Piezoelectricity, Acoustic Waves and Device Applications

FOREWORD.

ORGANIZERS AND COMMITTEES.

CONTENTS.

This paper briefly summarizes the current research progress in China and other countries of the acoustoelectric transducer materials, i.e. piezoelectric and piezomagnetic transducer materials. The structures, properties and applications are of these materials are analyzed and compared. The future research and development of the field are finally suggested.

Piezoelectric ceramics have important applications in many fields. However, with the consciousness of importace of people-orientation and environmental protection, the lead-involved piezoelectric ceramics such as PT and PZT become improper. This paper summarizes the status as well as certain problems in applications of lead-free piezoelectric ceramic materials. The effect of defects in the crystal lattice of piezoelectric ceramics on their performance is discussed. The research trends of lead-free piezoelectric ceramics, including BaTiO₃ (BT) or Bi_0.5Na_0.5TiO₃ (BNT) based piezoelectric ceramics and bismuth (Bi) layered structure piezoelectric ceramics, are pointed out. The piezoelectricity and emission properties of electronics of these piezoelectric ceramics and lead-free ferroelectric ceramics are also briefly discussed, with special emphasis on the effect of additives in the materials.

The superfine powder technology is a rising area that strides forward along with the developments of modern science and technology. This article clarifies the classification and characteristics of superfine powders. The current status and achievements in China are summarized from various aspects including the preparation methods, the graduation, and modification. The latest applications and research trends of superfine powder are also reviewed. The gap existing between China and other advanced countries in the superfine powder technology is noticed, which shows clearly how we shall do immediately.

This paper describes briefly the history of research on piezoelectricity effect and piezopolymers. Then attention is focused on several important piezopolymers and their composites (for example PVDF, PA11, piezoelectric rubber, etc.). A study of the structures, properties, applications and fabricating techniques is presented. Finally, the development trend of piezopolymers and some problems which need further research are discussed.

The Stroh formalism of piezoelectric material, Fourier analysis and singular integral equations technique are used to investigate the existence of the pulse in presence of local separation at frictionless interface between two contact piezoelectric solids, which are pressed together by uniaxial tractions and laid in the electric field. The problem is cast into a set of singular integral equations with Cauchy kernel of which the closed solutions are derived. The numerical discussion on the existence of such slip pulse is presented. The results show that such slip pulse, which has square-root singularities at both ends of the local separation zone, can propagate in most material combinations. And the existence of such slip pulse will be affected by applied mechanical and electric fields in some special material combinations.

In this paper, the motion stability of the flexible piezoelectric beams is studied. The Hamilton principle is applied to derive the equation of motion and the method of multiple scales is used to solve the stabile regions of the stationary motion. The numerical example is given to analyze the effects of the voltage, axial force and damping ratio on the stabile regions. From the results it is seen that the larger the difference between the applied outer voltage and the electric potential deference between the upper and lower surfaces of the piezoelectric layer, the larger the stable regions; the smaller the axial force, the larger the stable regions; and the larger the damping ratio, the larger the stable regions.

Effect of initial stresses on dispersion relation for transverse surface waves circulating around a piezoelectric cylinder covered with a perfectly conducting layer is investigated. Two overlay materials are considered: namely, Gold and Aluminum. The piezoelectric substrate is considered to have the symmetry of a hexagonal crystal, and the layer is a perfectly conducting. The dispersion equation has been derived for the two overlays materials in the form of determinant involving Bessel functions. The roots of the dispersion equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots are numerically calculated by "Bisection method iterations technique" and presented graphically for various thickness of the overlayer and for different values of the initial stresses. The effect of the initial stresses on the natural frequencies is illustrated on the figures. It is found that both the thickness of the overlayer and the initial stresses have a substantial effect on the dispersion behavior. Moreover, it is seen that dispersion relation for a PZT-4 core covered by a Gold is much smaller than of the Aluminum layer. The results obtained in this paper not only may help us insight into the electro-mechanical coupling behavior of the piezoelectric composites cylinders, but also can offer theoretical basis and meaningful suggestion for the design of piezoelectric probes and electro-acoustic devices in the nondestructive evaluation technology. Finally, The results are compared graphically when the overlay is Gold or Aluminum and with those do not have initial stress and electric field which have been studied in the classical cases.

In this paper, the three-dimensional coupled fields in simply supported solid and annular circular piezothermoelastic plates subjected to uniform coupled load are solved and expressed in elementary functions. For this object, the general solutions of Chen [1] for transversely isotropic piezothermoelastic materials are rewritten to a non-dimensional form. Then, the coupled field in hollow circular plates can be obtained by virtue of four constructed harmonic functions and the non-dimensional general solutions. This solution can be degenerated to the corresponding ones of solid circular plate. At last, the numerical results of coupled fields in cadmium selenide annular circular plate, including displacements, stresses, electric potential and electric displacements, are presented in details. And the displacement, stress and temperature increase induced by thermal-mechanical loadings are compared with those obtained for the same material where the piezoelectric and pyroelectric effects are ignored.

The influence of piezoelectric phase volume fraction and composite shape (height/width) on resonance of 1-3 and 1-3-2 type piezoelectric composites which applied on low frequency band has been investigated. 1-3 and 1-3-2 composite samples were fabricated by dice-fill technology. The performance of two type composites with volume fraction of ceramic was analyzed and compared. In sum, 1-3-2 composite was the same to 1-3 composite on performance when ceramic bottom volume fraction of 1-3-2 composite was less then 30%. In addition, height/width ratio of composite was altered by adjusting the height of samples. Then, the resonant frequency and electromechanical coupling coefficient of composites were measured. The result showed that the resonant frequency has been affected by the variety of geometries of samples and volume fraction of ceramic.

