Piezoelectric Ceramic Cylinder Research Articles

Quantitative measurement of disturbances based on optical-fibre multiparameter optimization method

Phase-sensitive optical time domain reflectometry (φ-OTDR) has been applied in security monitoring. However, φ-OTDR cannot directly measure strain and intensity of an applied disturbance, thereby limiting the choice of features for intrusion pattern recognition and hazard assessment. This paper proposes a quantitative method to measure disturbances using amplitude-based φ-OTDR. The optical-fibre multiparameter optimization (FMPO) method is developed. The FMPO analyses the curve pattern of optical intensity signals to calculate strain. No extra module is needed, instead a specially designed bio-inspired algorithm is introduced. Quantification indices to gauge disturbance intensities are derived for practical use. A piezoelectric ceramic cylinder test demonstrated a linear correlation between the quantification indices and the vibration amplitude (R2 = 0.8956). The calculated strains of 34 driven voltages agreed well with theoretical values within 1000 nε. In a pendulum-impact experiment, five intrusion intensities were successfully identified, which indicated that FMPO performed well in the field.

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.

Exact series model of axially polarized hollow piezoelectric ceramic cylinders of finite length.

An analytical model is presented of axisymmetric circular hollow piezoelectric ceramic cylinders with arbitrary dimensions and boundary conditions. Forced vibrations of the cylinders with specified potentials on the electroded surfaces and displacement or stress on the boundaries are considered. The exact, linearized, axisymmetric governing equations are used in the analysis. Three series solutions are used, and each term in each series is an exact solution to the exact governing equations of motion. The terms in the series expressions for components of displacement, stress, electric potential, and electrical displacement are products of Bessel and sinusoidal functions and are orthogonal to other terms. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is, therefore, possible to satisfy arbitrary boundary conditions on all surfaces of the hollow piezoelectric cylinder. Numerical results are presented for hollow piezoelectric cylinders of various dimensions. Input electrical admittance and displacements are computed for three special cases in bands that include several resonance frequencies, and they are in excellent agreement with those computed using atila-a finite element package.

Real-Time Phase-Sensitive OTDR Based on Data Matrix Matching Method.

Phase-sensitive optical time-domain reflectometry (Φ-OTDR) is an effective technique to accomplish fully distributed vibration measurement along the entire fiber link. In this paper, a novel data matrix matching method is proposed and successfully employed in the Φ-OTDR system for real-time vibration detection and type identification. By using the novel method, the quantized response time is presented and improved to millisecond level for the first time. Meanwhile, the data can be extracted completely without packet loss, thus allowing vibration type identification to be obtained while maintaining the system simplicity. The experimental results demonstrate that the vibration signals can be detected and located with an average response time of 50.1 ms, under a data transmission speed which can go up to 77.824 Mbps. Moreover, different vibration types such as sine waves and square waves which are applied to the sensing fiber through a piezoelectric ceramic (PZT) cylinder can also be successfully identified. This method provides an efficient solution for real-time vibration location and type identification, thus exhibiting considerable application potential in many practical situations.

Analysis on the three-dimensional coupled vibration of composite cylindrical piezoelectric transducers.

Three-dimensional coupled vibration of the composite cylindrical piezoelectric transducer is analyzed. The composite cylindrical piezoelectric transducer consists of an inner axially polarized piezoelectric ceramic cylinder and an outer metal cylinder with the same height. Coupled vibration of the composite cylindrical piezoelectric transducer is analyzed by equivalent elasticity method, which is an approximate analytical approach. According to this method, coupled vibration of the cylindrical transducer is regarded as an interaction between a plane radial vibration and a longitudinal vibration. The radial and longitudinal electromechanical equivalent circuits of the piezoelectric transducer are acquired. Input impedances as functions of the resonance frequency and the mechanical coupling coefficient are derived to obtain resonance frequency equations. The analytical results are supported by experimental and numerical simulated results of two prototypes of the piezoelectric transducer. The composite cylindrical piezoelectric transducer presented in this paper is superior to single cylindrical piezoelectric transducers, composite ring-type, and tube-type transducers in the field of high output power and efficiency.

