no extra time delay is needed during excitation and reception. An analytical model is proposed to guide the design of the transducer to obtain the desired wave beam. The beam deflection properties of the MSBPT are validated by finite element simulations and experiments. It is observed that the MSBPT can concentrate the energy of the generated SH0 mode only in one desired direction with a small divergence angle. Moreover, the MSBPT can also serve as a sensor that only receives the SH0 mode propagating from the deflection angle and filters out the wave energies from other incident angles. Due to the simple configuration, the proposed MSBPT will be helpful in the controllable generation and reception of SH0 mode in SHM.

Geometric eccentricity effect on thickness-shear vibration of an elliptical flexoelectric crystal plate

In this paper, a thickness-shear vibration model for a two-dimensional finite flexoelectric crystal plate with slowly varying thickness and elliptical cross section is presented. The influences of eccentricity and flexoelectricity on the fundamental frequencies of thickness-shear vibration and electric potential distributions under short circuit boundary condition are investigated. The proposed model uses the first order McLaughlin series to approximate the elliptical function and the first derivative of elliptical function is ignored since the plate thickness varies slowly. For the finite plate, the symmetric mode in length and antisymmetric mode in thickness are adopted for the displacement function. In addition, only the shear strain gradient through the thickness is used in the mathematical model for the thin and long flexoelectric crystal plate. By implementing the variational principle, the governing equations are obtained and further solved by the Galerkin method. The obtained frequencies of thickness-shear mode are expressed in terms of eccentricity and length-to-thickness ratio. The results show that the eccentricity has great influence on the nondimensional fundamental frequencies. A small reduction in eccentricity results in significant increment of the nondimensional frequency implying that it is possible to increase the fundamental frequency by changing the cross section of the elliptical flexoelectric plate. The flexoelectric effect is also found to affect the nondimensional frequency and electric potential distribution significantly. Thus, for accurate design of nano/micro scale high precision and high frequency flexoelectric/piezoelectric devices, flexoelectricity must be taken into consideration.

Staphylococcus aureus Detection in Milk Using a Thickness Shear Mode Acoustic Aptasensor with an Antifouling Probe Linker.

Contamination of food by pathogens can pose a serious risk to health. Therefore, monitoring for the presence of pathogens is critical to identify and regulate microbiological contamination of food. In this work, an aptasensor based on a thickness shear mode acoustic method (TSM) with dissipation monitoring was developed to detect and quantify Staphylococcus aureus directly in whole UHT cow's milk. The frequency variation and dissipation data demonstrated the correct immobilization of the components. The analysis of viscoelastic properties suggests that DNA aptamers bind to the surface in a non-dense manner, which favors the binding with bacteria. The aptasensor demonstrated high sensitivity and was able to detect S. aureus in milk with a 33 CFU/mL limit of detection. Analysis was successful in milk due to the sensor's antifouling properties, which is based on 3-dithiothreitol propanoic acid (DTTCOOH) antifouling thiol linker. Compared to bare and modified (dithiothreitol (DTT), 11-mercaptoundecanoic acid (MUA), and 1-undecanethiol (UDT)) quartz crystals, the sensitivity of the sensor's antifouling in milk improved by about 82-96%. The excellent sensitivity and ability to detect and quantify S. aureus in whole UHT cow's milk demonstrates that the system is applicable for rapid and efficient analysis of milk safety.

A Filter-Free Third Overtone Quartz Oscillator Based on Micromachining Technology.

This work investigates an AT-cut quartz crystal oscillator (XO) operating at its enhanced third overtone thickness shear (TS) mode while suppressing the fundamental TS mode by micromachining technology. A unique quartz plate structure has been proposed to alleviate the strong resonant signal from the first mode. A finite-element method (FEM) was used to characterize the first mode suppression while improving the performance of third overtone in terms of Q -factor and motional resistance ( Rm ) of the proposed device. In measurement, the unloaded Q -factor of the fundamental TS mode is from several tens of thousands (the reference design) to only several hundred (the proposed design). Meanwhile, the unloaded Q -factor of the third overtone response for the proposed design could reach Q ∼95 000 with a decent Rm . The Q -factor ratio attains 170-180 between the third overtone and fundamental modes. With the feature of low Q -factor on the fundamental mode, the oscillator system could successfully oscillate at a higher frequency without the help of bandpass filtering. Finally, the closed-loop oscillation measurement is performed for the phase noise (PN) characterization. The PN performance could reach -154.5 dBc/Hz at a 1-kHz offset at the carrier frequency of ∼ 60 MHz. This technique has proven its potential as a future solution of high-frequency quartz oscillator technology.

