Piezoelectric transducer vibrations in a one-dimensional approximation

Summary The theory of piezoelectric transducer vibrations, which may be treated as onedimensional, is developed in detail for thin discs vibrating in a pure thickness extensional mode. An effort has been made to obtain relations of general validity, which include losses, and which are in a simple explicit form convenient for practical calculations. The behaviour of transducers is discussed with special attention to their characteristics at the two fundamental frequencies, the so-called parallel and series resonances. Several peculiarities occur when transducers are coupled to media with considerably different acoustic impedances. These peculiarities are discussed and illustrated by numerical results for quartz and PZT 4 piezoelectric discs radiating into water, air and liquid hydrogen. The application of the theory to different types of vibrations is briefly illustrated for thin bars vibrating longitudinally. Short discussions are included on compound transducer systems, and on the properties of thin discs as receivers.     

Einfluss Eines Magnetischen Feldes auf ein Schwingendes Piezoelektrikum

The influence of a magnetic field on a vibrating piezoelectric medium is studied. It is found that the magnetic induction weakly influences the vibrations of this medium.     

Study on fast linear scanning for a new laser scanner

In the field of lidar system design, there is a need for laser scanners that offer fast linear scanning, are small size and have small a rotational inertia moment. Currently, laser scanners do not meet the above needs. A new laser scanner based on two amplified piezoelectric actuators is designed in this paper. The laser scanner has small size, high mechanical resonance frequencies and a small rotational inertia moment. The size of the mirror is 20 mm×15 mm. To achieve fast linear scanning performance, an open-loop controller is designed to compensate the hysteresis behavior and to restrain oscillations that are caused by the mechanical resonances of the scanner's mechanical structure. By comparing measured scanning waveforms, nonlinearities and scan line images between the uncontrolled and controlled scanner, it was found that the scanning linearity of linear scanning was improved The open-loop controlled laser scanner realizes linear scanning at 250 Hz with optical scan angle of ±12 mrad.     

Diversion of energy flow near crack tips of a vibrating plate using the structural intensity technique

The structural intensity (SI) of a vibrating rectangular plate with a crack is computed using the finite element method. The overall behavior of power flow patterns of the cracked plate is investigated. The presence of the crack can be identified by the changes of the directions of SI vectors near the crack. The effects of orientation of the crack and crack length on the energy flow pattern are also investigated. The SI method is then used to explore the positioning of dampers in vibrating thin plates to divert the vibration energy flow away from crack tips. This approach is proposed as a temporary measure to prevent further propagation of the crack before repair of the crack can be done.     

Theory of arachnid prey localization

Sand scorpions and many other arachnids locate their prey through highly sensitive slit sensilla at the tips (tarsi) of their eight legs. This sensor array responds to vibrations with stimulus-locked action potentials encoding the target direction. We present a neuronal model to account for stimulus angle determination using a population of second-order neurons, each receiving excitatory input from one tarsus and inhibition from a triad opposite to it. The input opens a time window whose width determines a neuron's firing probability. Stochastic optimization is realized through tuning the balance between excitation and inhibition. The agreement with experiments on the sand scorpion is excellent.     

Scanned-cantilever atomic force microscope with large scanning range

A scanned-cantilever atomic force microscope (AFM) with large scanning range is proposed, which adopts a new design named laser spot tracking. The scanned-cantilever AFM uses the separate flexure x-y scanner and z scanner instead of the conventional piezoelectric tube scanner. The closed-loop control and integrated capacitive sensors of these scanners can insure that the images of samples have excellent linearity and stability. According to the experimental results, the scanned-cantilever AFM can realize maximal 100 × 100 (μm) scanning range, and 1-nm resolution in z direction, which can meet the requirements of large scale sample testing.     

