Radial Vibration Mode Research Articles

Tunable Imaging Distance Focusing Module Directly Driven by a Thin‐plate Piezoelectric Actuator

AbstractWith the advancement of imaging technology, the performance of optical focusing modules becomes crucial for determining imaging quality. Conventional focusing modules frequently face challenges of excessive bulk and weight, complicating the integrated design and limiting application fields. Herein, this study presents a piezo‐actuated optical focusing module (POFM) and the construction strategy to alleviate these issues. A novel radial‐bending resonant‐type piezoelectric actuator (RB‐RPA) is developed to directly drive the POFM. The RB‐RPA, which features a hollow structure (27 × 27 × 7 mm3), utilizes both radial and bending vibration modes of a thin metal plate. It achieves a speed of 122.93 mm s−1, a thrust force of 0.14 N, and a displacement resolution of 0.52 µm. Employing the proposed construction strategy, RB‐RPA is integrated with imaging components to fabricate a POFM prototype. Furthermore, the micrometer‐level displacement resolution of POFM facilitates optical focusing on imaging targets, allowing the acquisition of sharp images within 70 ms. It achieves an image resolution of 119.57 lp mm−1 within a 42 mm segment of the captured image. Finally, a QT‐based interface for the POFM, enables real‐time image capture and sharpness evaluation, thereby enhancing imaging efficiency and integration. This work provides a potential candidate for next‐generation imaging devices.

Complex electromechanical parameters and microstructure peculiarities of PZT-type porous piezoceramics

In this work, we studied the microstructure peculiarities and complex electromechanical parameters of porous piezoelectric ceramics based on the PZT system with different relative porosity and pore sizes. The complex elastic, dielectric, and electromechanical parameters of the porous piezoceramics were measured on the radial vibrational mode of standard samples and analyzed using piezoelectric resonance analysis (PRAP) software. It was revealed that the microstructural features of porous piezoceramics defined the character of the porosity dependences of real and imaginary parts of dielectric, piezoelectric, and electromechanical properties of porous piezoelectric ceramics.

String loop vibration around Schwarzschild black hole

String loop vibrations in a central plane of a Schwarzschild black hole are investigated for various string equations of state. We discuss string loop stability and derive frequencies of vibrational modes. Using the vibrating string loop model we fit the quasi-periodic oscillation (QPO) observed in X-ray signal coming from some compact sources. We demonstrate how the string-loop parameters are related to the radial and vertical fundamental vibration modes, and how the vibrational instability can be related to the Q-factor characterizing the observed QPOs.

Development of a novel radial-torsional hollow ultrasonic motor and contact interface coating test

A novel miniature radial-torsional hollow ultrasonic motor is proposed in this work, which is mainly composed of a base, a hollow rotor, a stator. One piece of piezoelectric wafer bonded on the bottom face of the stator is used to excite the radial in-plane vibration mode of the outer ring, which is converted into the revolved motion of the inner ring through the connection beams. The revolved motion of the inner ring can drive the rotor pressed on the inner ring to rotate through friction. The finite-element method was performed to verify the working principle of the motor and optimize the key dimensions of the motor. One prototype motor with the appearance size of Φ35 mm × 12 mm and weight of 20.1 g is fabricated and characterized. In addition, Si3N4 thin film is coated on the contact interface of the stator by the magnetron sputtering coating machine to improve the output performance of the ultrasonic motor. The experiment results show that the locked-rotor torque of the motor with coated stator can reach 0.42 mN m, which is 55.56 % higher than that of the uncoated motor.

Circuit Simulator Compatible Model for the Ring-Dot Piezoelectric Transformer

A lumped-element equivalent circuit model for the ring-dot piezoelectric transformer (PT) is derived based on a one-dimensional analysis of the radial vibration mode. Initially, equations for the magnitudes of force, vibration velocity at the boundaries of each Section of the device are derived based on the piezoelectric constitutive equations and using Kirchhoff plate theory. Similarly, equations for the amplitudes of input and output currents are derived from the electric displacement field and Gauss’ law. From this analytical approach, an equivalent circuit model is developed and, using a Taylor expansion, approximated as the Mason equivalent circuit. A key contribution of this work is the development of a circuit simulator compatible model which can be used by electronic engineers, without in-depth knowledge of the underlying material science, to design ring-dot PTs for power conversion applications. The resulting model is verified against both COMSOL finite element simulations and experimental impedance measurements. Compared to COMSOL, the model estimates the resonant circuit elements to within 1% and the input and output capacitance are estimated to within 10%. Experimental results match the simulation to within 10% for most parameters, and 1% for resonant frequency. [2022-0154]