The electric impedance of a segmented beam with surface piezoelectric actuators is studied. The two layer piezoelectric actuators are in parallel in the electric circuit. The dynamics of the piezo-laminated segment and the elastic segments in the whole beam are presented by the 5 × 5 and 4 × 4 impedance matrix, respectively. Considering the mechanical-electric boundary conditions and the continuum conditions among these beam segments, the electric impedance of the whole system is obtained by solving its linear impedance equations. The experiment on a free-free segmented beam is done, the measured electric impedance of the system agrees with the theoretical value. For the resonance frequencies of such system, the relative errors between the measured and the theoretical values are smaller than 1.62% in the frequency range of 2800Hz. The parameter study of piezoelectric elements shows the change of the system impedance has the same trend with the change of their elastic modulus and absolute value of piezoelectric strain constant. However, the change of the system impedance has the opposite trend with the change of its dielectric constant.

Pb_0.99Ca_0.006Nb_1.98Ti_0.01O_5.986 (PCNT)-x wt% CeO₂ (x=0-0.4) system with high Curie temperature piezoelectric ceramics were fabricated by traditional ceramic technique. XRD results show orthorhombic symmetry tungsten bronze structure with ferroelectric characteristic existed in these compositions. The lattice constant of crystals were calculated from the XRD data. It is found that the lattice constant and the unit-cell volume decrease with the increasin₂. When x = 0.3 wt %, the piezoelectric constant d₃₃ reaches to 75 pC/N which is the maximum value of all the compositions, and the longtitude electromechanical coupling factor kt is 0.33, the dielectric constant ε₃₃^T/ε₀ is 248, the dielectric loss tanδ is 0.01 and the Curie temperature of dopant CeO₂ content reaches to 550 °C. This piezoelectric material is desirable for high temperature application.

On the basis of the classical theory of Kirchhoff plate and assuming the physical properties obey a power law in the thickness of piezoelectric functionally graded materials, the modified classical laminate theory involving piezoelectric coupling terms is used. The governing equations of piezoelectric functionally gradient thin plate subjected to mechanical load and applied electric field are developed. Applying bi-triangle series expansion, the stress and displacement are obtained for piezoelectric functionally gradient rectangular thin plate with different boundary conditions subjected to the electric field. Then the influences of gradient parameter on its behaviors are discussed. These results obtained satisfy engineering requirement and the solving is straightforward.

Using the microcomputer control electron universal testing machine, both 1-3 and 1-3-2 PZT/epoxy piezoelectric composites prepared in our lab have been test with directional pressure. The permittivity, resonant frequency and dielectric loss of the composites have been measured under vertical force. Simultaneously, the parameters can be measured with a temperature test box, and the variety of the material properties can be obtained with pressure and temperature. The result showed that both the permittivity and the resonant frequency of 1-3 and 1-3-2 PZT/epoxy piezoelectric composites increased with pressure enhancing, 1-3-2 composites increase less than 1-3 composites. With the increase of temperature, the permittivity of two type composites decrease, the resonant frequency increase. The fluctuation range of dielectric loss of all these samples is very small while the pressure varied from 0 to 6 MPa. It is no more than 0.04. While or the temperature changed from -50 to 100 °C, the state is the same. The experimental data of these two type composites indicated that the stability of 1-3-2 composite with pressure is better than that of 1-3 composite, and the stability of these two types are almost the same with temperature.

This paper considers the plane stress problem of anisotropic piezoelectric beam subjected to linearly distributed load, with the coefficients of elastic compliance, piezoelectric and dielectric impermeability being arbitrary functions of the thickness coordinate. Based on the basic equations of the plane stress problem, the stress function and electric displacement function are assumed in forms of polynomials of the longitudinal coordinate, and can be determined absolutely by the compatibility equations and boundary conditions.

A new approximate method based on the concept of wavelet is suggested to combined with the conventional finite element method. Hamilton's principle is employed to derive the governing equations in discrete form for structures such as beams and thin plates. Numerical results are given, indicating that the suggested method performs quite well.

The propagation of plane longitudinal waves at an interface of a semi-infinite piezoelectric elastic medium under the influence of the initial stresses is discussed. The free surface of the piezoelectric elastic medium is considered to be adjacent to vacuum. We assumed that the piezoelectric material is anisotropic and of a type of transversely isotropic crystals (hexagonal crystal structure, class 6 mm). For an incident of longitudinal plane wave, four types (two for the displacement and two the electric potential) of reflected plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves are shown to exist. The relations governing the reflection coefficients of these reflected waves for various boundary conditions (mixed-free-fixed) are derived. It has shown analytically that reflected coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as will as the initial stresses presented in the medium. The numerical of reflection coefficients for different values of initial stresses have been carried out by computer for PZT-5H Ceramic as an example and the results are given in the form of graphs. These graphs show the prominent effect of the prestressing, the parameters of electric potential and the angle of incidence as well on the reflection coefficients. Finally, a particular case is considered in the absence of the initial stresses and the electric potential. Some earlier studies have been compared to the special case and are in good agreement with it.

In the present paper, we focus on the free vibration and steady-state response of a smart cylinder, which consists of an intermediate functionally graded elastic layer bonded with two inner and outer homogeneous piezoelectric ones. The bonding adhesives between the functionally graded layer and piezoelectric ones are considered by a spring layer, which may be perfect or imperfect. For a hybrid cylinder simply supported at its two ends, an exact elasticity (piezoelasticity) method based on state space formulations is employed. To approach the radial inhomogeneity of the functionally graded layer and facilitate the solving of state space equations, we adopt an approximate laminated model. In the above process, the anisotropy of materials and the polarized direction of piezoelectrics are considered. Finally, the effect of the related parameters on the free vibration and steady-state response of the hybrid cylinder is discussed in numerical examples.

