Band gaps of lamb waves in one- dimensional piezoelectric composite plates: effect of substrate and boundary conditions

We theoretically study the band structures of Lamb waves in one-dimensional phononic crystal plates consisting of piezoelectric ceramics placed periodically in epoxy with epoxy or piezoelectric ceramic substrate by the virtual plane wave expansion method. The dependences of the widths and starting frequencies of first band gaps (FBG) on the substrate's thickness, the filling fraction, and the lattice spacing are calculated for different materials of substrate under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). The FBG width decreases gradually as the substrate's thickness increases and the FBG starting frequency increases progressively as the thickness increases on the whole. The FBG widths and starting frequencies with SC are always larger than with OC. Our research shows that it is possible to control the width and starting frequency of the FBG in the engineering according to need by choosing suitable values of the substrate?s thickness, the filling fraction, and the lattice spacing.     

A 3-D Ritz solution for free vibration of circular/annular functionally graded plates integrated with piezoelectric layers

This paper addresses three-dimensional (3-D) free vibration characteristic of thick circular/annular functionally graded (FG) plates with surface-bonded piezoelectric layers on the basis of 3-D Ritz solution. Three displacement components along with electrical potential field of the plate are expressed by a set of Chebyshev polynomials multiplied by geometry boundary functions. Both open-circuit and closed-circuit surface conditions are taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey either exponent or power law distribution of the volume fraction of the constituents. The effect of thickness-to-radius ratio, inner-to-outer radius ratio, piezo-to-host thickness ratio and gradient index on the natural frequencies of coupled piezoelectric FG circular/annular plates is investigated for different electrical and mechanical boundary conditions. It is observed that, unlike isotropic homogeneous circular/annular plates, frequency parameters of their piezoelectric coupled FG counterparts significantly increase with an enhancement in the host plate thickness to radius ratio. Results also show that the frequency parameters for open-circuit condition are higher than those for closed-circuit condition.     

Network formalism for modeling functionally gradient piezoelectric plates and stacks and simulations of RAINBOW ceramic actuators

A simple network representation is given for a stack of thin, homogeneous piezoelectric plates, executing a single thickness mode of motion. All plates may differ in thickness and material properties, including dielectric loss, ohmic conductivity, and viscous loss. Each plate is driven by a thickness-directed electric field, and all stack elements are connected electrically in series. Functionally gradient single plates and composites are readily modeled by the network, to a desired precision, using a sequence of circuit elements representing stepwise variations in material properties and layer thicknesses. Simulations of RAINBOW (reduced and internally biased oxide wafer) ceramics are given     

Calculations of Lamb wave band gaps and dispersions for piezoelectric phononic plates using mindlin's theory-based plane wave expansion method

Based on Mindlin's piezoelectric plate theory and the plane wave expansion method, a formulation is proposed to study the frequency band gaps and dispersion relations of the lower-order Lamb waves in two-dimensional piezoelectric phononic plates. The method is applied to analyze the phononic plates composed of solid-solid and airsolid constituents with square and triangular lattices, respectively. Factors that influence the opening and width of the complete Lamb wave gaps are identified and discussed. For solid/solid phononic plates, it is suggested that the filling material be chosen with larger mass density, proper stiffness, and weak anisotropic factor embedded in a soft matrix in order to obtain wider complete band gaps of the lower-order Lamb waves. By comparing to the calculated results without considering the piezoelectricity, the influences of piezoelectric effect on Lamb waves are analyzed as well. On the other hand, for air/solid phononic plates, a background material itself with proper anisotropy and a high filling fraction of air may favor the opening of the complete Lamb wave gaps.     

Researching on resonance characteristics influenced by the structure parameters of 1-3-2 piezocomposites plate

The 1-3-2 composite is made of 1-3 composite and ceramic base. Its effective properties are calculated based on the linear piezoelectric theory and uniform field theory. The influence of piezoelectric phase volume fraction and composite aspect (thickness/width) on resonance characteristic of square 1-3-2 piezoelectric composite plate has been researched. In addition, some 1-3-2 composite samples were fabricated by dice-fill technology. The resonance frequency of samples was investigated. The results show that the experiment agrees well with the calculation. The pure thickness resonance mode of 1-3-2 composite will be gained when the volume fraction of ceramic bottom is less than 30%; that of ceramic rods is in the range of 30 approximately 80% and the ratio of thickness to width is less than 0.35.     