Piezoelectric lattice vibrations at optical frequencies

A relationship is proposed between the piezoelectric coefficient and the dielectric constant (or refractive index) based on classical dispersion theory. Piezoelectric lattice vibrations are associated with ionic polarizations at optical frequencies. This relation is applied to study the piezoelectric lattice vibrations in α-quartz, and agreement is found between the calculated and the measured value of the piezoelectric coefficient. No direct experimental method for measurement of piezoelectric coefficients at optical frequencies exists; however, in terms of the proposed relation, piezoelectric coefficients at optical frequencies can be evaluated from infrared reflection measurements.     

对2-2型压电复合材料横波换能器产生的纵波特性的研究

在固体测量中，横波换能器所产生的波列中常伴随有纵波，认识纵波产生的原因可以解释横波测试中出现的现象，以及抑制纵波提供有效的方法，本文利用实验研究的方法，用一对纵波偶极子换能器的对比实验，分析了２－２型压电复合材料厚度切变换能器产生纵波的机理，发现这是一种伴随着晶片厚度切变振动而产生的“偶极子”纵波，并由此解释了这种纵波的伴随性，频率特性及其首波与横波首波位相相反等问题。     

The determination of electrical parameters of quartz crystal resonators with the consideration of dissipation

Recently, as the dissipation of quartz crystal through material viscosity is being considered in vibrations of piezoelectric plates, we have the opportunity to obtain electrical parameters from vibration solutions of a crystal plate representing an ideal resonator. Since the solutions are readily available with complex elastic constants from Mindlin plate equations for thickness-shear vibrations, the calculation of resistance and other parameters related to both mechanical deformation and electrical potential is straightforward. We start with the first-order Mindlin plate equations of a piezoelectric plate for the thickness-shear vibration analysis of a simple resonator model. The electrical parameters are derived with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity. All the electrical parameters are frequency dependent, enabling the study of the frequency behavior of crystal resonators with a direct formulation. Through the full consideration of complications like partial electrodes and supporting structures, we should be able obtain electrical parameters for practical applications in resonator design.     

An approach based on tool mode control for surface roughness reduction in high-frequency vibration cutting

The presented research work, aimed at deeper understanding of vibrational process during high-frequency vibration cutting, is accomplished by treating cutting tool as an elastic structure which is characterized by several modes of natural vibrations. An approach for surface quality improvement is proposed in this paper by taking into account that quality of machined surface is related to the intensity of tool-tip (cutting edge) vibrations. It is based on the excitation of a particular higher vibration mode of a turning tool, which leads to the reduction of deleterious vibrations in the machine-tool-workpiece system through intensification of internal energy dissipation in the tool material. The combined application of numerical analysis with accurate finite element model as well as different experimental methods during investigation of the vibration turning process allowed to determine that the most favorable is the second flexural vibration mode of the tool in the direction of vertical cutting force component. This mode is excited by means of piezoelectric transducer vibrating in axial tool direction at the corresponding natural frequency, thereby enabling minimization of surface roughness and tool wear.     

多学科应用可大范围搜索的紧凑型扫描隧道显微镜

本文展示了结构紧凑的（高度为66 mm,直径为25 mm）扫描隧道显微镜,配备了一套拥有原子级分辨精度的三维压电马达。其中Z方向定位依靠的是自行发明的由轴向切割的压电扫描管驱动的摩擦型步进器。X-Y方向（即样品面方向）的移动是将Z向步进器作为一个惯性滑块垂直嵌入压电扫描管内同时一端平放在压电扫描管的顶部。其设计具有在极端条件下（低温、强磁场等）从宏观尺度样品区域（平方毫米级别）搜索微观靶向（缺陷位、掺杂位、边界及纳米器件等）的能力。在室温大气下对高定向热解石墨进行测量,得到了高分辨率的原子图像.     

Thickness vibrations of a piezoelectric plate under biasing fields

Thickness vibrations of a piezoelectric plate under uniform initial thermoelectromechanical fields are investigated in this article. An exact solution is obtained for materials with general anisotropy. A plate of langasite, a relatively new piezoelectric material with strong piezoelectric coupling, is analyzed with imposed uniform acceleration as the biasing field as an example. The results show that the biasing fields have remarkable effect on the free vibrations of piezoelectric plate.     