Dynamics of a collapsible tube with internal constriction

The deformation and oscillation dynamics of a thin-walled collapsible tube carrying internal flow with and without internal constriction is studied experimentally and theoretically for a constant chamber pressure. The internal constriction of different blockage ratios is employed by attaching spherical balls of different diameters to the inner wall of the tube. The effect of the axial location of the constriction is also studied. Without any internal constriction, the tube response is observed to be steady collapsed, periodic/aperiodic oscillatory or steady distended, depending on the Reynolds number. With constriction of low blockage ratios near the inlet of the collapsible tube, the system exhibits oscillatory response; however, no aperiodic oscillations are found. With bigger constrictions, the oscillations are completely suppressed. The viscous pressure drop due to the constriction is responsible for this behavior. When the constriction is present at the middle of the tube, the downstream half of the tube is under high tension, leading to the excitation of first and second radial vibrational modes of the tube (which are different from the milking-mode oscillations), depending upon the Reynolds number and blockage ratio. The results from a lumped parameter-based theoretical model are able to capture most of the qualitative features of the tube response such as the shift of the Hopf bifurcation point and the shrinkage of the oscillatory regime.

A New Topology of DC–DC Converter Based on Piezoelectric Resonator

The emergence of new piezoelectric materials makes it possible to offer high performances in terms of power density and integration. These new materials can be used in dc–dc power converters as a solution to replace the magnetic components and to meet the growing demand for miniaturization, high power density, and high-efficiency applications. This article deals with a new topology of a dc–dc converter based on a piezoelectric resonator. The conversion mechanism based on energy and charge balance is explained in detail through an analytical model and validated by experimental results. A prototype has been designed for an input–output voltage up to 250–125 V and a power range up to 175 W. It provides an efficiency higher than 93% for wide operating points in radial mode vibration. As an example, we have obtained an efficiency of 93.8% for 250–117 V input–output voltage at 50 W output power. In addition, the thickness mode operation is experimentally validated at 1 MHz and exhibited a peak output power of 175 W with an efficiency of 80% for 200–60 V input–output voltage. The experimental results show the promising performances of the proposed dc–dc power converter based on a piezoelectric resonator for high-to-low voltage, high efficiency, and low-to-medium power applications.

5DOF planar – rotary motion piezoelectric robot

A novel resonant type five degrees of freedom (5DOF) mobile piezoelectric robot is proposed and analysed. The piezoelectric robot performs unlimited linear working motion in the plane and rotates the positioning table or sphere about three axes independently. The piezorobot can be used for precise positioning or transportation of small objects and make complicated locomotion trajectories. The piezoelectric robot is designed as a compound structure and includes a piezoelectric ring and a special ring-shaped bronze layer. Electrodes of the piezoelectric ring are divided into six equal sections. Excitation of the piezoelectric robot is performed by using a single switched harmonic signal applied to the particular electrode. The operation principle of the piezoelectric robot is based on the excitation of the third radial vibration mode of the piezoelectric ring. The numerical and experimental study was performed, and the operating principle was validated. The maximum linear velocity of 18.8 mm/s and rotational speed of 31.3 rpm were achieved when load of 25.1g and excitation voltage of 200 Vp-p were applied.

Flame features and oscillation characteristics in near-blowout swirl-stabilized flames using high-speed OH-PLIF and mode decomposition methods

Flame features and dynamics are important to the explanation and prediction of a lean blowout (LBO) phenomenon. In this paper, recognition of near-LBO flame features and oscillation characterization methods were proposed based on flame spectroscopic images. High-speed planar laser-induced fluorescence measurements of OH were used to capture unique dynamic features such as the local extinction and reignition feature and entrained reactant pockets. The Zernike moment demonstrated a good performance in recognition of stability and near-LBO conditions, though the geometric moment had more advantages to characterize frequency characteristics. Low-frequency oscillations, especially at the obvious self-excited oscillation frequency around 200 Hz, were found when approaching an LBO condition, which can be expected to be used as a novel prediction characteristic parameter of the flameout limit. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) were used to conduct dynamic analysis of near-LBO flames. POD modes spectra showed the unique frequency characteristics of stable and near-LBO flames, which were basically in line with those at the heat-release frequency. The primary POD modes demonstrated that the radial vibration mode dominated in a stable flame, while the rotation mode was found to exist in a near-LBO flame. Analysis of modal decomposition showed that flame shedding and agminated entrained reactant pockets were responsible for generating self-excited flame oscillations.