The transient responses of infinite elasto-piezoelectric composite hollow cylinder with an isotropic core under radial vibration are obtained. According to the charge equation of electrostatics, the expression of electric displacement for piezoelectric layer is first expressed by a product of a known function about radial distance and an unknown function about time. Then the governing equations for mechanical field of the piezoelectric layer, involving the unknown time function, are derived. By the method of superposition, the dynamic solutions for both elastic and piezoelectric layers are divided into two parts named as quasi-static and dynamic parts. The quasi-static part is obtained in an explicit form and the dynamic part is solved by the separation of variables method. Both the quasi-static and dynamic parts thus obtained involve the undetermined time function. By means of the electric boundary conditions, a Volterra integral equation of the second kind with respect to the unknown time function is derived. Interpolation method is introduced to solve the integral equation efficiently. The displacements, stresses and electric fields are finally determined. Numerical results are presented.

Commonly, the shear piezoelectric constant value for d15 is almost two times higher than those for d33 and d31. Also the value of share electro-mechanical coupling coefficient k15 is higher than those of k31 and k33. Sometimes a design for ultrasonic motor based on share coefficients d15 has the potential for superior performance. In the paper, we propose a new mechanism for exciting shear-bending vibration in piezoelectric ceramic rod. A solid piezoelectric ceramic rod is polarized along its axial direction. The surface of the cylindrical rod used as an electrode is plated with nickel. The cylindrical electrode was divided into four pairs and each pair has two parts symmetrically along the axes. If opposite voltage signals are applied to the electrode parts which are opposite on circumferential direction or along the axial direction, a shearing strain should be induced on the piezoelectric ceramic. Using a pair of alternating voltage signals (sine and cosine) on four pairs of electrodes, a shaking head vibration (wobbling motion) was generated circumferentially. A mini-ultrasonic motor prototype with this concept and a diameter of 6mm was designed. And its characteristics were determined experimentally. The design concept presented in this paper is much promising for applications in small motors, especially in those with piezoelectric ceramic rod stators with a large diameter-length ratio.

Singular electro-elastic fields near the corners of wedges/junctions in piezoelectric-piezoelectric or elastic materials under antiplane loadings are analyzed. At first, a new weak form for solving eigenpair problems in piezoelectric materials is derived with stress equilibrium equations, Maxwell equation and boundary conditions; Then, with the asymptotic exponential assumption along the radial distribution and the bubble mode assumption along the circumferential distribution of the displacement and electric potential in an element around the tip of wedge/junction, a simple one-dimensional finite element formulation that only discretize the displacement and electric potential circumferentially is established. The polarization orientation of piezoelectric materials may be arbitrary. In numerical examples, the influences of wedge angles, poling orientation and boundary conditions are discussed. Through comparing the existing solutions, the validity and high precision of present method is proved.

Based on the theory of liner piezoelectric elastic, the governing equations of the coupled waves are reduced to Bessel and Laplace equation. The boundary conditions imply that the displacements, shear stress, electric potential and electric displacement are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The electrically open and short conditions at cylinder surface are applied to solve the problem. The effect of the initial stress on the phase velocity and the electromechanical coupling factor are discussed in detail for piezoelectric ceramics PZT-5H, substrate for Aluminum. We find that the initial stress has an important effect on the SH wave propagation in a circular cylindrical layered structure.

AlN thin films were deposited on Si (111) substrates by midfrequency dualtarget magnetron sputtering. X-ray diffraction (XRD) and atomic force microscopy (AFM) are employed to characterize the AlN thin films. In order to control structure and roughness of the films for high frequency surface acoustic wave (SAW) devices, the influences of different processing parameters were investigated. It was found that substrate temperature and annealing temperature have a great effect on the microstructure and surface morphology of the films.

For plate bending and stretching problems in piezoelectric materials, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to establish necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; for the case of axisymmetric bending and stretching of a circular plate, these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution.

Based on the basic equations of a transversely isotropic magnetoelectroelastic axisymmetric problem, a three-dimensional (3D) analytical solution for a functionally graded, magnetoelectroelastic disc rotating with a constant angular velocity is obtained. The displacement components, electric potential and magnetic potential are assumed in forms of polynomials of the radial coordinate (r), with coefficients being unknown functions of the axial (thickness) coordinate (Z), which can be determined by solve a group of simply governing equations. Since the material parameters can be arbitrary functions of the Z-coordinate, the present solution can be degenerated into that for corresponding homogeneous materials cases and various uncoupled cases. The numerical results of a particular functionally graded magnetoelectroelastic rotating disc clearly show the effect of material inhomogeneity (i.e. gradient index) on the elastic, electric and magnetic fields, which can be used to guide the optimization design of rotating discs.

With the electronic devices being miniaturized, piezoelectric transformer has got more and more broad attention. It is necessary to study the connections of piezoelectric transformers because the output power of single piezoelectric transformer is low. This paper introduces a method to calculate the connected PTs' output characteristics using admittance parameter matrix of two port network, and analyses the gain, power and efficiency versus load and frequency for four possible connections. All calculations are performed with MATLAB, it is found that the parallel-parallel connection and parallel-series connection can enhance step-up ratio and output power, and the output characteristics of parallel-series connection are better than that of parallel-parallel connection.

A beam embedded piezoelectric layers is widely used as actuator to excite or control the vibrations of machines and structures. It is also applied as sensor to measure their vibrations. By using the hypothesis of Euler-Bernoulli in beam theory and assuming the distribution of the electric potential in the z-direction, this paper derives the governing equations for sandwich beams coupled with piezoelectric layers. The frequency equation of the free vibration is then obtained and numerical results are presented to demonstrate the availability of the presented theory.

Based on the classical lumped parameter model, using two-port network admittance Y-parameter matrix, the electrical characteristic of voltage gain, output power and efficiency of parallel-parallel connected piezoelectric transformers is analyzed in detail. In addition, how the number of paralleled identical Rosen type piezoelectric transformers contributes to the voltage gain and output power is simulated by the Pspice. The theoretical analysis and the simulation results show that, parallel connection of piezoelectric transformer is an effective way to improve the output power. Compared single piezoelectric transformer, the parallel connection of piezoelectric transformer can not only supply more power but also improve the voltage gain.