A Quartz Crystal Microbalance (QCM) Study on the Formation of Aqueous κ-Carrageenan-Chitosan Composite Bilayers with NaCl and Graphene Oxide

Biomaterials and thin biofilms play a fundamental role in the medical, food and pharmaceutical industries. The Quartz crystal microbalance (QCM) measurement technique is one of the attractive techniques which have been used for monitoring the thin-film formation process. In the current work described here, κ-carrageenan and chitosan solutions were used for the layer-by-layer (LBL) deposition of polyelectrolyte multilayers (PEMs) on the gold surface of a 5 MHz AT-cut (thickness-shear mode) quartz crystal in a flow module. A sensitive QCM system was designed to detect 0.1 Hz differences in the resonance frequency (Δf) and 10−7 changes in the energy dissipation (ΔD) values, which are the measures of the deposited mass and the film rigidity, respectively. Negatively charged carrageenan and positively charged chitosan biomolecules in the solutions were used to build up sequential and very thin bilayers on the modified gold surface. The effects of NaCl and graphene oxide (GO) addition on the mass of the deposited films were also investigated. Intermolecular interactions between the biopolymer chains, Na+ cations and GO sheets were explained by interactions between molecules, such as electrostatic forces and hydrogen bondings.

Time-delayed layer-based piezoelectric transducer for unidirectional excitation and reception of SH guided wave

Unidirectional excitation of a single-mode guided wave (GW) is of great significance in GW-based structural health monitoring (SHM) and nondestructive testing (NDT). Currently, very few transducers are capable of generating unidirectional propagation GW in plate-like structures, so such a goal is usually achieved by using phased array transducers, which are relatively expensive and only work within a narrow frequency range. In this work, a time-delayed layer-based piezoelectric transducer (TDLBPT) is developed for unidirectionally generating and receiving pure SH0 wave (zero-order shear horizontal wave). The TDLBPT consists of a time-delayed layer and two rectangular thickness-shear (d15) mode piezoelectric wafers. The time-delayed layer component is designed for achieving the phase gradient over a wide range of frequencies, so in both unidirectional excitation and reception, no extra time delay is required for the proposed TDLBPT. An analytic model is proposed to predict the SH0 wavefields generated by the TDLBPT, which can provide guidelines for designing the TDLBPT. Finite element (FE) simulations and experiments are performed to examine the performance of the developed TDLBPT. Both simulated and experimental results show that the TDLBPT can generate pure SH0 wave and focus the wave energy along a given direction in a plate over a wide range of frequencies. Moreover, the reception performance of the TDLBPT also shows excellent unidirectionality. Due to the excellent performance and easy fabrication, the proposed TDLBPT will be very useful in unidirectional excitation and reception of SH0 wave in SHM and NDT.

Degenerate normal-mode states above the cutoff frequency as analogs of the thickness-shear mode for finite Timoshenko–Ehrenfest beams with free ends

In this work, we demonstrate, analytically and numerically, that degenerate states of a beam with free ends, with anti-symmetrical transverse mode shape and occurring in the first-degeneracy points above the cutoff frequency, tend asymptotically to the thickness-shear mode in the infinitely long beam limit, which has not been previously reported. We compare our numerical results, obtained using a Timoshenko–Ehrenfest beam theory of second order, with those obtained with the Finite Element method and plane stress elastodynamics theory, obtaining an excellent agreement. We show that anti-symmetric states within the vicinity of these first-degeneracy states are very similar and closely resemble the so-called thickness-shear mode but for a finite beam with free ends under flexural vibrations.