Radial and axial vibration modes of graphyne nanotubes

The radial breathing modes (RBM) of carbon nanotubes (CNTs) arise from the collective inward and outward vibration along the radial direction of tubes, becoming characteristic Raman vibrational modes widely used for determining the radii of CNTs. The graphyne nanotubes (GNTs) can form by rolling graphyne sheets in a similar way as the CNT formation from rolled graphene sheets. In this work the atomic configuration and vibration modes of the GNTs with varied chirality and radii were investigated by classical molecular dynamics. The GNTs exhibit RBMs with an inversed linear relationship between the RBM vibration frequencies and radii, similar with those of CNTs. More importantly, we reported an axial vibrational mode (AVM) of the GNTs where the vibration waves propagate along the axial direction of the GNTs. The AVM is a unique vibration mode of GNTs due to the more flexible sp bonded carbon chain atoms arranged along the tube axis, providing additional axial vibration degree of freedom. The features of phase difference of the standing axial waves depend on the structure types of GNTs: The armchair GNTs exhibit zigzag-like sawtooth waves, while the zigzag GNTs have armchair-like square waves. The AVMs of GNTs can be regarded as transverse acoustic phonon modes of carbon atom chains at low frequency ranges. Moreover, the AVMs of GNTs generally have higher frequencies than the RBMs of CNTs with similar diameters. Therefore, our simulation suggests that AVM may be used as a fingerprint vibrational mode of GNTs for the refined structure characterization in experiments. The AVM may also be the origin of low thermal conductivity of GNTs with implications as thermoelectric materials.

Triangular-Shaped 5-DOF Piezoelectric Robot for Optical Lens Positioning

The paper represents numerical and experimental investigations on a 5-DOF piezoelectric robot that can provide rotary and planar motions of the payload. The design of the robot is based on a single piezoelectric ring and a triangular-shaped passive layer made from stainless steel. Six semispherical contacts of alumina oxide were used as contact points for rotary and planar motions. Finally, the top electrode of the piezo ceramic ring was divided into six equal segments to control the 3-DOF angular and 2-DOF planar motions of the payload. Two harmonic signals of different frequencies are used to drive the piezoelectric robot. The robot operation is based on the excitation of the third radial vibration mode of the ring and the first bending mode of the trapezoidal-shaped cantilever. Motion control is performed by switching electric signals between the particular segments of the piezoelectric ring. A numerical investigation was performed to validate the operation principle of the robot and to analyze electrical and mechanical characteristics. Numerical investigations showed that the first bending mode of trapezoidal cantilevers and the third radial mode of the piezo ceramic ring were obtained at a frequency of 13.79 kHz and 95.75 kHz, respectively. Moreover, it was revealed that the coupling ratio between vibration amplitudes of passive and active segments is more than 4 times. The prototype of the piezoelectric robot was made and an experimental study was performed to validate the operating principle of the robot, as well as to investigate the dynamic characteristics. The investigation showed that the highest velocity of the planar motion is 22.3 mm/s while the maximum angular motion speed is 29.3 RPM when an excitation voltage of 200 Vp-p and payload of 25.1 g was applied.

Radial and Axial Vibration Modes of Graphyne Nanotubes

Radial and Axial Vibration Modes of Graphyne Nanotubes

A New Method for Evaluation of the Complex Material Coefficients of Piezoelectric Ceramics in the Radial Vibration Modes.

