具有弹性放大器的双稳态压电俘能器建模及参数影响分析

利用广义Hamilton变分原理,建立了具有弹性放大器的双稳态压电俘能系统BPH+EM的动力学方程。考虑谐波激励,采用调和平衡法获得了BPH+EM系统的位移、输出电压和功率的解析解。利用求得的解析解,讨论了BPH+EM系统扩大能量俘获的频率范围和提高能量俘获效率的机理,研究了弹性放大器的刚度质量比对BPH+EM系统的动力性能影响规律。当弹性放大器的刚度质量比趋于无限大时,具有弹性放大器的双稳态压电俘能系统退化为双稳态压电俘能系统BPH。弹性放大器的刚度质量比趋于0但不等于0时,BPH+EM的俘能效率低于BPH。结果表明,在合适的刚度质量比范围内,BPH+EM的俘能效率显著优于BPH。研究结果为BPH+EM系统的优化设计提供了理论指导。     

具有压电材料弹性环形板的屈曲

对在不同位置粘有任意多对压电片的弹性环形板在电压和径向压力作用下的轴对称屈曲进行了研究．根据压电效应的等效作用量，初参数法以及传递矩阵方法得到了环板屈曲的特征方程．对不同位置及不同宽度的压电片，计算了结构的屈曲载荷．并得到了稳定性边界曲线．     

压电堆在结构振动隔离中的应用

利用压电材料的逆压电效应,压电堆可用于振动激励,也可用于振动隔离。本文推导了了压电堆的有限元控制方程,采用数值方法研究了压电堆的隔振作用。作为算例,分析了支架采用压电堆振后的振动特性,为改善支架的动态特性提供了理论指导。     

梁板结构埋入压电片的深度和厚度优化研究

根据梁的弯曲变形理论，以及压电材料的压电效应，对压电复合材料梁结构的应变和应力状态进行了分析。推导了压电材料埋入梁结构时其埋入深度和压电材料本身厚度的优化目标函数。根据优化目标函数，绘制出了在给定的基体材料和压电材料弹性模量比之下，压电材料的驱动力矩随埋入深度和压电材料厚度变化的三维曲面和等高线图，直观地表示出了埋入型压电材料智能结构获得最佳驱动力矩的配置方案。同时也分析了结构和压电材料两者的弹性模量之比对其结果的影响。结果表明，压电材料对于结构的作动力矩与其埋入基体材料的深度、本身厚度以及基体材料和压电材料的弹性模量之比都有着密切的联系。同时将结果也推广到了压电板结构，此时压电材料和基体材料的泊松比时其结果也有一定的影响。     

Theoretical transient analysis and wave propagation of piezoelectric bi-materials

The transient response of piezoelectric bi-materials subjected to a dynamic anti-plane concentrated force or electric charge with perfectly bonded interface is examined in the present study. The problem is solved by using the Laplace transform method and the inverse Laplace transform is evaluated by means of Cagniard’s method. Exact transient full-field solutions of the contribution for each wave are expressed in explicit closed forms. The transient behavior of field quantities is examined in detail by numerical calculations. The existence condition of a propagating surface wave along the interface is discussed in detail. A surface wave can be guided by the interface of two semi-infinite materials in contact if one, at least, of these two materials is piezoelectric. The propagation velocity of the surface wave is explicitly expressed and is found to be less than the lower shear wave velocity of the two materials. The existence of the surface wave for piezoelectric–piezoelectric bi-materials is restricted to the situation that the shear waves of the two piezoelectric materials are very close. The possibility for the existence of the surface wave for piezoelectric–elastic bi-materials is much greater than that of the piezoelectric–piezoelectric bi-materials.     

面内压电振动能量采集动力学设计与性能研究

压电振动能量采集将环境中普遍存在的机械能转换为电能,可以实现自供能传感、控制与驱动,具备灵活、节能环保、可持续的优势,具有广阔的应用前景。为了促进压电振动能量采集器件的集成与融合,提出面内压电振动能量采集,将压电振动能量采集器进行扁平化设计,使其在二维平面内采集振动能量,在保证较大功率输出下能够显著减小器件所需三维空间。为了提高输出功率与工作频宽,设计了具有双稳态与力放大机制的面内压电振动能量采集器。考虑弯张小变形,通过能量法建立了面内压电振动能量采集器的机电耦合动力学模型。分析了关键设计参数对面内压电振动能量采集器性能的影响。数值仿真了面内压电振动能量采集器在简谐激励下的俘能性能,结果表明,通过合理的设计,面内压电振动能量采集器可以低频、宽频弱激励下有效俘获能量。面内压电振动能量采集设计方法有利于推动便携式、可穿戴式自供能等方面的应用和产业化。     

Exact solution of orthotropic cylindrical shell with piezoelectric layers under cylindrical bending

An exact elasticity solution for an orthotropic cylindrical shell with piezoelectric layers is obtained in this paper. The stress and displacement distributions are presented. The influence of the piezoelectric layers on the mechanical behavior of structures is studied. Both the direct piezoelectric effect and the converse piezoelectrical effect of the piezoelectric material are investigated. Results presented in this paper can be used to study various approximate shell theories used in the numerical simulations of piezoelectric structures.     