Charge transport and acoustic loss in lithium niobate-lithium tantalate solid solutions at temperatures up to 900 °C

Polar oxides, in particular solid solutions of lithium niobate and lithium tantalate (LNT, LiNb1-xTaxO3) are a variable model system to study fundamental materials properties due to miscibility of the edge compounds lithium niobate (LN, LiNbO3) and lithium tantalate (LT, LiTaO3) as well as tunable domain structures. Further new applications in the field of high-temperature actuators are aimed as LNT crystals potentially combine the advantages of the edge compounds with respect to high thermal stability and high piezoelectric coefficients. Beside LN and LT, LNT crystals of two compositions (LiNb0.88Ta0.12O3 and LiNb0.5Ta0.5O3) were grown by the Czochralski technique. Electrical conductivity, lithium diffusion and acoustic loss of LNT at high temperatures were investigated and correlated. Two techniques, namely impedance spectroscopy and resonant piezoelectric spectroscopy (RPS) are applied in this investigation. The electrical conductivity of investigated samples increases linearly in an Arrhenius presentation up to ∼605 °C. After a transition range of 605–620 °C, the conductivity increases linearly again for LT, but the slope is decreased by about 0.15 eV. This indicates that the conductivity below and above the Curie temperature is governed by a slightly different process. In contrast, LN shows a gradually increasing slope in the Arrhenius representation above the transition temperature range mentioned above. Here, a single activation energy cannot be assigned. The increase can be explained by the limited thermal stability of LN at elevated temperatures. Further, the acoustic loss in LNT thickness-shear mode resonators operated at about 2 and 10 MHz is determined by RPS and found to strongly increase above about 450 °C. In addition, the acoustic loss is modelled using independent materials data including electrical conductivity as determined here, and found to be in excellent agreement with the RPS data for the 10 MHz resonator. Based on the modelling, the loss above 450 °C is governed by conductivity-induced piezoelectric/carrier relaxation which can be attributed to lithium migration.

Mesoscopic Monitoring of Human Skin Explants Viscoelastic Properties

The investigation of the mechanical properties of skin is of great interest for monitoring physiological and pathological changes in the cutaneous barrier function for dermatological and cosmetic issues. Skin constitutes a complex tissue because of its multi-layered organisation. From a rheological point of view, it can be considered to be a soft tissue with viscoelastic properties. In order to characterise ex vivo mechanical properties of skin on the mesoscopic scale, a biosensor including a thickness shear mode transducer (TSM) in contact with a skin explant was used. A specific experimental set-up was developed to monitor continuously and in real-time human skin explants, including the dermis and the epidermis. These were kept alive for up to 8 days. Skin viscoelastic evolutions can be quantified with a multi-frequency impedance measurement (from 5 MHz to 45 MHz) combined with a dedicated fractional calculus model. Two relevant parameters for the non-destructive mesoscopic characterisation of skin explants were extracted: the structural parameter αapp and the apparent viscosity ηapp. In this study, the validity of the biosensor, including repeatability and viability, was controlled. A typical signature of the viscoelastic evolutions of the different cutaneous layers was identified. Finally, monitoring was carried out on stripped explants mimicking a weakened barrier function.

Stepped electrode designs of TSM langasite resonators for high-temperature applications

In this paper, we report the simulation and fabrication of thickness-shear mode langasite resonators with stepped elliptical electrode designs to investigate their effects on energy trapping and suppression of spurious modes at elevated temperatures. Finite element analysis was conducted to analyze the design of a stepped elliptical electrode on a contoured langasite crystal. Based on the simulation findings, langasite resonators with stepped electrodes were fabricated, and their displacement profiles and frequency–temperature properties were characterized using network analysis and laser Doppler vibrometry. Results demonstrate improved frequency separation between the resonant and spurious modes, and enhanced spurious mode suppression at both room and higher temperatures, suggesting that stepped elliptical electrode designs can effectively enhance the sensing performance of langasite resonators.