The determination of complex elastic, piezoelectric, and dielectric coefficients of piezoelectric ceramics is important for precision engineering devices. Here, a novel method for determining the optimal material coefficients is presented. This method minimizes the average relative error in the values of conductance, susceptance, resistance, and reactance obtained from the 1-D model in the IEEE Standard (ANSI/IEEE Std 176-1987) and the experimental measurements of the first and second radial modes. Poisson's ratio is assumed to be a complex number in addition to the elastic, piezoelectric, and dielectric coefficients in the present method. The global minimum of the average relative error is found by searching the minimum among all local minima of the average relative error, which are obtained with the Levenberg-Marquardt modification of Newton's method from randomly chosen initial conditions. The optimal material coefficients of an APC 850 disk and an APC 855 disk are calculated with this method. The uncertainties in the optimal material coefficients are evaluated by calculating the minimum average relative error when the real or imaginary part of each coefficient is prescribed.

Development of a Novel 2-DOF Rotary-Linear Piezoelectric Actuator Operating under Hybrid Bending-Radial Vibration Mode.

The paper presents a numerical and experimental investigation of a novel two degrees of freedom (2-DOF) piezoelectric actuator that can generate rotary motion of the sphere-shaped rotor as well as induce planar motion of the flat stage. The actuator has a small size and simple design and can be integrated into a printed circuit board (PCB). The application field of the actuator is small-dimensional and high-precision positioning systems. The piezoelectric actuator comprises three rectangular bimorph plates joined with arcs and arranged by an angle of 120 degrees. A high-stiffness rod is glued on the top surface of each bimorph plate and is used to rotate the rotor or move flat stage employing contact friction force. Three U-shaped structures are used for the actuator clamping. 2-DOF rotational or planar movement is obtained by applying a harmonic or asymmetric electrical signal. The operation principle of the actuator is based on the superposition of the B20 out-of-plane bending mode of the bimorph plates and the B03 radial vibration mode of the ring. Design optimization has been performed to maximize amplitudes of contact point vibration. A prototype of the actuator was made, and a maximum rotation speed of 795.15 RPM was achieved while preload of 546.03 mN was applied. The linear velocity of 36.45 mm/s was obtained at the same preload force. Resolution measurement showed that the actuator can achieve an angular resolution of 17.48 µrad and a linear resolution of 2.75 µm.

Influence of Pole and Slot Combination on Torque Characteristics and Radial Force of Fractional Slot Permanent Magnet Machines

The fractional slot concentrated winding structure effectively solves the difficulty of low‐speed and high‐torque permanent magnet (PM) machines with a large number of poles and slots, but it also brings a wealth of magnetomotive force (MMF) harmonic. The winding function method is used to compare and analyze the stator MMF distribution and harmonic content of the fractional slot PM machines with different pole and slot combinations, and the cogging torque waveform and torque ripple are calculated by the finite element method. The influence of pole and slot combination on radial force and vibration modes of fractional slot PM machines is studied. The main vibration mode can be determined from the lowest order of radial force harmonics. The results show that in a fractional slot PM motor, the radial force is the main cause of noise and vibration, rather than the cogging torque and torque ripple. The dominant radial force is mainly produced by the interaction of rotor field harmonics and armature reaction field harmonics, and the vibration and noise will significantly increase with the decrease of the dominant vibration mode order, which largely depends on the pole and slot combination. This paper provides a certain reference for the selection of pole and slot combination in the electromagnetic design process of low speed high torque fractional slot PM motors. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Multicomponent complex oxide media – the basics of the functional materials for electronic engineering: the selection of the promising compositions for assessing the ferrohardness

According to the optimal technological regulations, the solid solutions of two four-component systems based on lead titanate-zirconate and alkali metal niobates were prepared: (1-x) Na0.875Li0.125NbO3 – xPbTi0.5Zr0.5O3 (0.05 ≤x < 0.95, Δx = 0.025-0.10) and (1-x) Na0.875K0.125NbO3 – xPbTi0.5Zr0.5O3 (0.0 ≤x ≤1.0, Δx = 0.05-0.10). The electrophysical parameters of the solid solutions of these systems were determined and the degree of their ferrohardness and efficiency was assessed according to the main characteristics: the relative permittivity of the polarized samples, ε33T/ε0, the mechanical quality factor, Q M, the coefficient of electromechanical coupling of the radial vibration mode, Kp, the piezomodule, |d 31|. It was shown that, depending on the chemical composition and the position of the solid solutions on the phase diagram of the systems, they can be characterized by different degrees of the ferrohardness and efficiency, which made it possible to select promising compositions: ferrohard ones – for the converters with high specific power (in step-down piezotransformers, piezoelectric motors, etc.) ); of the medium ferrohardness – for highly sensitive receivers of the ultrasonic vibrations (telemetry sensors, automatic control systems, etc.); ferrosoft materials with high efficiency – in the low-frequency devices (microphones, hydrophones, deflectors of the optical systems, robotics devices, etc.).