A 300 kHz High-Frequency Underwater Transducer

A new type of piezoelectric composite ultrasonic transducer with high frequency in radial vibration is studied. A high-frequency acoustic transducer has been designed and prepared with pzt-5-type piezoelectric ceramic cylinder. When the piezoelectric ceramic cylinder vibrates along the direction of its radial direction, the working frequency is high. It is composed of a piezoelectric ceramic tube and a steel bracket which is inserted in the inner of the ceramic tube. Use the finite element method by ANSYS for analyzing the radial vibration of a piezoelectric tube. On that basis, through managing ANSYS simulation the vibration mode of transducer system is obtained, and analyzed the working frequency of transducer. According to the simulation, the high-frequency cylindrical acoustic transducer has been produced. Comparing the products and the traditional cylindrical transducers, the products haven’t only a good all-round circle directional, but it also has a high working frequency (300 kHz).

Working-point control method for readout of dynamic phase changes in interferometric fiber-optic sensors by tuning the laser frequency

A simple but reliable method, namely the working-point control by tuning the laser frequency, for the dynamic phase shift measurement in a passive homodyne interferometric fiber-optic sensor is proposed. A dc voltage calculated from the photodetector output is applied to the light source to control the interferometer at the condition of maximum sensitivity. Then the signal's phase shift can be obtained from the components of zero and fundamental frequencies. To test the method, an all polarization-maintaining Mach-Zehnder interferometer with a piezoelectric ceramic (PbZrTiO(3), or PZT) cylinder in one arm is constructed. The experimental results show that the simulation signal's phase shift generated by the PZT cylinder can be read out correctly with the method. It has the advantages of simplicities of operation, no-active element in the sensing head, and large operating bandwidth. It can be used for readout of dynamic phase shifts in various interferometric fiber-optic sensors.

Experimental investigation of coupled vibrations in piezoelectric cylindrical shells

An experimental investigation of the electromechanical properties of radially polarized thin-walled piezoelectric ceramic cylinders as a function of the height-to-diameter aspect ratio is presented. The focus of this investigation is on the lowest order axially symmetric modes of vibration for cylinders with free ends having aspect ratio less than 3 with emphasis on the region of strongest coupling around aspect ratio π∕2. The resonance frequencies and coupling coefficients are presented vs aspect ratio and quantify the lower, upper, and an intermediate resonance branch. It is shown that the intermediate branch is flexural in origin and clearly crosses the so-called “dead zone,” which is an inadequacy of the membrane theory applied to the vibration of thin shells [Junger and Rosato, J. Acoust. Soc. Am., 26, 709–713 (1954)]. The coupling coefficient for the lower branch is shown to drop to zero at h∕2a=π∕2, whereas the coupling coefficient associated with the upper branch reaches a maximum at an aspect ratio near this region. As an example of the practical application of this study, the performance of two underwater electroacoustic transducers comprised of cylindrical elements having different aspect ratios is reported.

Effect of polarized electric field on piezoelectric cylinder vibratory gyroscope

The effects of the resonant frequency of the drive and sense modes and the mechanical quality factor ( Q) of vibratory gyroscopes have been investigated in many research papers. In this article, in addition to these factors, the effect of polarized electric field on the sensitivity of a piezoelectric cylinder-type vibratory gyroscope is discussed. We derive a relation for the sensitivity for the gyroscope using the Coriolis effect, the material properties of ceramics, and the applied polarized voltage, and find that the sensitivity is proportional to the polarized electric field. This study also looks at the influence of the geometry of the cylinder (diameter and length), and that of the electrodes (width and clearance) on the polarized electric field. From simulation using ANSYS models developed for six-electrode and eight-electrode cylinder gyroscopes, we conclude that diameter is a significant factor in determining the polarized electric field, and a large diameter requires a high polarized voltage for complete polarization. In addition, equal width of the electrode and equal clearance between neighboring electrodes yields a better polarized electric field. Also, the frequencies of the primary and secondary modes are seen to be nearly equal due to the axisymmetry of the cylinder gyroscope, which is an advantage of high sensitivity. The resonant frequency obtained from experiments on a ceramic cylinder gyroscope is a close approximation of the value calculated from the simulation models. There is a good linear relation between the sensing voltage and the rotation speed, suggesting that the piezoelectric ceramic cylinder gyroscope is a good candidate for low and medium rotation speed measurements.