As the size of quartz resonator continues to shrink, beveling of the plano-plano quartz crystal is needed to reduce mounting loss and to sustain energy trapping so to have low motional resistance for oscillation. The beveling process though is time consuming and difficult to control for small size and low frequency quartz crystals. In recent years, studies on stepped electrode (a.k.a bi-mesa electrode) began to appear. It's believed that stepped electrode on plano-plano crystal would do part of the job in energy trapping like beveled crystals. In this paper, we report our own study of stepped electrode with the following configurations: single layer electrode on plano-plano crystal, stepped electrode on plano-plano crystal, single layer electrode on beveled crystal, and stepped electrode on beveled crystal. The vehicle for this study was a 15 MHz 3.2mm × 2.5mm crystal. Preliminary results show that stepped electrode can provide to some degree of energy trapping as bevel crystals.

In recent years, demand for quartz crystal resonators continues to grow for the mobile phone market. To meet the stringent long-term frequency stability requirement, crystal makers usually use Au as the electrode baseplating material. Using layered electrodes with different metallic materials was reported in the past for different reasons. In this paper we report our own study of using a sputtered Cr/Ag/Au layered structure for the electrodes of AT-cut quartz crystal resonators with the sole intention of reducing the usage of Au for cost reason. We studied the physical parameter, electrical sheet resistance, of the layers along with thermal processes. The electrical characteristics of finished crystal resonators were compared with those made with the Cr/Au baseplated electrodes and the reliability performance of the crystals with new electrodes also be examined. Preliminary results show that AT-cut quartz crystal resonators with electrodes based on the Cr/Ag/Au layered structure meet the long-term frequency stability requirement for mobile phone application. The electrical characteristics are compatible to the Cr/Au baseplated crystal resonators. The physical characteristics study shows that the Cr/Ag/Au layered structure is stable under related thermal process environments.

In this paper, dynamic behaviors of a piezoelectric laminated axisymmetric circular plate structure are studied with a view to influence of the geometric nonlinearity and nonlinear piezoelectric effects. The nonlinear control equations of PDFs are gained by the math model of the problem derived from mechanics and piezoelectricity. The problem is divided into two sections for discussion. The exact solutions of static control equations of the plate for simply supported boundary condition are obtained by power series method. Galerkin method and KBM perturbation method are used to solve the dynamic control equations, and the nonlinear relations between large amplitude and natural frequencies are gained. The numerical calculation and analysis of unimorph piezoelectric actuator are given.

Based on the wave propagation model of the coated material, we proposed a laser impact wave method to detect the interfacial crack. The pulse-wave applied on the coating surface is used as an exciting source, the dynamic properties of the receivers along the surface are then collected, and using the waveform analysis, we can find the crack information. In the finite element simulation process, we analyzed different models and adopted the wavelet tool to get the detail coefficients. It shows that the coefficients at the crack area are different from those without crack, and it is pronounced at the crack center, thus we can detect the crack location and size. This paper provides a theoretical basis to non destructive evaluation of the coated materials.

In underwater environment acoustical waves can transmit a longer range away from the transmitter than electromagnetic waves do. Underwater acoustical transducer is utilized as the physical element for sound wave transmitting and receiving. By transmitting a sound wave from the transducers, the surface or underwater objects ranging several miles away from the transducers can be located by detected the reflected sound wave from the objects itself. So far, the Langevin type piezoelectric transducer is still the best candidate as acoustical telemetry transmitters. Since the operating frequency of the transducer determines the distance that the sound wave could travel, it is important to measure it. However, it takes a long time to simulate and measure the transducer's resonance frequency in the laboratory experiments. Some methods are proposed to calculate and prediction the frequency instead of experiments, but they caused more or less accuracy errors. In the meantime, the Mega-fuzzification is a machine learning method that aims at increasing the prediction accuracy in limited data or small data set learning. This study develops a prediction system using Mega-fuzzification to determine the frequency of the Langevin type piezoelectric transducer. The results indicate that the proposed system gets the prediction error less than other methods.

The biological effect of ultrasound depends significantly on the sound intensity, frequency and the tissue properties. Both reversible effect and irreversible effect exist. This paper presents some biological and physical explanations, including (1) ultrasound can change the permeation of cell membranes. The stimulation of ultrasound changes the structure of cell, causing the change the electricity of cell membrane; (2) the ultrasound of low frequency can stimulate some plant and animal cells' growth. The pH is indispensable to the growth of cell and ultrasound will change the pH; and (3) we give some ultrasound explanations about the killing effect on cancer cells.

In our previous study, with 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, in which both full and partial electrodes are considered. In fact, the electrodes of resonators are not symmetrically arranged due to the mounting points of crystal blanks are only in one side. As a result, the study of asymmetric electrodes is necessary for practical applications. Different from previous ones, the vibration solutions will contain both symmetric and anti-symmetric thickness-shear vibrations in the electroded area, which will introduce new boundary conditions. We start with the first-order Mindlin plate equations of a piezoelectric plate for the thickness-shear vibration analysis of a resonator with asymmetric electrodes. The electrical parameters are derived with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity. With this approach we can further analyze the actual resonator vibration influenced by the electrode position.

The propagation of surface acoustic waves in functionally graded materials is difficult to analyze because the differential equations have variable coefficients. In this study, Frobenius method is employed to obtain the analytical solution of this problem. The result is very close to that of layered model in our earlier study. Some results from the solution can be the fundamental guidelines for engineering applications including piezoelectric surface acoustic wave resonator and vibration control.

