Thickness Shear Mode Research Articles

Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

The acceleration effect on the vibration frequency of thickness-shear mode of an infinite isotropic plate

With large accelerations, the mechanical vibrations of device structures can be driven to nonlinear states yielding strong variations of vibration characteristics such as frequency change and modes shape distortions. The exact equation of motion with an external acceleration of the thickness-shear vibrations of an infinite isotropic plate is approximated through the coupling in frequencies and solved with harmonics matching, and the approximate solutions of frequency and displacements due to the acceleration are obtained. The analytical solution with good accuracy is obtained and the frequency variation is evaluated with the simple relationship between deformation, acceleration, and frequency.

Optimal Design of TSM Langasite Resonator for High-Temperature Applications: A Review.

In this review article, we address two vital design considerations that govern the high-temperature operation of a thickness-shear mode langasite resonator: 1) electrode design and 2) electrode material. Optimal electrode designs to mitigate unwanted spurious modes and achieve a high Q-factor for fundamental and higher overtone modes have been discussed in great detail. Governing equations that determine the size, shape, and orientation of these electrodes have also been presented. In addition, the suitability of six platinum-group metals as electrode materials for high-temperature resonators have been assessed and summarized. Furthermore, the adhesion to the substrate, electrical conductivity, thermal stability, and various other temperature-dependent properties of these metals have been discussed. Finally, several combinations and operating ranges of these electrode materials have been thoroughly evaluated.

Measurement of the attenuation of elastic waves at GHz frequencies using resonant thickness modes

We present an evaluation of attenuation of elastic waves in the GHz range, based on the decay of thickness-stretch resonances of plates. We measured the elastic response of micro-scale aluminum plates, using a laser-ultrasound technique. The thermo-elastic laser excitation provides significant coupling into thickness-stretch modes in the frequency range above 1.5 GHz. To suppress interference from other resonant and transient modes, we used an excitation spot size well above the plate thickness and applied signal processing in the time and frequency domain. We adapted existing theory on the decay of thickness-shear modes to apply for thickness-stretch modes, validated the derived theory with simulations, and applied it to experiments. A set of samples with different thicknesses in the range of 1.1–2.15 μm allowed us to obtain damping values in the corresponding frequency range of 1.5–3 GHz.

A second-order theory for lithium niobate piezoelectric plates with a ferroelectric inversion layer in coupled extensional, thickness-stretch and symmetric thickness-shear motions

A second-order plate theory for a lithium niobate piezoelectric plate with a ferroelectric inversion layer is established. The theory describes coupled extensional, thickness-stretch and symmetric thickness-shear motions of the plate. The two-dimensional theory obtained is validated by comparing the dispersion relations of the relevant waves with the three-dimensional exact theory. For long waves with small wave numbers, the dispersion curves obtained from the plate theory and the three-dimensional theory have the same cutoff frequencies and curvatures. Therefore, the plate theory is useful in the design of devices operating with these waves. A piezoelectric gyroscope based on symmetric thickness-shear modes is analyzed as an example.

Application of QCM in Peptide and Protein-Based Drug Product Development

AT-cut quartz crystals vibrating in the thickness-shear mode (TSM), especially quartz crystal resonators (QCRs), are well known as very efficient mass sensitive systems because of their sensitivity, accuracy, and biofunctionalization capacity. They are highly reliable in the measurement of the mass of deposited samples, in both gas and liquid matrices. Moreover, they offer real-time monitoring, as well as relatively low production and operation costs. These features make mass sensitive systems applicable in a wide range of different applications, including studies on protein and peptide primary packaging, formulation, and drug product manufacturing process development. This review summarizes the information on some particular implementations of quartz crystal microbalance (QCM) instruments in protein and peptide drug product development as well as their future prospects.

1-Port Piezoelectric Resonators With > 100 V/V Gain

This paper presents a 1-port thickness-shear (TS) mode quartz resonator with very high voltage gain, suitable for use in “near-zero-power” radios. These devices offer voltage gains >100x (referenced to $50~\Omega $ ) at ~50 MHz and >300x at ~75 MHz with ~60 fF load, which is the highest voltage gain directly measured to date in a piezoelectric micromechanical resonator. Six resonators with resonance ${f}_{{\text {r}}}\approx 50$ MHz and identical electrode dimensions are characterized by S11 measurements and by directly measuring the voltage gain using a high-impedance active probe. Quality factor ( ${Q}$ ) up to 140,000 at ~50 MHz and electromechanical coupling ( ${k}_{{\text {eff}}}^{2}$ ) up to 0.445% are demonstrated. In several devices, voltage gain around or above 100 V/V is observed for load ${C}~\approx ~60$ fF, and the gain changes as expected with decreasing load impedance. Additionally, a similar 1-port quartz resonator design at ${f}_{{\text {s}}}~\approx ~75$ MHz is demonstrated to have voltage gain over 300 V/V (referenced to $50\Omega $ ) and ${Q}$ around 335,000. These quartz resonators are fabricated in a mature, commercially available process, promoting widespread integration into radio-frequency (RF) wake-up receivers (WURs). [2020-0196]

Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates

A procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement of electrodes to yield superior performance in the design of quartz crystal resonators. Originally, Bechmann’s number is found through practical experiences, and analytical results were provided afterward to enable optimal design of novel resonator structures. The outcomes in this study are from a simplified theoretical prediction and they are consistent with known empirical results, making it is possible to design optimal quartz crystal resonators for cases without adequate experimental data for a higher frequency and smaller size.

Design Considerations for Frequency Shifts in a Laterally Finite FBAR Sensor in Contact With the Newtonian Liquid.

Mode-coupled vibrations in a thickness-shear (TSh) mode and laterally finite film bulk acoustic resonator (FBAR) with one face in contact with Newtonian (linearly viscous and compressional) liquid are investigated. With boundary conditions and interface continuity conditions, exact dispersion curves in FBAR sensors contacting with two kinds of liquids are obtained, and they are compared with the dispersion curves in a bare sensor without liquid contact. Frequency spectra, describing mode couplings between the main TSh modal branch and undesirable modal branches, are calculated by employing weak boundary conditions at lateral free edges constructed based on the variational principle. Mode shapes of mechanical displacements in both the sensor and liquid layer are presented, and mode transformations are observed due to the liquid contact and lateral edge effect. The effect of liquid thickness on frequency spectra is also studied. Numerical results reveal that the generation of shear wave in the liquid layer results in the shifts of spectrum curves along the frequency axis and hence it is the main factor of frequency shifts of FBAR sensors. The compressional wave causes the shifts of spectrum curves along the lateral aspect ratio axis. Then for a given FBAR sensor, the liquid thickness changes could also cause frequency shifts. Therefore, desirable vibration modes should be chosen based on the frequency spectra to avoid strong mode couplings and to eliminate frequency shifts induced by the liquid thickness changes in real applications.

Radiation-Activated Pre-Differentiated Retinal Tissue Monitored by Acoustic Wave Biosensor.

A thickness-shear mode acoustic wave biosensor operated within a flow-through system was used to examine the response of mouse retinal tissue to radiation. Control experiments conducted with respect to exposure of the bare gold electrodes of the device under various conditions of light intensity and bathing solution yielded reversible changes in resonant frequency (Fs) and motional resistance (Rm). The magnitude of transient changes was proportional to light intensity, but independent of solution type. These alterations in acoustic parameters were ascribed to acoustic coupling phenomena at the electrode-to-liquid interface. Pre-differentiated retina from mouse samples deposited on the thickness shear mode (TSM) electrode exposed to a high light intensity condition also exhibited reversible changes in both Fs and Rm, compared to control experiments involving a coating used to attach the tissue to the electrode. In this case, the radiation-instigated reversible responses for both acoustic parameters exhibited a reduction in magnitude. The changes are ascribed to the alteration in viscoelasticity of the retinal matrix on the TSM electrode surface. The precise biophysical mechanism responsible for the changes in Fs and Rm remains a challenge, given the complex make up of retinal tissue.

Long-distance structural health monitoring of buried pipes using pitch-catch T(0,1) wave piezoelectric ring array transducers

In modern industries, long-distance guided wave inspection has been routinely used for various types of pipelines. The usage of T(0,1) wave is always of great interests since it is the only non-dispersive wave mode in pipes. In this work, a pair of pitch-catch piezoelectric ring arrays were proposed for long-distance structural health monitoring (SHM) of buried pipes. Firstly, the working principle of the proposed transducer was introduced. Next, the performances of thickness-shear (d15) and face-shear (d24) modes based piezoelectric ring transducers in T(0,1) wave generation and reception were comparatively tested. It was found that at most frequencies, it is best to employ the d15 ring as the exciter and the d24 ring as the receiver. Then, the signal-to-noise ratio (SNR) of the generated T(0,1) wave and its attenuation in pipes with different coating conditions were investigated to estimate the detectable distance using the proposed transducer. Results showed that after applying acoustical isolation layer on pipes, the proposed ring transducers can inspect buried pipes over 20 m. Finally, the performance of the ring transducers in defect detection was validated. This work is expected to provide a promising solution to long-distance SHM of buried pipes.