Accurate coupled vibration analysis of a piezoelectric ceramic cylinder by the superposition method

The radial and thickness extensional vibration modes in piezoelectric cylinders are always inevitably coupled due to the finite dimension, Poisson’s ratio, and piezoelectric effect. In this paper, an analytical model based on the superposition method is developed to obtain the coupled dynamic response of a piezoelectric cylinder under an applied voltage. The problem can be described mathematically by three partial differential equations with mixed boundary conditions in the cylindrical coordinates system. To solve this, the problem is decomposed first into two building block – vibrations in radial and thickness directions. In each building block, the expressions of displacements and electric potential are assumed and then the induced dynamic responses, such as in-plane stress and electric displacements, are calculated. Finally, the vibration responses of the two building blocks are superimposed to satisfy the mixed boundary conditions using Fourier and Fourier-Bessel series expansions. Electrical impedance of a typical piezoelectric disk and frequency spectrum of piezoelectric cylinders of different diameter-to-thickness ratios are calculated by the present analytical method as well as by finite element method. Comparison shows an excellent agreement. This analytical model can be applied to material characterization and the design and the optimization of the active elements of piezoelectric devices.

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.

Transfer matrix model and experimental validation for a radial-torsional ultrasonic motor

Traditional traveling-wave rotary ultrasonic motors have been widely used in many applications due to their excellent output performances. However, the structure optimization have be hindered by the specific requirements on the piezoelectric ceramics with complex polarizations and shapes. To address such issues, a compact type ultrasonic motor operating at radial-torsional conversion mode is proposed in this paper, which is simply excited by one ring type piezoelectric wafer with a single polarization. This motor basically consists of one rotor and one disk type stator, which can be divided into an outer ring, four connection beams and an inner ring. A ring type piezoelectric wafer is bonded to the bottom face of the outer ring. Upon an excitation signal at resonance frequency, the proposed motor is able to rotate, driven by the torsional vibration mode of the inner ring converted from the radial vibration mode of the outer ring via the connecting beams An electromechanical model utilizing the transfer matrix method is built to analyze the dynamic behavior of the motor. This transfer matrix model of the system could provide an effective approach for simulating the coupled mechanical and electrical properties. Based on the proposed model, the dynamic process for converting the radial vibration mode into the torsional mode is quantatively assessed. Last, the vibration characteristics of the prototype motor is tested by using a 3D laser Doppler vibrometer and the experimental results are in good agreement with the calculations, confirming the validity of the transfer matrix model and the feasibility of the motor design.

Vibration-based inverse graphical technique for thickness estimation of bulk acoustic wave (BAW) resonators: application for corrosion monitoring of sacrificial anodes

Resonant acoustic sensors have been used in a variety of applications that leverage the large sensitivity of mechanical resonance frequency to shift in geometric or mechanical properties of the sensor induced by the measurand. In applications such as structural health monitoring, accurate damage quantification requires development of precise models for resonator-measurand interactions or advanced system identification or optimization algorithms. In this paper, we utilize a graphical technique originally proposed for damage assessment in beams, to determine the extent of corrosion of sacrificial zinc anode discs instrumented with piezoelectric transducers. We develop analytical models for expressing natural resonance frequencies of the radial and transverse vibration modes of a disc in terms of material and geometric properties of its constituent elements. The underlying parameters (in this case, the thicknesses of the zinc and zinc oxide films) are extracted from measured resonance frequencies by finding roots of the characteristic determinant of these modes through graphical technique. Even though accelerated corrosion induced by impressed current results in non-uniform corrosion of the anode, the graphical technique with uniform-corrosion model shows excellent agreement with experimental results and is suitable for in-situ monitoring of sacrificial anodes used in cathodic protection systems. This technique requires no calibration or model of corrosion dynamics, and is computationally inexpensive unlike optimization techniques.