This study presents the controller design and tests of a new piezodriven two degree-of freedom (DOF) monolithic stage for precision motion. The computer-controlled system was developed, designed and employed for better displacement error compensation by proportional-integral-derivative (PID) controller based on Internal Model Control (IMC), Iterative Learning Control (ILC) and Disturbance Observer (DO). Experimental results show that stage positioning is precisely controlled (error ≈ 1.42%) for tracking sinusoidal waveforms by IMC and P-type ILC with repeatable disturbance. With additional DO, experiment tests perform error ≈ 0.5% with non repeatable disturbance up to 16% of the maximum traveling length in roughly 5 iterations. This is close to the hardware reproducibility level. Experimental results show the piezo-stage controlled system can be potentially used for nano technology applications for precision engineering in industrial systems.

In this paper, PSPICE is implemented to model and simulate the characteristic of thin film bulk acoustic resonator (FBAR). Both analogy equivalent circuits of Acoustic transmission line and Mason model is proposed and transferred to the PSPICE model by using the controlled-source method. The physical parameters such as piezoelectric materials and its thickness, electrode material, area and its thickness affecting the properties of the FBAS are discussed. Finally, we have implemented the FBAR to design a ladder type filter with a center frequency at 1.1 GHz and bandwidth about 60.9%. The study results in that PSPICE is an effective tool for the FBAR modeling and ladder type filter design.

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein-Gulyaev wave exists only in crystal class 6mm and mm2 materials. It is a shear-type surface wave, for which the energy concentrates on the material surface and it does not radiate energy into the adjacent liquid. This causes the B-G wave to be sensitive to changes in both mechanical and electrical properties of the surrounding environment. These features make B-G wave a good candidate for liquid sensing application. In this paper, we investigate the potential application of B-G wave in 6mm crystals for liquid sensing. The dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.

Our study starts from the interaction of a thin liquid layer and surface acoustic waves in an isotropic semi-infinite substrate, and we obtain the relationship between wave velocity and thickness of ideal fluid layer. This result is similar with earlier experimental and research results. We further extend substrate to an isotropic semi-infinite plate, at which both symmetric and anti-symmetric modes of a plate can be captured as thickness of liquid layer becomes extremely thin. This result is very close to plate vibrations without the liquid layer. Finally, we analyze the characteristics of surface acoustic waves propagating in an anisotropic semi-infinite solid and plates covered with an ideal liquid layer. It is observed from an ST-cut quartz crystal substrate that there are many displacement modes and corresponding velocities due to the interaction of waves in the plate and liquid layer.

The propagation behaviors of surface acoustic waves in an isotropic semi-infinite solid and infinite plate with initial stress field are investigated, and we obtain the phase velocity equations of Rayleigh waves in a semi-infinite solid and infinite plate. By comparing surface acoustic waves velocity in plate under initial stress with that without initial stress, it is clear that velocity of surface acoustic waves are evidently affected by initial stress. When the stress is in the same direction of the propagation of the surface acoustic waves, the change of the wave velocity of the surface acoustic waves has certain relation to the stress within small numerical value of stress.

In the analysis of a surface acoustic wave resonator for modeling and design, wave velocity considering the influence of complications of the structure is a very important parameter. Currently, solutions of surface acoustic wave velocity are mainly obtained from the simplified semi-infinite model. In this study, we analyze surface acoustic waves in a finite isotropic substrate with periodic electrodes by using the two-dimensional theory for finite elastic solids. Numerical examples, which use isotropic materials as substrates, show that surface acoustic waves will have a lower velocity with the increase of electrode thickness. When the thickness of electrode is zero, surface acoustic wave will have the same velocity with the corresponding semi-infinite substrate case.

The analyses of surface acoustic waves propagating in finite elastic solids are mainly done with the simplified semi-infinite model. In this study, we analyze the characteristics of surface acoustic waves in finite anisotropic substrates with periodic electrodes by using the two-dimensional theory for finite elastic solids. Through the solutions of surface acoustic wave velocities, we find that surface acoustic waves will have a lower velocity with the increase of periodic electrode thickness. When the thickness of periodic electrode is zero, surface acoustic wave will have the same velocity with the corresponding semi-infinite substrate case. The analytical model we use is closer to the actual surface acoustic wave resonators, and at the same time the finite sizes of structures and the effect of electrodes for their layout, size, and material properties are considered. The method and results from this study will have important practical applications in the analysis of surface acoustic wave resonator for modeling and design.

The elastic wave behavior in dynamic deforming medium is studied in this paper. Based on Chen R-S additive decomposition formulation, the motion equation for dynamic deforming medium is established firstly. Introducing perturbation on the displacement field, the wave equations for incremental deformation (P wave and S wave) are obtained. The results show that: for homogenous stretching medium, the incremental P wave velocity is anisotropy and the incremental S wave velocity is anisotropy, the wave velocity is tuned by the stretching of medium; for small local rotation deforming medium, the incremental S wave velocity is isotropic and it tuned by the local rotation angular parameter Θ; the small local rotation deforming medium has no effects on incremental P wave velocity, however the incremental P wave vibration direction in the small local rotation deforming medium is anisotropy. The related velocity equations are given in the paper. The conclusion of this research is that: by detecting the wave features (velocity anisotropy, vibration direction anisotropy, or the time-shift velocity variation) the deformation features of dynamic deforming medium can be obtained.

The change in the frequency of guided EM waves in infinite and anisotropic dielectric plates affected by stress fields are studied based on the perturbation method. For the effect of uniform stress field, frequency shifts from first order perturbation and second order perturbation are calculated, and compared with those from exact solution. It's found that, a perturbation method only accurate to the first order is not enough for the prediction of frequency jump behavior. For the effect of thickness-dependent stress field, a dielectric plate attached to a rigid base and subjected to steady acceleration is considered. It is found the maximum frequency shift is about (3~15) × 10^-10/g for plate thickness 2b = 3.27mm.