A microfabricated thickness shear mode electroacoustic resonator for the label-free detection of cardiac troponin in serum

Portable, and automated biosensors for the detection of cardiac biomarkers are important for the early diagnosis of acute myocardial infarction. We demonstrate a label-free microfabricated thickness shear mode electroacoustic device based on a ZnO piezoelectric film for the assay of cardiac biomarkers. This device combines an immunologic sensitive element with the resonator working in biological liquids. Based on the gravimetric mechanism, the immunoreaction between the target antigens and antibodies was detected by monitoring the frequency change in real-time to determine the concentration of cardiac troponins I. The device exhibits a linear response from 0.04 to 2 ng/ml and a low detection limit of 20 pg/ml in serum containing cardiac troponin I. The clinical samples collected from healthy controls and cardiac patients were directly used without any additional pre-treatment. The cardiac troponin concentrations measured by the proposed device shows good linear correlation and consistency compared with standard laboratory methods. The results indicate that the device can to be a feasible tool for sensitive, rapid, and miniaturized point-of-care analytical systems.

High frequency thickness expansion mode bulk acoustic wave resonator using LN single crystal thin plate

In this report, a thickness expansion mode film bulk acoustic resonator (FBAR) was fabricated using 4 μm thick 36°Y-LiNbO3(LN) single crystal thin plate. The LN thin plate was made by polishing after bonded to a Si bare wafer. The LN FBAR showed a bandwidth of 10.3% and an impedance ratio of 45 dB at 800 MHz. The spurious response due to a thickness shear (TS) mode was much smaller than the main mode, because the optimal cut angle was chosen. The quality factor of anti-resonance is poor probably due to acoustic loss caused by a misalignment of the upper and lower electrodes, the series connection of two resonators etc. By minimizing the acoustic loss, the impedance ratio can be improved up to 60 dB.

Quantitative domain engineering for realizing d36 piezoelectric coefficient in tetragonal ceramics

Piezoelectric devices based on d36 mode are remarkably stable that depolarization rarely occurs in d36 face shear mode, because d36 mode is completely different from d15 thickness shear mode, where the applied electric field is perpendicular to poling direction and depolarization is ineluctable due to 90° dipole rotation. However, piezoelectric ceramics conventionally possess three piezoelectric coefficients (i.e., d33, d31, and d15), while d36 only exists in single crystals of specific point groups and cut directions. In this work, we propose a method to realize d36 piezoelectric coefficient in tetragonal piezoelectric ceramics by mechanical and electric domain engineering. This method is successfully applied in bismuth scandium-lead titanate (abbreviated as BS-PT) high-temperature piezoelectric ceramics with a resultant d36 up to 160 pC/N, which broadens the application of BS-PT ceramics, such as face shear actuator, energy harvester, transducer, etc. We find that domain engineering by transversal electric poling is preferred compared with the transversal mechanical poling, due to the simpler process, higher reliability, and higher resultant d36 piezoelectric coefficient. By combining the Diffraction-Plane-Transformation (DPT) model with the domain engineering via transversal electric poling, we demonstrate a quantitative domain engineering method for the first time, which could be used for optimizing the piezoelectric properties by precise design of the domain structures in piezoelectric materials.

Examinations of vibration frequency and mode shape variations of quartz crystal plates in a thermal field with strain and kinetic energies

The frequency-temperature behavior has long been analyzed to ensure the smoothness of functioning frequency of a quartz crystal resonator during the temperature variation and maintain its operations in a stable state. It has been proven that vibrations of quartz crystal plates in the thickness-shear mode can be well described by the theory of incremental thermal field in conjunction with the Mindlin plate equations, demonstrating the possibility that vibration frequencies and mode shapes can also be well predicted with the temperature as a targeted variable. By studying the vibrations with temperature changes in a given range, the frequencies and vibration modes can be calculated as a function of temperature, then they can be used in the calculations of both strain and kinetic energies for vibration mode identification or characterization based on energy proportion and changes. The trends of changes of vibration frequency, amplitudes, and energy with temperature variation make it possible for characterization the variations of vibrations and particularly the weakening or enhancement of the dominance of specific vibration modes. With such relations between vibration properties and temperature known, possible analytical tools can be developed to aid the optimal design by avoiding significant mode changes or occurrences of mode conversion.

Bulk and Surface Acoustic Wave Sensor Arrays for Multi-Analyte Detection: A Review.

