AN EXACT ANALYSIS OF FORCED THICKNESS-TWIST VIBRATIONS OF MULTI-LAYERED PIEZOELECTRIC PLATES

This paper deals with the thickness-twist vibration of a multi-layered rectangular piezoelectric plate of crystals of 6 mm symmetry or polarized ceramics.An exact solution is obtained from the three-dimensional equations of linear piezoelectricity.The solution is useful to the understanding and design of composite piezoelectric devices.A piezoelectric resonator,a piezoelectric transformer,and a piezoelectric generator are analyzed as examples.     

Influence of Energy Losses on the Performance of a Piezoelectric Transformer Plate

The influence of dielectric, mechanical, and piezoelectric energy losses on the electroelastic characteristics of a piezoelectric transformer plate is analyzed. It is shown that only mechanical loss occurs at resonance frequencies     

基于反激变压器的压电振动能量双向操控技术

压电材料因其具有良好的机电耦合特性, 在振动能量俘获和结构振动控制领域有着良好的应用前景. 基于同步开关和电感的压电元件接口控制电路, 可以通过振荡电路工作原理调节压电元件的电压幅值和相位, 优化压电振动系统的机电能量转化. 优化型同步电荷提取技术即基于上述接口控制电路实现了压电振动能到电能的高效转换. 本文提出了一种衍生于优化型同步电荷提取电路的压电阻尼半主动控制电路, 借鉴反激变压器的原、副边能量转换特性, 实现了压电振动控制系统从电能到机械能的能量操控, 进而达到结构振动抑制的效果. 至此, 结合了压电电荷能提取与压电阻尼半主动控制技术的新电路, 以反激变压器为核心实现了压电振动能量的双向操纵. 论文首先介绍了相应的控制电路及工作原理, 推导了新型同步开关阻尼技术下的结构的振动阻尼比模型, 搭建了压电悬臂梁振动控制实验平台, 最终通过实验验证了理论模型, 并使用更简单的控制方法解决了振动控制系统的稳定性问题.      

Electroelastic Characteristics of a Piezoelectric Transformer Plate

The expressions for the electrostatic induction and input admittance of a piezoelectric transformer plate are generalized     

NONLINEAR ANALYSIS OF A 5-LAYER BEAM-LIKE PIEZOELECTRIC TRANSFORMER NEAR RESONANCE

The paper examines the weakly nonlinear behavior of a 5-layer beam-like piezo- electric transformer operating near resonance, where the main structure of the device consists of properly poled and electroded flexible piezoceramic four-layers separated by a central metallic layer. Nonlinear effects of the large deflection to induce the incidental implane extension near res- onance are considered, which is shown that on one side of the resonant frequency the output-input relation becomes nonlinear, and the other side output voltage experiences jumps.     

The Stress State of a Rectangular Piezoceramic Plate with Transverse–Longitudinal Polarization

Longitudinal mechanical stresses in the exciting and generating sections of a planar piezoelectric transverse–longitudinal transformer are analyzed. It is shown that the longitudinal stresses in both sections are axisymmetric about the boundary line. The results obtained in experimental studies of the stress state in the exciting section by using piezotransformer transducers are presented     

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.     

带附加质量块的压电圆板能量采集器振动分析

基于圆板的压电能量采集技术在取代化学电池为低功耗电子器件提供能源方面具有巨大的潜能. 本文通过理论建模和数值仿真研究了考虑附加质量接触面积的压电圆板能量采集器的采集性能. 首先, 基于基尔霍夫薄板理论, 用广义哈密顿原理推导了带附加质量块的压电圆板能量采集器的机电耦合方程, 并用伽辽金法对方程近似离散, 通过离散方程得到电压、功率输出和最优负载阻抗的闭合解. 用有限元仿真对所提出的理论模型进行了验证, 结果表明该理论模型可以成功地预测压电圆板能量采集器输出电压和功率. 最后, 基于闭合解探讨了负载阻抗、附加质量块、压电圆板的内外半径等相关参数对压电圆板能量采集器固有频率、输出电压和功率的影响. 结果表明, 当质量块与复合板的接触半径足够小(本文中接触半径小于板半径的1/14)时, 质量块与复合圆板的接触面积可以忽略; 相较于无孔的压电片, 内径位于2.5 ~ 4 mm范围内的压电片可以提高能量采集器的采集性能; 附加质量、压电片外径和负载阻抗的合理选择既可以降低压电圆板的固有频率, 还可以提高其采集性能.      

压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

A Circular Indenter on a Piezoelectric Layer

This paper investigates a piezoelectric layer with a rigid indenter on its surface. Exact solution is given for a piezoelectric medium whose thickness is considerably larger than the diameter of the indenter. Different electrical boundary conditions that employ conducting or insulating indenters are presented. Effect of the permittivity of air (which surrounds the piezoelectric medium) is considered and is found to be negligible. Expressions for the singular mechanical and electric fields near the indenter front are established. Those expressions are useful for investigating the possible failure behavior of piezoelectric material near the indenter front. In addition, a numerical solution technique for an indentured piezoelectric layer of finite thickness is also given.     