In this paper, a hybrid method, which combines the traditional concept of guided waves and FEM (finite element method), is proposed to analyze the spurious modes of aluminum nitride (AlN) film with electrodes. First, the guided wave modes in plated area are obtained by 1-D FEM. Second, a mode-match method is used to satisfy the boundary conditions. The vibration of the film resonator is a superposition of all the guided modes. With respect to AlN film resonator, which is a thickness-stretch mode resonator, we have identified three families of spurious modes, extension, thickness-stretch and thickness-shear. The spectrum of spurious modes is calculated and the influence of the spurious modes is discussed.

In this paper, an ultrasonic wave experiment is carried out for detecting viscosity property of cement mortar. The specimen of cement mortar of length 0.5m and radius 0.045m is formed. In order to detect the property of ultrasonic wave propagation at different position, the large specimen is cut into short specimens. Then, ultrasonic wave experiments for the specimen with different length are performed. The experimental results show that the clear attenuation of the amplitude of ultrasonic wave, and this implies the cement mortar is a material that possesses viscous properties. A viscoelastic model is proposed and related parameters in the model are numerically determined with the ultrasonic wave experimental results. This is an effective method to measure parameters of the constitutive relation of cement mortar by ultrasonic wave technique.

In this paper, we study the acoustic properties of single-wall and double-wall carbon nanotubes, and set up the analytical models of wave propagation in carbon nanotubes (CNTs). For single-wall carbon nanotubes, the continuum elastic model is used to analyze the acoustic properties of longitudinal wave and flexural wave modes, and then the relationship of the structure parameters of single-wall carbon nanotube and the frequency of acoustic wave is studied; for double-wall carbon nanotubes, the van der Waals force interaction between two adjacent tubes can cause the nonlinear free vibration, we establish the governing equation of longitudinal wave propagation by considering the effect of the van der Waals force, which is described as the transverse distribute pressure, by the model, the influence of the structure parameters of double-wall carbon nanotubes to the acoustic resonant frequency is investigated. Based on this, the difference of acoustic properties between single-wall CNT and double-wall CNT is obtained. The results show that the acoustic properties of single-wall CNT and double-wall CNT are quite different even with the same wave source. If the length of the CNT is more than several microns, the frequency of its fundamental acoustic mode can be within 10 GHz range, which is obtainable by using MEMS-based ZnO or AlN thin film micro resonator.

Mono-base multi-electrode quartz crystal resonators were designed and produced by the energy trap theory. Influence of surface processing (polishing or not) and edge shape (edge beveling or not) to that was researched; then compared and analyzed with classical mono-base mono-electrode quartz crystal resonators. Experiment result shows that surface polishing and edge beveling to mono-base multi-electrode quartz crystal resonators can effectively improve the characteristic of the resonator. By a certain mode of force infliction, mono-base multi-electrode quartz crystal resonator have better force-frequency characteristic than mono-electrode one.

This paper analyzes the frequency temperature characteristic of a new type of single-base multi-electrode quartz crystal resonator in air environment and the result proves that AT-cut frequency temperature characteristic curve is cubic. Through the experiment, the frequency temperature characteristic of this resonator shows basically consistent with that of the single-base singular electrode of the same fundamental frequency and basal piece. We can conclude that the multi-electrode resonator is more available in practical use and it can implement multiplex compensation in measurement.

The propagational characteristics of free waves in wave guides can be utilized for NDE, vibration reduction, and oil exploration. A vast of researches have been conducted on isotropic and anisotropic laminated plates, but few concerning the behavior in high frequency range or at large wave numbers, for which numerical instability may generally be encountered in conventional analysis methods. Based on the state equation for anisotropic elasticity, this paper constructs the formulations for the method of reverberation-ray matrix to analyze the wave propagation in anisotropic elastic laminated plates. Since unknown wave amplitudes are appropriately retained in the formulations, large numbers at high frequencies are excluded, making the calculation stable in the high frequency range. The matrix inverse operation is also avoided in the scattering relations to assure the stability in the low frequency range. Numerical examples are presented and good agreement is obtained.

According to energy trap theory and finite element analyze, we plated several electrodes on the same quartz substrate. And an integrate quartz crystal resonator is created. We study the force-frequency characteristic of resonators and output of slip frequency on different positions of quartz substrate by adding radial force simultaneity the resonator vibration state stability of this kind structure is testy and analyzed by using crystal frequency stability instrument the result proved that the force-frequency characteristic of resonators on different positions of quartz substrate is different and the difference of corresponding force-frequency coefficient can reach six times more. When resonators were driven by integrate circuit, the stability of vibration can get to 10-10 degree.

Surface acoustic wave resonators are fabricated on a finite elastic substrate with proper mountings. In the analysis of the wave propagation of finite elastic solids with complications such as electrodes, mountings, and boundary conditions, approximate theory has to be developed based on dominant vibration modes and actual boundary conditions. In considering the effect of mountings in a finite elastic plate and vibration mode changes, we start from an elastic plate with one face rigidly fixed to examine the vibration frequency and mode changes in the vicinity of the surface acoustic wave velocity. For an isotropic elastic plate, we introduce two potential functions for the three-dimensional elasticity equations. Solutions satisfying the boundary conditions of one rigidly fixed face and one free face are obtained along with frequency equation. It is found that with the increase of the plate thickness, solutions of the velocity and displacements approach to Rayleigh wave solutions we are familiar with. We further obtain stresses of the plate with known plate thickness and wave velocity to see the overall changes in addition to the velocity itself and displacements. These results will be used in the analysis of surface acoustic waves in finite solids in conjunction of our recent work on the two-dimensional theory for the analysis of surface wave propagation in finite plates. Such analytical methods and procedures are essential in the analysis and design of surface acoustic wave resonators, which are based on finite anisotropic piezoelectric solids with structural complications.