Forced responses of solid axially polarized piezoelectric ceramic finite cylinders with internal losses

A method is presented to determine the forced responses of piezoelectric cylinders using weighted sums of only certain exact solutions to the equations of motion and the Gauss electrostatic conditions. One infinite set of solutions is chosen such that each field variable is expressed in terms of Bessel functions that form a complete set in the radial direction. Another infinite set of solutions is chosen such that each field variable is expressed in terms of trigonometric functions that form a complete set in the axial direction. Another solution is used to account for the electric field that can exist even when there is no vibration. The weights are determined by using the orthogonal properties of the functions and are used to satisfy specified, arbitrary, axisymmetric boundary conditions on all the surfaces. Special cases including simultaneous mechanical and electrical excitation of cylinders are presented. All numerical results are in excellent agreement with those obtained using the finite element software ATILA. For example, the five lowest frequencies at which the conductance and susceptance of a stress-free cylinder, of length 10 mm and radius 5 mm, reach a local maximum or minimum differ by less than 0.01% from those computed using ATILA.

A tri-modal directional transducer.

Acoustic transducers made from piezoelectric ceramic cylinders usually exploit the breathing or omnidirectional (omni) mode of vibration. However, with suitable voltage distribution, higher order extensional modes of the cylinder can be excited which produce directional radiation patterns. These modal radiation patterns can then be combined to synthesize desired beam patterns which may be steered by incrementing the excitation. This paper describes a model for the combined acoustic response of the extensional modes of vibration of a piezoelectric ceramic cylinder, a method of synthesizing a desired radiation pattern, and an experimental implementation of a directional transducer that uses these techniques. This tri-modal transducer is broadband and directional with a frequency independent beam pattern yet simple, small, and lightweight.

Impact Response of a Piezoelectric Ceramic Cylinder with a Penny-Shaped Crack

Impact Response of a Piezoelectric Ceramic Cylinder with a Penny-Shaped Crack

Study on the equivalent circuit and coupled vibration for the longitudinally polarized piezoelectric ceramic hollow cylinders

Longitudinally polarized piezoelectric ceramic disks with central holes have been the most commonly used elements in underwater acoustics and ultrasonics. For very thin piezoelectric ceramic disks, its vibration can be regarded as one-dimensional thickness extensional vibration, or plane radial vibration, and the coupling between these two different vibrational modes is neglected. However, for practical piezoelectric ceramic disks with central holes, the geometrical dimensions do not satisfy the requirements for the thin ring, and the coupling must be considered. In this paper, the coupled vibration of the longitudinally polarized piezoelectric ceramic disks with central holes is studied using an approximate analytical method. When the mechanical coupling coefficient is introduced and the shearing strain is ignored, the coupled vibration of the piezoelectric ceramic hollow cylinder is divided into two equivalent vibrations. One is the equivalent longitudinal extensional vibration, and the other is the equivalent radial vibration. These two equivalent vibrations are not independent; they are correlated together by the mechanical coupling coefficient. The equivalent circuit for the piezoelectric ceramic hollow cylinders in coupled vibration is derived, and the resonance frequency equations are obtained. Based on the coupled frequency equations, the longitudinal and radial resonance frequencies can be obtained when the dimensions and the material parameters are given. Compared with one-dimensional theory, the computed resonance frequencies in this paper are in good agreement with the measured results. Compared with the numerical methods, the analytic method presented in this paper is simple in computing the longitudinal and radial resonance frequencies and in analyzing the coupled vibrational modes of the piezoelectric ceramic disks with central holes.

Penny-shaped crack in a piezoelectric cylinder under electro-mechanical loads

The fracture behavior of a penny-shaped crack in a axisymmetrical piezoelectric ceramic cylinder of finite radius under mechanical and electrical loads is analyzed under electric continuous boundary conditions on the crack surface. The potential theory and Hankel transform are used to obtain a system of dual integral equations, which is then expressed as a Fredholm integral equation. Singular mechanical and electrical fields and field intensity factors of mode I are obtained. The numerical values of various field intensity factors for PZT-6B piezoelectric ceramics are graphically shown for a uniform load and a ring-shaped load, respectively. The effects of the radius of the cylinder on the field intensity factors are investigated.

Analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on flat surfaces.

A method to analyze axially polarized piezoelectric ceramic cylinders with arbitrary length to radius ratio and arbitrary boundary conditions on the flat surfaces is presented. The method is based on the use of functions that individually exactly satisfy the axisymmetric equations of motion and the Gauss electrostatic conditions. The axial and radial components of displacement and the potential are expressed as weighted sums of these functions. The functions form complete sets in the radial direction and arbitrary boundary conditions can, therefore, be satisfied on the flat surfaces. On the curved surface, certain uniform boundary conditions can be exactly satisfied. The weights are easily determined by using the orthogonal property of the functions. The input electrical admittance is a function of only the average boundary conditions and is very easily determined. Several special cases and numerical results are presented for electrically and mechanically excited cylinders to illustrate the method. The series expressions for displacements, potential, and stress converge rapidly and they are in good agreement with results obtained using ATILA--a finite element program. The method can be extended to analyze hollow cylinders with arbitrary boundary conditions on all surfaces.