A semi-analytical solution for static and dynamic analysis of plates with piezoelectric patches

A modified mixed variational principle for piezoelectric materials is established and the state-vector equation of piezoelectric plates is deduced directly from the principle. Then the exact solution of the state-vector equation is simply given, and based on the semi-analytical solution of the state-vector equation, a realistic mathematical model is proposed for static analysis of a hybrid laminate and dynamic analysis of a clamped aluminum plate with piezoelectric patches. Both the plate and patches are considered as two three-dimensional piezoelectric bodies, but the same linear quadrilateral element is used to discretize the plate and patches. This method accounts for the compatibility of generalized displacements and generalized stresses on the interface between the plate and patches, and the transverse shear deformation and the rotary inertia of the plate and patches are also considered in the global algebraic equation system. Meanwhile, there is no restriction on the thickness of plate and patches. The model can be also modified to achieve a semi-analytical solution for the transient responses to dynamic loadings and the vibration control of laminated plate with piezoelectric patches or piezoelectric stiffeners.     

DAP增强梁结构形状控制的机理研究

对称粘贴在梁结构上下表面上的压电元件在外部电场的作用下能使梁结构发生弯曲变形，通过分析驱动构件与结构中的应变分布，采用定向固定的压电元件(DAP，即directional attached piezoelectric)来代替传统的压电元件(CAP，即conventional attached piezoelectric)，减小了驱动构件的横向效应，提高了压电驱动的效率，并进行了实验对比验证。     

弱界面压电／压磁层状结构中的SH波

研究了弱界面压电层/压磁半空间结构中SH波的频散特性, 界面性能由 ``弹簧'模型表征, 压电层的表面考虑电学短路和电学开路两种边界条件. 推导了显函形式的 频散方程, 并结合算例分析了界面性能和电学边界条件对SH波传播特性的影响. 数值结果表 明: 弱界面降低了SH波传播的相速度; 对于短路电边界条件, 弱界面可以使一阶模态的相速 度小于B-G表面波的速度; 对于开路电边界条件, 一阶模态的相速度总是大于剪切体波的波 速.     

基于碰撞升频的MEMS压电振动能量采集系统

本文提出了一种基于碰撞升频机制的微型压电能量采集系统，由一对共振频率不同的悬臂梁平行叠放组成。在外界低频振动激励下，底部低频S形金属曲梁产生共振，在运动过程中碰撞顶部高频微型压电直梁，从而将低频环境振动转换为高频压电梁的振动，解决了压电直梁的固有频率与外界激励频率不匹配问题，同时提高能量收集的效率。本文建立了悬臂梁受迫振动和碰撞耦合振动的动力学模型，讨论了压电悬臂梁的电压输出特性。通过实验测试了压电能量收集系统和单个压电悬臂梁的开路电压并计算了输出功率，结果表明当振动加速度为1.0 g时，升频式压电能量采集系统在25 Hz的激振下输出功率达到8.6 μW，高于单个压电悬臂梁的最大输出功率。     

具有表面效应的压电半空间中的表面波

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.     

A theoretical model for electroelastic analysis in piezoelectric fibre push-out test

A theoretical model is presented to study the elastic deformation process and frictional sliding behavior in single piezoelectric fibre push-out tests. Based on the theoretical model and some necessary simplifications, stress and electric fields are obtained for push-out tests of a circular piezoelectric fibre embedded in an elastic matrix. Numerical results of a piezoelectric fibre/expoxy matrix system are presented to verify the proposed formulation. The study shows that there is a significant effect of the piezoelectric parameter and embedded fibre length on stress transfer, electric field distribution and load-displacement curve of the frictional sliding process. This study also indicates that the piezoelectric effect has a distinct influence on the mechanical behavior and properties of the interface in a fibre/matrix system.     

A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.     

A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator

This paper investigates the electro-mechanical behaviour of a thick, laminated actuator with piezoelectric and isotropic lamina under externally applied electric loading using a new two-dimensional computational model. The elastic core is relatively thick and thus it is modelled by Timoshenko thick-beam theory. Although the piezoelectric lamina is a beam-like layer, it is formulated via a two-dimensional model because of not only the strong electro-mechanical coupling, but also of the presence of a two-dimensional electric field. It is shown in this paper that a one-dimensional model for the piezoelectric beam-like layer is inadequate. The piezoelectric model is constructed within the scope of linear piezoelectricity. The actuation response is induced through the application of external electric voltage. Under the strong coupling of elasticity and electricity, the strain energy and work of electric potential are presented. The electro-mechanical response of the laminated Timoshenko beam is formulated and determined via a variational energy principle. Numerical examples presented illustrate convincing comparison with finite element solutions and existing published data. New numerical solutions are also presented to investigate the geometric effect on the electro-mechanical bending behaviour.     

SH波在压电材料条中垂直界面裂纹处的散射

研究了SH波在压电材料条中裂纹处的散射.压电材料条两侧涂有相同梯度参数的两个半无限大功能梯度材料,裂纹垂直于界面.通过Fourier变换,利用边界条件把问题转化为柯西核奇异积分方程,然后利用Chebyshev多项式对奇异积分方程进行数值求解.通过数值计算,分析讨论了压电条的几何参数和SH波频率对标准动应力强度因子的影响.     

A close-form solution to simply supported piezoelectric beams under uniform exterior pressure

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