Based on the Timoshenko beam theory, a symplectic analysis is established for a functionally graded beam whose Young's modulus varies exponentially with the axial coordinate. The analysis procedure is presented in detail to show how the conventional symplectic method can be extended and applied. In particular, in contrast to the Hamilton matrix (operation) appearing in the conventional analysis, a new concept of shifted Hamilton matrix (operation) is put forward to indicate the corresponding matrix for functionally graded material. The wave induced resonance of a semi-infinite homogeneous beam connected to a functionally graded beam of finite length is finally considered to illustrate the present theory.

Based on the linear piezoelectricity theory, this paper sets up and solves the surface acoustic wave (SAW) wave equation with gyroscopic effect in the piezoelectric medium. Taking three typical piezoelectric materials, quartz, LiNbO₃ and PZT-5H as examples, the influence of substrate rotation on SAW propagation characteristics is analyzed and compared quantitatively. According to the theoretic calculations, not only the different materials but also the same materials with different cut orientations and propagation directions have different SAW gyroscopic effects. Furthermore, the sensitivity of the gyroscopic effect is related to the rotation direction. When the substrate suffers rotation, in most cases the formerly decoupled wave would generate new coupling, but others with certain cuts and rotation axes remain the decoupled state. The rotation induced change of SAW dispersion relation and propagation parameters should be considered and studied when designing SAW gyroscope. The investigations mentioned above provide theoretical guide for the research of SAW devices with gyroscopic effect.

The free vibration of a multi-span continuous Euler-Bernoulli beam is studied by employing a recursive algorithm for the method of reverberation-ray matrix (MRRM). The algorithm is numerically stable at high frequencies or/and large span-to- thickness ratios. Numerical results are finally presented to show the effectiveness and efficiency of the proposed recursive algorithm. The present algorithm may be readily applied in wave propagation in laminated plates.

This paper describes the requirements on RF filtering derived from multi-band, multi-mode RF front ends for cellular phone applications. Drivers are forward integration – e.g. from PA function via transmit front-end to a fully integrated radio – and new influences are introduced by new requirements of 3G systems and the integration of complementary access (e.g., Bluetooth; WLAN, GPS, DVB-H). Filter components such as SAW and BAW filters have to solve several aggravated requirements simultaneously. New technologies are required to follow the demand for improved RF performance, reduced PCB area consumption, and continuously decreased overall component costs.

Due to its high Q and temperature stable properties, for many years, quartz crystal based oscillators are important clock sources in consumer, commercial, industrial, and military digital sub-modules and modules. The demand for quartz crystal resonators and oscillators continues to rise. The unique fabrication and encapsulation requirements though render quartz crystal resonators and oscillators difficult or close to impossible to be integrated onto the mature silicon based IC platforms. The recent technical breakthroughs of MEMS (Micro Electro Mechanical Systems) based resonators and oscillators seem to re-ignite the interest in displacing/replacing the quartz crystal technology and to open up again the prospect in clock source integration.

This paper discusses and assesses, from the viewpoint of a quartz crystal manufacturer, such development and its possible impact on the quartz crystal industry which also experiences major progresses in miniaturization, performance enhancement, cost reduction, etc., in the past few years. This paper is not to discredit the MEMS oscillator efforts but to help the quartz crystal manufacturers to understand more about the efforts and advise them what they need to prepare for.

By energy trap theory and normalized criterion, we analyze the rationality of Mono-base integrate quartz resonator force sensor dimension structure, and the vibration characteristic of different structure. The result of theory analysis is consistent with experiment nearly. We find out the optimal integrate dimension structure of AT cut quartz resonator which frequency is 10 million. Based on this optimal structure, a differential frequency quartz resonator sensor is made which improves the temperature effect largely.

After proper electric charging, polymer foams show the behavior similar to ferroelectric material. Since the charged polymer foams combine the characteristics of ferroelectric materials (hysteresis loop) and electrets (surplus charges), they are named ferroelectrets. This paper introduces a method of preparation of laminated polytetrafluoroethylene (PTFE) and fluoroethylenepropylene (FEP) films with cellular structure. The character of such ferroelectret is that the layers of compact FEP are the electrets storing charges and the layers of porous PTFE are the framework of the cellular structure. The results show the quasi-static piezoelectric d33 coefficients of the laminated films are up to 200-500pC/N and relatively independent on the static applied pressure in the range of 12kPa; after 160 minutes of aging d33 of the complex films can retain 43% of the original and tends to stabilization.

A new method for preparing piezoelectric polymer with cellular structure (piezoelectret) is introduced. Their piezoelectric activity and thermal stability are investigated for the fluorocarbon piezoelectret films produced in this method. The quasistatic piezoelectric d33 coefficients up to 2200 pC/N are obtained for the fluorocarbon piezoelectret films; d33 coefficients are relatively independent on the static applied pressure in the range of 20 kPa; comparing to polypropylene piezoelectret film the new fluorocarbon films show not only higher values of d33, but also much better thermal stability; Furthermore, the thermal stability of the fluorocarbon piezoelectret film can be further improved by the process of pre-ageing.

The feasibility of a piezoelectric quartz Cuprum (II) sensor based on a molecularly imprinted σ-PD is described. The Cuprum (II) sensor was devised by depositing the polymer onto one side of an Pt-cut quartz crystal through an electro-polymerization process. The author screened the factors which affect the electrochemical polymerization reaction, such as the concentration of template molecule and the concentration of monomer. The sensor showed high selectivity and sensitivity in aqueous system. The sensor response exhibited a linear relationship between frequency shift and the Cuprum (II) concentration in the range of 10-5~10-4 mol/L and the detection limit was 10-6mol/L.

This study focuses on the characteristics of film bulk acoustic-wave resonator (FBAR) on Pt electrodes for high frequency wireless applications, and the critical parameters of the sputtering process such as RF power, deposition pressure, substrate temperature and Ar/N2 flow rate ratio were studied to clarify the effects on the Pt electrodes characteristic of the zinc oxide (ZnO) films using reactive RF magnetron sputter system.

