Piezoceramic Disk Research Articles

An exact analytical solution for coupled vibration analysis of a piezoelectric resonator

Abstract Piezoelectric resonators are widely used as the active components in devices such as sensors, actuators, communication filters, and micro/nano-electro-mechanical systems (MEMS / NEMS). Due to the piezoelectric effect, Poisson’s ratio, and its finite dimension, the thickness and lateral vibration modes in a piezoelectric resonator are inevitably coupled. In this paper, an exact analytical model for coupled vibration analysis of a piezoceramic disk is developed based on a new superstition method. The free vibrations are decomposed into thickness and lateral directions in a new form of Fourier-Bessel series and then they are superimposed to satisfy the boundary conditions. To verify the validity of the analytical model proposed here, numerical simulations are performed using COMSOL Multiphysics. An excellent agreement is observed. This analytical model can be applied to the design and optimization of piezoelectric devices.

Demonstrating the feasibility of monitoring bone fracture healing using electromechanical impedance spectroscopy – a comparison between three different inputs in Ward’s hierarchical clustering method

Current methods for monitoring the progression of bone fracture healing require large, complex, and expensive imaging technology and, if used repeatedly, can expose patients to harmful ionizing radiation. Recent development of miniaturized, implantable, inexpensive microelectronic sensing technology now makes it possible to continuously monitor fracture healing non-invasively at the patient's bedside. This proof-of-concept study demonstrates a novel, smart, implantable medical device based on electromechanical impedance spectroscopy. The setup consists mainly of a piezoceramic disk (PIC255 from PI Ceramics), an impedance chip (AD5933 from Analog Devices) and an inductive battery recharging system. The system operates autonomously for 24 hours of measurements. Every 20 minutes, the health state of the bone is measured. To test the setup, 20 tibia bones of sheep limbs obtained from a butcher's shop are used. By drilling five holes into the bone one after another, different defects mimicking bone fractures of different sizes are created. This simulates an inverse bone healing process. The collected data is transmitted via Bluetooth LE to a portable device that displays the impedance spectra. After the results have been reviewed, the data is transferred to a computer for statistical evaluation, such as the Root Mean Square Deviation (RMSD). Preliminary results have shown an increasing trend in RMSD with increasing number of holes in the bone. Based on these observations, an in-vivo study is planned.

Piezoelectric hysteresis and relaxation process in ferroelectric ceramics in a weak electric field

In this work, the piezoelectric hysteresis and relaxation process induced by a weak DC electric field in ferroelectric ceramics were studied using the impedance spectroscopy method and piezoelectric resonance analysis program (PRAP). The DC field and time dependences of the complex dielectric constants were measured for the radial extensional mode of vibrations of thin piezoceramic disks. It was found that the hysteresis and relaxation nature of the field and time dependences of the complex dielectric constants were caused by the reversible displacements of 90° domain walls as well as the space charge transformation.

Sensitivity-Adjustable force sensors based on one-dimensional superlattice structures

A proposed force sensor contains a one-dimensional periodic superlattice and piezoceramic wave generator–receiver pair. For force sensing, the strain induced by an applied force in the phononic structure causes stop band frequency variations because the sound velocity varies with the induced strain (stress). When the input wave frequency coincides with the margins of the stop band, it results in noticeable variations in the wave transmission rate with the applied strain. As a result, sensitivity, represented by the transmission rate variation, can be adjusted by introducing distinct acoustic wave frequencies within a phononic structure. A high sensitivity level is suitable for the detection of light forces. Conversely, when dealing with large force measurements, the sensitivity should be reduced to prevent saturation. This study presents theoretical models for analyzing the variation of the transmission rate with frequency and the variation of the stop band with different acoustic parameters. To enhance the signal reaching the receiver, a piezoceramic disk whose axial resonance frequency corresponds to the frequency of the stop band margin is designed. The results indicated that the sensitivity of a prototype of the designed force sensor varied from 15 to 45 mV/N under a compressive force of 50 N.

Nonlinear and relaxation processes in piezoceramics in weak electric fields

We study the effects of piezoelectric hysteresis and relaxation induced by a weak constant electric field in ferroelectric ceramics. Using the piezoelectric resonance analysis method and program, precision measurements of the impedance spectra for thickness and radial vibrations of thin piezoceramic disks were performed for various polarities of the applied constant electric field and polarization of the piezoceramic. An analysis of the field and time dependences of the complex piezoelectric constants of piezoceramics obtained by processing sequentially measured impedance spectra is carried out, and a physical interpretation of the results is proposed.