纤维厚度和体积分数对压电纤维复合物应变性能的影响

实验制备了不同纤维厚度和体积分数的压电纤维复合物, 并在0.1 Hz的激励电压下测试了压电纤维复合物的自由应变性能和驱动性能, 研究复合物典型结构参数对其性能的影响。实验发现, 随着压电纤维厚度增加, 复合物自由应变和顶端位移下降, 1000 V激励电压下, 纤维厚度为200 μm样品纵向自由应变为665 με, 驱动Mylar膜产生的顶端位移为1.9 mm, 而纤维厚度为300 μm和400 μm样品的纵向自由应变仅为纤维厚度为200 μm样品的23.2%和11.7%, 顶端位移为纤维厚度为200 μm样品的45.8%和19.0%。压电纤维复合物具有驱动正交异性, 横向自由应变、纵向自由应变以及横向效应系数随着纤维体积分数的降低而减小, 纤维体积分数为74%的复合物其横向自由应变和纵向自由应变分别为体积分数为59%样品的2.04倍和1.72倍, 横向效应系数也从0.519减小到0.451。     

一维光子晶体的带隙特性研究

一维光子晶体是指介质只在一个方向成周期性排列的材料。利用薄膜光学的特征矩阵法研究了一维光子晶体的禁带特性,分析了填充率变化、厚度的随机扰动对光子带隙的影响。结果表明,随着填充率的变化,各能级的带隙率变化,并且存在一个极大值;厚度的随机扰动对光子带隙也有一定的影响,随机度不同,对光子带隙的影响也不一样。本研究对一维光子晶体的设计与制备有一定的参考价值。     

Fabrication of PZT-polymer composite materials having 3-3 connectivity for hydrophone applications

Lanthanum-modified lead zirconate titanate (PZT) powder and volatilisable polymethylmethacrylate (PMM) polymer particles have been used for fabrication of porous sintered ceramics of interconnected porosity varying from 25% to 59%. Sintered ceramics are converted into piezoelectric PZT-polymer composites by incorporating silicone rubber elastomer followed by electroding and poling. Influence of the variation of PZT-PMM ratio and sintering temperatures on the open and closed porosity of the sintered ceramics as well as volume fraction PZT in the composites has been studied and correlated for the optimization of piezoelectric properties. The PZT-polymer composites possess low density, considerably high piezoelectric voltage coefficient and considerably lower ageing characteristics and are therefore considered suitable for designing highly sensitive hydrophone systems.     

An exact analysis of a rectangular plate piezoelectric generator

We study thickness-twist vibration of a finite, piezoelectric plate of polarized ceramics or 6-mm crystals driven by surface mechanical loads. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The plate is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy to electrical energy. Analytical expressions for the output voltage, current, power, efficiency, and power density are given. The basic behaviors of the generator are shown by numerical results.     

Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment

In the present study, finite element formulation based on higher order shear deformation plate theory is developed to analyze nonlinear natural frequencies, time and frequency responses of functionally graded plate with surface-bonded piezoelectric layers under thermal, electrical and mechanical loads. The von Karman nonlinear strain–displacement relationship is used to account for the large deflection of the plate. The material properties of functionally graded material (FGM) are assumed temperature-dependent. The temperature field has uniform distribution over the plate surface and varies in the thickness direction. The considered electric field only has non-zero-valued component E_z. Numerical results are presented to study effects of FGM volume fraction exponent, applied voltage in piezoelectric layers, thermal load and vibration amplitude on nonlinear natural frequencies and time response of FGM plate with integrated piezoelectric layers. In addition, nonlinear frequency response diagrams of the plate are presented and effects of different parameters such as FGM volume fraction exponent, temperature gradient, and piezoelectric voltage are investigated.     

Measurement of Structural Changes in Tetragonal PZT Ceramics under Static and Cyclic Electric Fields Using a Laboratory X-ray Diffractometer

In situ structural characterization techniques that are capable of characterizing piezoelectric ceramics under different electrical loading conditions are important to understand the behavior of materials during their use. In this work, we report the use of a laboratory X-ray diffractometer for the measurement of various structural changes in tetragonal La-doped lead zirconate titanate (PZT) ceramics under the application of static and cyclic electric fields. The changes in the volume fractions of the 90° domains parallel to the electric field direction are calculated from the intensities of the {002} diffraction peaks. In addition, the components of lattice strains are monitored from the changes in the (111) crystallographic planes. It is observed that, under the application of static electric fields, both 90° domain switching and the 111 lattice strains showed similarity with the macroscopic strainelectric field hystersis loop. To measure the structural changes under cyclic electric fields, a time-resolved X-ray diffraction technique was used. Under application of a square-wave electric field of amplitude ±650 V/mm and frequency 0.3 Hz, a change of ~5% in the volume fraction of the 90° domains and ~0.07% strain of the 111 lattice planes are observed. Both the amount of 90° domain switching and the 111 lattice strains are observed to increase with an increase in the amplitude of the cyclic electric field. The implications of the measured structural changes for the macroscopic piezoelectric properties of ceramics are discussed.     

Buckling analysis of a porous circular plate with piezoelectric sensor–actuator layers under uniform radial compression

This study presents the buckling analysis of a solid circular plate made of porous material bounded with piezoelectric sensor–actuator patches. The porous material properties vary through the thickness direction of the plate following a given function. The general mechanical nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The buckling load is derived for solid circular plates under uniform radial compressive loading for the clamped edge condition. The effects of piezoelectric layers on the buckling load of the plate, piezoelectric layer-to-porous plate thickness ratio, feedback gain, and variation of porosity are investigated. The results are verified with the known results in the literature.     