Bulk acoustic wave (BAW) and surface acoustic wave (SAW) sensor devices have successfully been used in a wide variety of gas sensing, liquid sensing, and biosensing applications. Devices include BAW sensors using thickness shear modes and SAW sensors using Rayleigh waves or horizontally polarized shear waves (HPSWs). Analyte specificity and selectivity of the sensors are determined by the sensor coatings. If a group of analytes is to be detected or if only selective coatings (i.e., coatings responding to more than one analyte) are available, the use of multi-sensor arrays is advantageous, as the evaluation of the resulting signal patterns allows qualitative and quantitative characterization of the sample. Virtual sensor arrays utilize only one sensor but combine it with enhanced signal evaluation methods or preceding sample separation, which results in similar results as obtained with multi-sensor arrays. Both array types have shown to be promising with regard to system integration and low costs. This review discusses principles and design considerations for acoustic multi-sensor and virtual sensor arrays and outlines the use of these arrays in multi-analyte detection applications, focusing mainly on developments of the past decade.

High temperature piezoelectric properties of flux-grown α-GeO2 single crystal

The temperature dependence of the piezoelectric properties of trigonal α-GeO2 single crystals obtained by the high-temperature flux method was measured by the resonance technique of the electrical impedance in the 20 °C–600 °C range. To approach the values of the two independent piezoelectric coefficients d11 and d14, we first measured as a function of temperature the elastic coefficients S11, S14, and S66 and the dielectric permittivity ε11, which are involved in the coupling coefficient k of both the thickness shear mode and the transverse mode. A Y-cut plate with a simple +45° rotation [(YXtwl) +45°/0°/0°] was used to measure the coupling coefficient of the thickness shear mode, and two X-turned plates [(XYtwl) +45°/0°/0° and (XYtwl) −45°/0°/0°] were prepared to characterize the coupling coefficient of two transverse modes. From the whole experimental measurements, the piezoelectric coefficients of α-GeO2 were calculated up to 600 °C. They show that this crystal is one of the most efficient in regard to the α-quartz-like family at room temperature and that its thermal comportment retains large piezoelectric properties up to 600 °C.

AT-Cut Quartz Piezoelectric Transformers for Passive Voltage Gain in an RF Front-End

The purpose of this work is to assess the performance of an AT-cut quartz device as a two-port resonant transformer for near-zero power-consuming wake-up receiver applications. The device consists of two, coupled thickness-shear mode trapped-energy ~50 MHz resonators on a single quartz substrate. Passive voltage gain up to 84 V/V (referenced to $50\Omega $ ) is observed when the device is driven by a low-power signal (≤ −30 dBm) at resonance. This transformer offers high voltage gain suitable for use in the front-end of a near-zero-power wake-up receiver. Additionally, this work shows that connecting two coupled-resonator quartz devices in a parallel-input, series-output (PISOT) configuration provides improvements in voltage gain. A 17% increase in gain is demonstrated for PISOT over that of a single coupled resonant transformer for various load impedances. This work is the first use of quartz piezoelectric transformers (PTs) for passive voltage gain, and the highest open-circuit gain demonstrated in a two-port micromechanical PT.

Mathematical modelling of magnetoelectric effect in multiferroic in thickness-shear mode region

The article discusses the magnetoelectric effect in the thickness-shear mode region in a layered structure of a piezoelectric bimorph and a magnetostrictive material. Numerical estimates according to the proposed theoretical model of the magnetoelectric effect in the structure of the langatate bimorph and yttrium-iron garnet show that the value of ME voltage coefficient is much higher than for the bilayer of langatate and yttrium-iron garnet.

Two-Dimensional Coupling Vibration Analysis of Laterally Acoustically Coupled Two-Port Thin-Film Bulk Acoustic Resonators

In this paper, we present an approach to studying the mode coupling vibrations in two-port thin-film bulk acoustic wave resonator (FBAR) devices with two pairs of electrodes deposited on the zinc oxide film. The two-dimensional plate theory established in our previous work is employed, which takes into account the coupling of the operating thickness-extensional mode with the extensional, flexural, fundamental and second-order thickness-shear modes. The propagation of straight-crested waves in the plate is studied, and the state-vector approach is successfully used to simplify the derivation process. For a structurally symmetric device, the modes are separated into quasi symmetric and antisymmetric ones. Frequency spectra and corresponding mode shapes are obtained under the stress-free boundary conditions, respectively, and then coupling effects and energy trapping phenomenon are discussed in detail. Some results for structures with asymmetric electrode distributions are also shown. It is found that the choice of aspect ratio has a great effect on mode couplings of FBAR devices. This study will be useful for the design of FBAR filters and sensors.