Ultrahigh electrostrain >1% in lead-free piezoceramics: Role of disk dimension

Recently, a series of reports showing ultrahigh electrostrains (>1%) have appeared in several Pb-free piezoceramics. The ultrahigh electrostrain has been attributed exclusively to the defect dipoles created in these systems. We examine these claims based on another report (G. D. Adhikary and R. Ranjan, “Ultrahigh measured unipolar strain >2% in polycrystalline bulk piezoceramics: Effects of disc dimension,” arxiv.org/abs/2208.07134), which demonstrated that the measured electric field driven strain increased dramatically simply by reducing the thickness of the ceramic disks. We prepared some representative Pb-free compositions reported to exhibit ultrahigh strain and performed electrostrain measurements. We found that these compositions do not show ultrahigh electrostrain if the thickness of the disks is above 0.30 mm (the disk diameters were in the range of 10–12 mm diameter). The ultrahigh strain values were obtained when the thickness was below 0.30 mm. We compare the electrostrain obtained from specimens designed to exhibit defect dipoles with those obtained from stoichiometric compositions of Na0.5Bi0.5TiO3 and K0.5Na0.5NbO3-based lead-free systems and could obtain much higher strain levels (4%–5%) in the later specimens in the small thickness regime. Our results do not favor the defect dipole theory as the exclusive factor for causing ultrahigh strain in piezoceramics. A new approach is called for to understand the phenomenon of ultrahigh electrostrain caused by the thickness reduction of piezoceramic disks.

Piezoelectric hysteresis in ferroelectric ceramics in a weak electric field

In this work, we studied the piezoelectric hysteresis effect induced by a weak dc electric field in ferroelectric ceramics. Precision measurements of the impedance spectra for the thickness vibrational mode of thin piezoceramic disks at different polarities of applied dc electric field were performed using the method and program of piezoelectric resonance analysis (PRAP). The field dependences of the complex piezoelectric constants of piezoelectric ceramics obtained by processing successively measured impedance spectra were analyzed and a physical interpretation of the results was proposed.

Design of a novel 2D ultrasonic transducer for 2D high-frequency vibration–assisted micro-machining

Ultrasonic vibration–assisted machining (VAM) is a process in which a tool or workpiece is vibrated using ultrasonic frequency small-amplitude vibrations to improve cutting performance, and an ultrasonic transducer usually generates these vibrations. This study investigates how two-dimensional vibrations are generated using axially polled piezoceramics. Modifying the wave propagation in geometric ways by creating a notch at the front mass, the longitudinal response excited by the axially polled piezoceramic discs can be converted into combined longitudinal and bending vibrations at the transducer front mass. Finite element analysis (FEA) software COMSOL is used to study wave propagation, and ANSYS is used to optimize the transducer’s mechanical structure, while an equivalent circuit approach is used to analyze the electrical impedance spectra and confirm its resonance frequency. An experimental analysis of impedance response and amplitude of generated vibrations using the novel 2D ultrasonic transducer is conducted to validate the numerical and analytical results, which shows that resonance frequency results are in very good agreement with the theoretical model. Finally, the proposed design is validated by preliminary test results that demonstrate its performance and principles.

A fully-coupled vibro-acoustic model of an electronic stethoscope

A piezoelectric based stethoscope picks pressure fluctuations originating from the patient and the physician sides. This may include unwanted acoustic signals from the patient and the doctor sides of the stethoscope, which needs to be filtered either electronically or mechanically by appropriately designing the vibro-acoustic elements of the electronic stethoscope. This work intends to establish a mathematical model of the piezoelectric stethoscope. Initially, a multi-degrees of freedom vibration model of the electronic stethoscope is developed. The model is used to compute the response of the piezoelectric plate due to the pressure excitations on the input side and that due to the displacements of the connected mechanical elements in the stethoscope. Further, a two-port lumped parameter model of the piezoelectric composite plate is developed to compute the output voltage created by the displacement of the piezoceramic disc. Here, an axisymmetric plate vibration model (Kirchhoff's plate theory) is used to find the displacement of the piezoelectric composite plate. Subsequently, the vibration and the lumped parameter piezoelectric models are combined to represent the vibro-acoustic characteristics of the piezoelectric stethoscope. Further, using the developed fully-coupled vibroacoustic model, the output voltage of the device is studied for different patient and physician side excitations.