决定二维声子晶体带隙的关键材料参数

从弹性波动方程入手,获得决定二维声子晶体z模态带隙的关键材料参数是散射体对基体的质量密度比和剪切模量比.利用平面波展开法计算带隙结构,研究正方点阵、三角点阵以及不同填充率时材料参数对带隙的影响.发现质量密度比对带隙起决定作用.仅以声阻抗比或波速比的大小不能决定带隙的存在和大小.给出不同点阵形式下产生带隙的材料参数取值范围.给出材料参数-带隙图,对以材料参数设计带隙具有直观的指导作用.     

Thermo-Electro-Mechanical Buckling of Shear Deformable Hybrid Circular Functionally Graded Material Plates

Buckling analysis of perfect circular functionally graded plates with surface-bounded piezoelectric layers based on the first-order shear deformation theory is presented in this article. The material properties of the functionally graded (FG) layer are assumed to vary continuously through the plate thickness by distribution of power law of the volume fraction of the constituents. The plate is assumed to be under constant electrical field and two types of thermal loadings, namely, the uniform temperature rise and nonlinear temperature gradient through the thickness. Also, the stability of a plate under radial mechanical compressive force is examined. The equilibrium and stability equations are derived based on the first-order shear deformation plate theory using a variational approach. The boundary condition of the plate as an immovable type of the clamped edge is considered. Resulting equations are employed to obtain the closed-form solution for the critical buckling temperature for each loading case. The effects of electric field, piezo-to-host thickness ratio, and power law index of functionally graded plates subjected to thermo-mechanical-electrical loads are investigated. The results are compared with the classical plate theory and verified with the available data in the open literature.     

State vector approach of free-vibration analysis of magneto–electro-elastic hybrid laminated plates

In this paper, state variable formulation for free vibration of the laminated structures bonded and embedded actuators and sensors (piezoelectric and/or piezomagnetic) is established. The present mixed type formulation has the great advantage that the size of the system to be solved is independent of the number of layers and is of order three for free vibration of the laminate with bonded and embedded piezoelectric and/or piezomagnetic layers. Analytical solutions of 3D free vibration of simply supported piezoelectric and piezomagnetic composite plates have been presented. The transfer matrices for either closed circuit or open circuit piezoelectric and piezomagnetic layers are derived. The special case of elastic layer is also treated. The assembly procedure is described for the different electric and magnetic surface conditions. Numerical examples are analyzed to study the vibration characteristics of smart laminate plates with different stacking sequence and different span to thickness ratio.     

三角晶格固/气型声子晶体的弹性波带隙结构

将椭圆钢柱散射体引入到三角晶格固/气型声子晶体中,用平面渡法计算了其带隙结构.研究表明,通过降低散射体横截面的对称度,可在几乎不改变带隙中心频率的条件下获得更宽的低频带隙,还能在极低的填充率下实现低频带隙.随着填充率的增大,带隙变宽,中心频率下降.当散射体绕其中心轴的旋转角度小于60°时,带隙宽度随旋转角度的增大而减小,但带隙中心频率基本不受影响.     

Theoretical analysis of a ceramic plate thickness-shear mode piezoelectric transformer

We perform a theoretical analysis on a ceramic plate piezoelectric transformer operating with thickness-shear modes. Mindlin's first-order theory of piezoelectric plates is employed, and a forced vibration solution is obtained. Transforming ratio, resonant frequencies, and vibration mode shapes are calculated, and the effects of plate thickness and electrode dimension are examined.     

Polarization-electric field relations of ferroelectric/antiferroelectric layered ceramics in Pb(Nb, Zr, Sn, Ti)O3 system

Ferroelectric/antiferroelectric bi-layer ceramics with different ferroelectric and antiferroelectric phase thickness ratio (FE/AFE thickness ratio) in Pb(Nb, Zr, Sn, Ti)O₃ system were prepared and characterized. With increasing the maximum external electric field from 0 to 40 kV/cm, polarization-electric field relation was always ferroelectric-like or underwent an antiferroelectric-ferroelectric transition, depending on the FE/AFE thickness ratio. All layered ceramics showed ferroelectric-like hysteresis loops with maximum external electric field of 40 kV/cm, and much higher remanent polarizations were attained than those of the ferroelectric/antiferroelectric heterostructures reported previously.     

折板型网壳的优化分析

 研究了折板型网壳的矢跨比、周边矢高和中心矢高的比值对网壳用钢量的影响，并以网壳用钢量为目标函数，网格数和网壳厚度为设计变量，采用穷举法和0．618法，对20-40m跨度的四角点支承的正方形平面两向正交正放折板型网壳进行了优化分析，给出了不同跨度和不同矢跨比时的最优网格数和最优网壳厚度．研究结果对折板型网壳的设计有一定的参考作用．     

(Bi0.5Na0.5)TiO3(BNT)基无铅压电陶瓷研究进展

(Bi0.5Na0.5)TiO3(BNT)基无铅压电陶瓷体系是目前研究最广泛的功能陶瓷材料之一.综述了BNT基无铅压电陶瓷的研究现状,讨论了相关体系的设计方法、铁电性、压电性以及BNT体系的制备方法.分析比较了BNT系压电陶瓷与Pb(Zr,Ti)O3(PZT)压电陶瓷的性能差异以及存在的问题,对BNT基无铅压电陶瓷进行了展望.