Temperature characteristics of a thickness shear mode quartz crystal resonator bonded to a support substrate

Thickness shear mode (TSM) resonators consisting of metal films and quartz plates are widely used for sensor applications such as film thickness monitoring, force sensors, and odor sensors. However, the current sensor geometry prevents further improvements in its sensitivity and stability. Thinning the plate is necessary for high sensitivity, and advanced fabrication technologies are required for their commercialization. The solution is to use a support substrate to increase the mechanical strength, which can guide the transmittance of the electric field. Herein, we report a TSM resonator bonded to a support substrate. An AT-cut quartz resonator with a floating electrode on the top side was bonded to the support substrate. Two excitation electrodes were placed under the substrate. The support substrates evaluated in this study included borosilicate glass, Z-cut quartz crystals, and AT-cut quartz crystal plates. The quartz crystal resonator (QCR) bonded to the AT-cut quartz crystal plate and positioned at 90° to the crystallographic x-axis shows an excellent temperature coefficient of frequency of −60 ± 14 ppb/°C for a temperature range 11–40 °C. The proposed method reduces temperature sensitivity to 1/4 or less compared to that without a substrate. Furthermore, the resonator could be used as a quartz crystal microbalance. The proposed method may inspire further high-frequency QCR-based biochemical chips or various sensor applications with TSM resonators.

Numerical investigations of Lamb waves excited by interdigital transducers and incident on piezoelectric plates

This study investigated the thickness mode and thickness shear mode of Lamb waves excited by a surface interdigital transducer and incident on piezoelectric ceramic plates. We numerically calculated the time-domain response, frequency-domain response, and propagation characteristics of these waves. To determine the electric field intensity of a surface interdigital transducer with a semi-infinite domain, the driving potentials of the surface electrodes of the piezoelectric plates were approximated using a series solution and the Legendre function. The wave propagation responses of the plates were determined by considering the electromechanical coupling effect of piezoelectric materials and assuming the electrical boundary conditions of three external excitation sources. A modified Clenshaw–Curtis numerical integration method was used to calculate the frequency-domain response of the Lamb wave displacement of the piezoelectric plates excited by an interdigital electrode. The time-domain response of this displacement was determined using the inverse fast Fourier transform method. This study also examined the near- and far-field Lamb wave responses of interdigital transducers with different electrode numbers and electrode widths.

BAW Resonator with an Optimized SiO2/Ta2O5 Reflector for 5G Applications.

In the present work, a lithium niobate (LN) 43°Y cut LN film is transferred onto a substrate with 11 layers of SiO2/Ta2O5 and solidly mounted resonators with a reflector are successfully fabricated with the multilayer structure. The design method and fabrication process are demonstrated. The finite element model and the Mason model are used. Scanning electron microscopy and atomic force microscopy are used to characterize film quality. An optimized design of a Bragg reflector to suppress the leakage of acoustic energy by thickness shear mode is proven to be effective. The influence of the reflector on parasitic modes and filter out-of-band suppression is analyzed. The resonator for 3.5 GHz shows an effective electromechanical coupling coefficient of 17.9%, and the figure of merit is 40.4, which is suitable for band pass filter on the N78 band with high rejection.

3.4 GHz strip-type thickness shear mode solidly-mounted bulk acoustic wave resonator using X-cut LiTaO3

This paper describes a high-frequency bulk acoustic wave resonator (BAWR) with a solidly-mounted (SM) structure using single crystal LiTaO3 (LT) thin plates. A Bragg reflector solidly supports the LT thin plate, which is fragile if self-suspended. The two kinds of BAWRs use a strip-type thickness shear mode in 0.56 μm thick X37°Y LT and X127°Y LT. The Bragg reflector is made of 5 pairs of Al and Ta films, i.e. 10 layers in total. The X37°Y LT SM structure BAWRs exhibited a resonance frequency (f r) of 3.250 GHz, an anti-resonance frequency (f a) of 3.463 GHz, a bandwidth (BW) of 6.6%, and an impedance (Z) ratio of 48 dB. The X127°Y LT BAWR has a similar characteristic with f r of 3.153 GHz, f a of 3.367 GHz, a BW of 6.8%, and a Z ratio of 46 dB. The X37°Y LT BAWR showed an advantage of 2 dB compared with the X127°Y LT one. The Al film acts as a low acoustic impedance film, but an acoustic impedance layer combination of Al and Ta films is not suitable and that of SiO2 and W films suitable among the four combinations, Al/Ta. SiO2/Ta, Al/W, and SiO2/W films. Although the acoustic impedance layer combination, the acoustic film quality, the structure, electrode design, and fabrication process of the fabricated BAWRs were not optimized yet, this result suggests the high potential of this device.