Theoretical, numerical and experimental investigation into vibration characteristics for composite structures of an annular membrane internally connected with a piezoceramic disk

Abstract This work analyzed the vibration characteristics of an annular membrane internally connected with a piezoceramic disk theoretically, numerically and experimentally. The general solution for the free vibration of an annular membrane under uniform tension was derived. Then, the displacement solutions for the piston modes and coupled modes of an annular membrane internally connected with a piezoceramic disk were derived. Two plate theories, Kirchhoff and Mindlin plate theories, were used to simulate the piezoceramic disk. The theoretical results are compared with the numerical results obtained from two finite element software packages: ABAQUS and COMSOL. The amplitude-fluctuation electronic speckle pattern interferometry was used to measure the resonant frequencies and associated mode shapes of five different type specimens with different sizes. Good agreements of dynamic characteristics determined by theoretical analysis, experimental measurements, and numerical calculation are presented for the annular membrane internally connected with piezoceramic disk structures.

FINITE ELEMENT CALCULATION OF DISK TRANSDUCER WITH CYMBAL-SHAPED END-CAPS AND ACTIVE ELEMENT FROM POROUS PIEZOCERAMICS WITH EXTREME CONDUCTIVITY OF PORE SURFACES

The paper presents a finite element analysis of a disk-shaped piezoelectric transducer with end-cap patches, which is usually called as Cymbal transducer. The efficiency of such a transducer is determined both by its geometric dimensions and by the values of the longitudinal and transverse piezoelectric moduli (piezoelectric charge coefficients) of the piezoceramic disc material. As was recently found, for porous piezoceramics with completely metallized pore surfaces, the effective transverse piezoelectric modulus does not decrease in absolute value with increasing porosity, as in conventional porous piezoceramics, but, on the contrary, increases, as does the longitudinal piezoelectric modulus. These unusual properties of porous piezoceramics with pore surface metallization are determined by the extreme properties of the phases that make up the piezocomposite material, and, in particular, the extremely high conductivity of the pore surface material inside the dielectric composite medium. In this regard, the main task was to study the efficiency of the Cymbal transducer depending on the type of porous piezoelectric disc material. Comparisons were made for solid piezoceramics, for ordinary porous piezoceramics, for porous piezoceramics with a very thin metal coating of the pores, and for porous piezoceramics with a relatively thick metallization layer on the surface of the pores with different porosities. In the ANSYS finite element package, steady-state oscillations of the cymbal transducer were calculated under nonresonant operating modes and near the first electrically active frequencies, which corresponds to the use of the transducer as a device for energy harvester and as a piezoelectric emitter of acoustic waves. In both cases, the results of computational experiments showed the promise of using new types of porous piezoceramic materials for the considered configurations of a disk piezoelectric transducer with end-cap cymbal patches. In this case, the best results were obtained for a porous piezoceramic material with a very thin metal coating of the pores.

Testing LAD1 of harvesting electric roads

Alternative power sources for roadway accessories have been brought to light through energy harvesting technologies. Several types of nanogenerators can harvest energy from rotating automobile tires by using the piezoelectric effect to generate electricity from these roads. As the wheel is pressed against the piezoceramic disks, energy is harvested by embedding them within a protective package. In this paper, we demonstrate the testing of several types of electric vehicles and how they are tested for electric performance and determine the output voltage and current.

Equivalent Circuit to Analyze the Transmitting Characteristics of a Cymbal Array.

A cymbal transducer has a simple structure consisting of a piezoceramic disk and metallic caps and has broadband characteristics when built as an array. The finite element method (FEM) is generally used to analyze the characteristics of acoustic transducers. However, the FEM requires a longer analysis time as the model becomes larger, which makes it limited and less efficient for analyzing the cymbal array. In this study, a new equivalent circuit with higher efficiency and accuracy, comparable to that of the FEM, was proposed to analyze the performance of cymbal arrays. The equivalent circuit for the array was constructed by connecting the equivalent circuits of individual cymbal transducers in parallel with a radiation impedance matrix that included both the self- and mutual radiation characteristics of the array. The validity of the new equivalent circuit was verified by measuring the transmitting voltage response of a cymbal array specimen and comparing it with that calculated using the circuit. The comparison confirmed the efficiency of the equivalent circuit in analyzing the characteristics of the cymbal array. The proposed equivalent circuit can facilitate the design of a large array of cymbal transducers.