Penny shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in-plane mechanical and electrical loads

The fracture problem of a penny shaped crack in a piezoelectric ceramic cylinder surrounded by an infinite elastic medium under in-plane normal mechanical and electrical loads is considered with the electric continuous boundary conditions on the crack surface. By using the potential theory and Hankel transform, a system of dual integral equations is obtained, and expressed to a Fredholm integral equation of the second kind. The mechanical and electrical field equations and all sorts of field intensity factors of mode I are obtained, and the numerical values of various field intensity factors for PZT-6B piezoelectric ceramic surrounded by several different elastic media are graphically shown for a uniform load and a ring-shaped load, respectively. And the effects of the size of the piezoelectric cylinder and the elastic material properties on various field intensity factors are obtained.

Analysis of axially polarized piezoelectric ceramic cylindrical shells of finite length with internal losses.

A thin shell analytical model of axially polarized piezoelectric ceramic cylinders with internal losses is presented. The Flugge assumptions for strain-displacement relations, Hamilton's principle extended to piezoelectric shells, and the assumption that electric potential has a quadratic variation between the curved surfaces, are used to derive displacement-potential relations that are similar to equations of motion of elastic shells. A solution, with 12 coefficients, to these relations is then derived. The coefficients are complex when the shell has internal losses and are determined by using three mechanical and three electrical boundary conditions at each end--on the flat surfaces. Computed values of input electrical admittance are presented for shells with and without internal losses, and for thin shells as well as shells with wall thickness comparable to the length. They are also compared with results obtained using the finite element program--ATILA. It is shown that the analytical values of resonance frequencies, the maximum value of input electrical conductance, and the maximum and minimum values of input electrical susceptance of thin shells are in excellent agreement with finite element results. The dependence of the maxima and minima in the complex input electrical admittance on the dimensions of the shell is inferred from the numerical results.

Multifrequency transducers fabricated using PZT/P(VDF-TrFE) 1-3 composite

A multifrequency composite ultrasonic transducer system is described. The transducer consists of lead zirconate titanate (PZT) piezoelectric ceramic cylinders embedded in a vinylidene fluoride/trifluoroethylene (P(VDF-TrFE)) copolymer matrix. Both phases are piezoelectrically active. By selecting an appropriate height to diameter ratio for the ceramic cylinders, the transducer can be made to resonate at a number of frequencies. The frequency of the resonance arising from the copolymer matrix depends on the composite thickness. The other resonance frequencies are determined by the height to diameter ratio of the ceramic cylinders. A number of multifrequency transducers have been constructed and the observed resonance frequencies agree well with the predictions, based on the mode coupling theory.

Three-port parameters and equivalent circuit of radially polarized piezoelectric ceramic cylinders of finite length

Three-port parameters of radially polarized piezoelectric ceramic cylinders of arbitrary length-to-radius ratio are presented. The three-port impedance matrix is first obtained by using two-dimensional electroelastic equations of state and the membrane approximation. It is then used to obtain an equivalent circuit. Admittance and A matrices are also derived. The matrices are then used to determine the input electrical admittance and the acceleration sensitivity for various boundary conditions to illustrate some of their uses.

Study of the sandwiched piezoelectric ultrasonic torsional transducer

The sandwiched piezoelectric ultrasonic torsional transducer was studied. The transducer consists of front and back metal cylinders, and coaxially segmented, tangentially polarized, piezoelectric ceramic tubes. The torsional vibration of the tangentially polarized piezoelectric ceramic slender tube was studied first and its electromechanical equivalent circuit was derived. Based on the network theory and the electromechanical equivalent circuit, the torsional vibration of the piezoelectric ceramic cylinder, formed by stacking a number of identical short piezoelectric ceramic rings, was analysed and the electromechanical equivalent circuit of the piezoelectric ceramic stack in torsional vibration was developed. Finally, the sandwiched ultrasonic torsional transducer was studied and resonance frequency equations were derived which can be used to design and calculate the torsional transducers for different applications.