Measurements of X-ray diffraction (XRD) and scanning electron microscopy (SEM) show that the ZnO film deposited on the Pt electrode exhibits highly c-axis orientation with well-aligned columnar and smoother surface. The fabricated two-port FBAR consisted of 1.5μm thick ZnO film with 0.2μm thick Pt top and bottom electrodes was characterized with a network analyzer have a resonant frequency of 1.5 GHz and the return loss is -24.76dB. Furthermore, the effects of varying ZnO thickness on the performance of of the fabricated FBAR devices are also discussed.

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This paper focuses on the fabrication of film bulk acoustic-wave resonator (FBAR) comprising an aluminum nitride (AlN) piezoelectric thin film sandwiched between two metal electrodes, and located on a silicon substrate with a low-stress silicon nitride (Si3N4) support membrane for high frequency wireless applications, and analysis the optimization of the thin AlN film deposition parameters on Mo electrodes using reactive RF magnetron sputter system.

Several critical parameters of the sputtering process such as RF power and Ar/N2 flow rate ratio were studied to clarify their effects on the different electrodes characteristic of the AlN films. The experiment indicated that the process for Mo electrode is easier compared with the Pt/Ti or Au/Cr bi-layer electrode as it entails only one photo resist and metal deposition step. Besides, Pt/Ti or Au/Cr electrodes reduced the resonance frequency due to it high mass density and low bulk acoustic velocity. Compared with the case of an Al bottom electrode, there is no evident amorphous layer between Mo bottom electrode and the deposited AlN film.

The characteristics of the FBAR devices depend not only upon the thickness and quality of the AlN film, but also upon the thickness of the top electrode and the materials used. The results indicate that decreasing the thickness of either the AlN film or the top electrode increases the resonance frequency. This suggests the potential of tuning the performance of the FBAR device by the carefully controlling AlN film thickness. Besides, increasing either the thickness of the AlN film or higher RF power have improves a stronger c-axis orientation and tend to promote a narrower rocking curve full-width at half-maximum (FWHM), but increased both the grain size and the surface roughness. An FBAR device fabricated under optimal AlN deposition parameters has demonstrated the effective electromechanical coupling coefficient and the quality factor (Q_fx) were about 1.5% and 332, respectively.

The paper presents the work principle and frequency spectrum of DDS. On the basis of these, the paper introduces a new DDS structure for eliminating spurs caused by phase truncation error, then introduce the design of FPGA and give the simulation results of the method using MATLAB software.

The Sonic Crystals (Acoustic Crystal, Phononic Crystal), a new kind of functional material, have the property of Sonic Band Gap, that is, the sound or elastic waves whose frequency are in the band gap can't propagate through the material. Based upon the property and the others, plenty of apparatus can be designed, including the sound-proof structure, the vibrations absorbable platform, filters, and so on. In this paper, a Sonic Crystal filter is designed. For this finite size apparatus, the finite element software FEMLAB is used to calculate its band gap by means of acoustic - structural coupled analysis. The results show that, such a structure can reflect specific bands of sound waves.

The tri-dimensional acoustic wave propagation in general anisotropic piezoelectric crystals is analyzed by adopting generalized characteristic theory. The characteristic differential equations and compatible relations along bicharacteristics are deduced. Instead of degenerated to 2D plane and using Umov-Poynting vector or ray method, the explicit expressions for phonons along an arbitrary direction in general anisotropic piezoelectric solids are obtained through the characteristic relations. The focusing patterns in piezoelectric crystals with different symmetry are discussed with the purpose to disclose the evolution rules of phonon focusing along with the increase of the material anisotropy.

In this paper, a new microdevice for on-chip separation of microparticles is presented, in which a micromachined silicon nitride membrane structure is bonded with a glass substrate and then PZT-4 plates are bonded to the silicon and glass substrates to excite the microdevice into vibration. Due to the energy coupling, silicon nitride membranes are excited into vibration as well, generating an ultrasonic standing wave field below the membranes, for which we can use it to separate microparticles within the fluids. In the paper, we start from the radiation force analysis and then design and fabricate the practical microdevice, and use finite element method in ANSYS to obtain its normal mode shapes and frequency response. In the end, the separation performance of micro and/or nano particles is calculated and analyzed.

In this paper, a piezoelectric accelerometer with different micromechanical structures is studied, in which the micromachined silicon mass block and cantilever, covered with ZnO piezoelectric thin films, are used as the sensing element. Starting from the mechanics theory, we design the structure of sensing element and then analyze the factors affecting the sensitivity of the microdevice, including the length and width of the cantilever, the thickness of both ZnO piezoelectric thin film layer and silicon cantilever. Furthermore, finite element method in ANSYS is used to make a 3-D analysis of the microaccelerometer, the resulted resonant frequency of the fundamental mode and higher order modes, which determines the device working bandwidth, and device sensitivity are presented in the end.

This paper presents the growth and characterization of ZnO piezoelectric thin film using magnetron sputtering technology. In this paper, we studied the influence of annealing process and different substrates, including silicon, aluminum layer and silicon nitride thin film on silicon, on the piezoelectric performance of ZnO thin film by using XRD and SEM to analyze C-axis orientation and crystalline quality of ZnO thin film. In the end, we develop a fabrication process, for which the aluminum is still used as the bottom electrode but isolated from the ZnO thin film by a layer of silicon nitride thin film, to meet the requirements of the quality of the ZnO thin film growth and the compatibility with CMOS technology.

In this paper, we start from the fundamental of fluidic dynamics to set up a 1-D analytical model for a MEMS-based microfluidic device, and then we investigate the fluid flow in microchannel influenced by the acoustic field on the basis of acoustic streaming theory. Furthermore, finite element method in ANSYS is used to analyze the structural-fluid coupled field in microchannel actuated by ultrasonic vibration. The results of the acoustic pressure, frequency, velocity and driving force for the fluid flow in microchannel are presented in the end.

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