New Equivalent Circuit of a Cymbal Transducer Incorporating the Third Harmonic Mode of Vibration

A cymbal transducer is composed of a pair of metal caps and a piezoceramic disk. Cymbal transducers arranged in an array exhibit broadband characteristics. Although the finite element method has been widely used for analyzing the transducer and its array, an equivalent circuit that allows efficient analysis was recently developed. However, this previously reported circuit was based solely on the fundamental vibration mode of the transducer, and is thus unsuitable for analyzing the broadband characteristics of the cymbal array. Therefore, to overcome this limitation, a new broadband equivalent circuit for the cymbal transducer was devised in the present study. The new circuit was constructed by incorporating terms related to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {rd}}$ </tex-math></inline-formula> harmonic vibration mode of the cap and corresponding radiation impedance into the existing equivalent circuit. The validity of this novel circuit was verified by comparing the analysis results with those obtained from the measurement of acoustic characteristics exhibited by a cymbal-transducer specimen. Compared with the previous circuit, the new equivalent circuit allows more accurate analysis and design of a cymbal transducer over a wider frequency range.

Lumped-Parameter Modeling and Performance Analysis of Fluid-Backed Piezoceramic Flexural Disc Acoustic Sensors

two-port lumped-parameter equivalent circuit model is presented to analyze the electroacoustic characteristics of piezoelectric flexural-mode acoustic sensors with fluid backing. The circuit parameters are determined from the measured electrical admittance spectra in water. Expressions for frequency-dependent receiving sensitivity are derived in terms of the equivalent circuit parameters under two extreme boundary conditions, namely, clamped and simply supported edges. The effect of geometric parameters of the composite flexural discs on the acoustic performance is analyzed. The model is validated by constructing flexural disc hydrophones of several dimensions and configurations, in which the overall thickness is much smaller than the radius. The model results agree well with the experimental data, validating the model. It is found that the receiving sensitivity of practical sensors lie in between clamped edge and simply-supported edge conditions which are the theoretical lower and upper bounds, respectively. Among all the sensors studied, the sensor with the lowest radius ratio (Rp/Rs) has the highest measured receiving sensitivity of -173 dB (ref. 1V/μPa) at low frequencies and -150 dB (ref. 1V/μPa) at resonance. The self-noise characteristics of these sensors are also analyzed with reference to underwater applications. The largest sensor has the highest Figure-of-Merit (FoM) with the measured M2C value of 743 × 10-28 V2F/μPa2, which is about three orders of magnitude higher than typical sensors. Piezoelectric sensors with high FoM is required to design acoustic systems with high Signal-to-Noise Ratio (SNR) with enhanced acoustic receiver characteristics.

Effects of transcranial ultrasound stimulation pulsed at 40\xa0Hz on A\u03b2 plaques and brain rhythms in 5\xd7FAD mice

BackgroundAlzheimer’s disease (AD) is the most common cause of dementia, and is characterized by amyloid-β (Aβ) plaques and tauopathy. Reducing Aβ has been considered a major AD treatment strategy in pharmacological and non-pharmacological approaches. Impairment of gamma oscillations, which play an important role in perception and cognitive function, has been shown in mouse AD models and human patients. Recently, the therapeutic effect of gamma entrainment in AD mouse models has been reported. Given that ultrasound is an emerging neuromodulation modality, we investigated the effect of ultrasound stimulation pulsed at gamma frequency (40 Hz) in an AD mouse model.MethodsWe implanted electroencephalogram (EEG) electrodes and a piezo-ceramic disc ultrasound transducer on the skull surface of 6-month-old 5×FAD and wild-type control mice (n = 12 and 6, respectively). Six 5×FAD mice were treated with two-hour ultrasound stimulation at 40 Hz daily for two weeks, and the other six mice received sham treatment. Soluble and insoluble Aβ levels in the brain were measured by enzyme-linked immunosorbent assay. Spontaneous EEG gamma power was computed by wavelet analysis, and the brain connectivity was examined with phase-locking value and cross-frequency phase-amplitude coupling.ResultsWe found that the total Aβ42 levels, especially insoluble Aβ42, in the treatment group decreased in pre- and infra-limbic cortex (PIL) compared to that of the sham treatment group. A reduction in the number of Aβ plaques was also observed in the hippocampus. There was no increase in microbleeding in the transcranial ultrasound stimulation (tUS) group. In addition, the length and number of microglial processes decreased in PIL and hippocampus. Encelphalographic spontaneous gamma power was increased, and cross-frequency coupling was normalized, implying functional improvement after tUS stimulation.ConclusionThese results suggest that the transcranial ultrasound-based gamma-band entrainment technique can be an effective therapy for AD by reducing the Aβ load and improving brain connectivity.