大角度低温光学扫描器

本文介绍了低温大角度扫描器的理论特性和制作技术。我们进行了利用压电陶瓷“逆压电效应”原理在常温条件下进行大角度、可控光扫描的探索性工作,并取得了可喜的成功,并在此基础上研究出了能在液氮环境下进行大角度扫描的低温扫描器。     

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency.The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.     

Inexpensive two-tip nanomanipulator for a SEM

One of the major obstacles for nanotechnology progress is the lack of effective tools and processes to build, characterize and manipulate nanosystems. Here, we present the development of a low-cost nanomanipulator with two probe tips that operates inside a scanning electron microscope. This manipulation system is based on parallel-guiding-plate-spring mechanism and inexpensive materials. The movements are divided on coarse and fine displacements, which are based on picomotors and piezoelectric elements, respectively. The nanomanipulator was applied to transport and manipulate nanotubes and semiconductor nanowires. The probe tips have independent electrical contacts, so that electrical two point measurements can be performed in situ. The system is expected to be a valuable tool for research laboratories working with nanostructures.     

Yerevan synchrotron injector electron beam transversal scan with vibrating wire scanner

We have developed extended-aperture (20 mm) vibrating wire scanner (VWS) for transversal scanning of electron beams with large transversal size. Test experiments were performed in open atmosphere on the 40 MeV electron beam of the Yerevan synchrotron injector with the 4–10 μA at outlet. A construction of VWS is elaborated for scanning beams with larger transversal size. This elaboration is a new precision tool for diagnostics of beams in accelerators, which may be successfully employed, because of universality of the used operation principle, for profiling of as well large-aperture proton and ion beams.     

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage. Supported by the National Natural Science Foundation of China (Grant No. 10532070), the Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KJCX2-YW-L07), and the LNM Initial Funding for Young Investigators     

Study on the prestressed sandwich piezoelectric ceramic ultrasonic transducer of torsional-flexural composite vibrational mode

Based on the classical torsional and flexural vibrational theory of a slender rod, the prestressed sandwich torsional-flexural composite mode piezoelectric ceramic ultrasonic transducer is studied. This type of transducer consists of the slender metal rods and the longitudinally and tangentially polarized piezoelectric ceramic rings. The resonance frequency equations for the torsional and flexural vibrations in the transducers are derived. The simultaneous resonance of the torsional and flexural vibrations in the transducer is acquired by correcting the length of the metal slender rods resulting from the piezoelectric ceramic elements. The experimental results show that the measured resonance frequencies of the transducers are in good agreement with the computed ones, and the measured resonance frequencies of the torsional and the flexural vibrations in the composite transducers are also in good agreement with each other.     

Experimental determination of damping of plate vibrations in a viscous fluid

A method of determining the aerodynamic-drag coefficient of flat vibrating plates from the vibrogram of free damping vibrations of cantilever-fixed duralumin samples has been developed. From the results of our experiments, simple approximating formulas determining the decrement of damping vibrations and the aerodynamic-drag coefficient through the dimensionless vibration amplitude and the Stokes parameter are proposed. The approach developed in this study for determining the aerodynamic-drag coefficient of a vibrating plate can be a useful alternative to purely hydrodynamic methods of finding the drag of vibrating solids.     

Modeling and experimental analysis of the linear ultrasonic motor with in-plane bending and longitudinal mode

A novel linear ultrasonic motor based on in-plane longitudinal and bending mode vibration is presented in this paper. The stator of the motor is composed of a metal plate and eight piezoelectric ceramic patches. There are four long holes in the plate, designed for consideration of the longitudinal and bending mode coupling. The corresponding model is developed to optimize the mechanical and electrical coupling of the stator, which causes an ellipse motion at the contact tip of the stator when the composite vibrations with longitudinal and bending are excited. Its harmonic and transient responses are simulated and inspected. A prototype based on the model is fabricated and used to conduct experiments. Results show that the amplitude of the stator’s contact tips is significantly increased, which helps to amplify the driving force and speed of the motor. It is therefore feasible to implement effective linear movement using the developed prototype.