Characterization of SH-SY5Y Neurons Subject to 92kHz Ultrasound Stimulation

Cellular microstructural changes due to ultrasound exposure are critical to understand and characterize in order to further the establishment of ultrasonics in cell and tissue engineering and medicine. In this study, neurite length, nuclear morphology, and cellular toxicity are assessed at varying intensities of 92 kHz ultrasound provided by a piezoceramic disk element and incident upon SH- SY5Y neurons in vitro. Findings suggest that stimulation increases neurite length up to 2.73 fold tested at α = 0.05 in an intensity dependent manner. Additionally, stimulation causes a statistically significant (α = 0.05) decrease in nuclear area and less elongated nuclei, by 1.78 fold and 1.38 fold respectively, also in an intensity dependent manner. For maximum transducer surface intensities ranging from 0 to 39.11 W/cm2, the toxicity of 92 kHz ultrasound is assessed and a nontoxic range is determined using Caspase-3 and Annexin V staining, in addition to Calcium imaging via Calcein-AM staining. Intensities of up to 1.6 W/cm2 are found to be nontoxic for the cells under the parameters used in this study.

Study of transient and relaxation processes in ferroelectric ceramics in weak electric fields

We studied the transient and relaxation processes occurring in ferroelectric ceramics under the influence of dc electric field. Precision measurements of the impedance spectra of ferroelectric ceramics of the PZT system at different values and polarities of applied dc electric field were performed using the method and program of piezoelectric resonance analysis (PRAP) for the radial vibration mode of thin piezoceramic disks. The time dependences of the complex piezoelectric parameters of piezoceramic elements obtained as a result of processing of successively measured impedance spectrta were analyzed and a physical interpretation of the results has been proposed.

The study of domain orientation processes in ferroelectric ceramics in weak electric fields

The paper studies domain orientation processes in ferroelectric ceramics induced by a weak dc electric field. The field dependences of the complex elastic, electromechanical, and piezoelectric parameters of the PZT type ferroelectric ceramics were measured using the piezoelectric resonance analysis method for the radial extensional mode of thin piezoceramic disks. The method used ensures high accuracy in determining the complex constants of piezoelectric materials, as well as their changes under external influences. A physical interpretation of the results is proposed.

Theoretical analysis of transverse and planar vibrations for the piezoceramic disk based on Mindlin plate theory

In this paper, the out-of-plane and in-plane displacements coupled behavior of the transverse and planar vibration characteristics for piezoceramic disks under fully-clamped and traction-free boundary conditions are investigated theoretically base on the Mindlin's and Kirchhoff's plate models. By varying the radius-to-thickness ratios, the piezoceramic disks with moderate and thin thickness are considered in the analysis. It is verified that Mindlin's plate theory with first-order shear deformation hypothesis provides sufficient accuracy for transverse vibration analysis in comparison with Kirchhoff's model; however, this circumstance does not occur for planar vibration analysis. With the aid of theoretical analysis, both the resonant frequency and the corresponding mode shape are obtained for piezoceramic disks with various radius-to-thickness ratios. In addition, maximum normalized displacement components in three directions are also explored to identify the coupled vibration modes. Numerical calculations using the finite element method (FEM) are performed and the results are compared with the theoretical analysis. Excellent consistence between the theoretical and numerical results are found for the three-dimensional coupled vibration characteristics of piezoceramic disks.