Dynamic focusing effect of piezoelectric fibers subjected to thermal shock

Based on finite Hankle transforms, this paper presents a theoretical method for analyzing the dynamic focusing effect of piezoelectric fibers subjected to the thermal shock of a transitory temperature change produced by a sudden electric current pulse. From analytical expressions and example calculations for two kinds of piezoelectric fibers, PZT-4 and BaTiO₃, it is found that the dynamic focusing effect is dependent on the material property of the piezoelectric fibers so that the maximum dynamic stress amplitude of the two kinds of piezoelectric fiber occur at different radial points. The mechanism of the dynamic focusing effect in piezoelectric fibers is relevant to the evaluation of the dynamic strength and electric signal of the piezoelectric fiber. The results carried out may be used as a reference to solve other transient coupled electrothermoelasticity problems in piezoelectric structures.     

有限长压电层合简支板自由振动的三维精确解

基于三维弹性理论和压电理论，导出了有限长矩形压电层合简支板的动力学方程及相应的边界条件，给出了一种求解压电层合板自由振动三维精确解的方法；分析了正、逆向压电效应对层合板振动频率的影响．本文所述的方法和结果对于求解其他三维动态问题，验证、比较其他简化模型、有限元计算结果以及工程应用都有指导意义．     

基于压电振动能量俘获的弯曲结构损伤监测研究

建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的.      

压电智能环形板的主动控制

对在不同位置粘有任意多组压电传感器和压电执行器的轴对称弹性环形薄板的振动控制进行了研究．根据压电执行元件的等效作用量得到了压电智能环板的振动控制方程和传感方程,再利用分离变量法以及由传感器测得的电量和作用在执行器上电压之间的控制模式得到振动方程的全解．实行了对整体结构的主动控制．对不同的压电片布置进行了数值计算．结果表明：当离散分布压电元件布置越密,振动衰减的效果越佳     

压电结构的热弹性比拟建模方法

通过比较逆压电效应本构方程和热弹性本构方程,在线性范围内建立逆压电效应和热弹性效应的比拟关系:将驱动电压比拟为温度载荷,压电应变系数比拟为热膨胀系数,用热弹性有限元方法分析逆压电效应,并采用热弹性比拟方法求解基于长度伸缩逆压电效应和厚度剪切逆压电效应的驱动器问题,给出了平面结构“热-机-电”耦合问题的热弹性比拟求解方法。热弹性比拟方法为快速建立复杂压电结构的有限元模型提供了一种有效的途径,可缩短复杂压电主动结构的设计周期,降低设计成本。最后给出数值算例说明文中方法的有效性。     

Interfacial fracture analysis of a graded piezoelectric layer on a substrate with finite dimension

In fracture analysis of piezoelectric devices, the structural dimension is often assumed to be infinite at least in one direction. However, all practical piezoelectric structures are finite and their dimensions in different directions are often comparable and cannot be simplified as infinite. The assumption of infinite dimension may lead to inexact theoretical results. The present work aims at studying the interfacial fracture behavior of a functionally graded piezoelectric layer on a dielectric substrate with finite dimension. The crack problem is solved by the methods of Fourier series and Cauchy singular integral equation. Parametric studies on the stress intensity factor (SIF) reveal the following: (a) when a crack tip is near to an interface end, its SIF is mainly governed by the end effect; (b) when a crack is far from the interface ends and the piezoelectric layer is thin, its SIF is principally affected by the thickness of the piezoelectric layer, and (c) only when a crack is far from the interface ends and meanwhile the piezoelectric layer is thick will its SIF be dominated by the non-homogeneity parameter, and in this case, the SIF increases with the increasing non-homogeneity parameter.     

压电/纤维复合材料耦合旋转驱动器力学设计模型

本文在经典层合板理论和三维压电材料本构方程的基础上,依据压电材料与纤维复合材料之间的相互作用、位移连续条件,建立了压电—纤维复合材料旋转耦合驱动器力学模型,并推导出电耦合方程。计算和初步实验说明,这种新型结构的压电伸缩变形—离轴纤维复合层扭转变形耦合旋转驱动器比同类型驱动器能量密度高、转矩大,且这种旋转电机结构简单紧凑、工作稳定、寿命长、预计随着研究的进一步深入,可望成为一种新型的微致驱动器而广泛应用于微型机械、精密测量和自动控制等领域。     

压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状,着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法;（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发,不引进任何变形假设,因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。     

压电功能梯度板自由振动的三维解

基于三维弹性理论和压电理论，导出了有限长矩形压电功率梯度板的动力学方程及相应的边界条件，并用幂级数展开法进行了求解，得到了压电功能梯度板自由振动的三维精确解公式，求解了自由振动的固有频率，并分析了压电系数的梯度变化对不同电学边界条件下压电板的自由振动频率的影响，结果可用于校核不同的近似理论及理解压电结构的动态行为。     

On the screw dislocation in a functionally graded piezoelectric plane and half-plane

In this paper closed-form expressions of the electroelastic field induced by a piezoelectric screw dislocation in a functionally graded piezoelectric plane and half-plane are derived. The material properties are assumed to vary exponentially along the x and y-directions. The solution for a screw dislocation in a functionally graded piezoelectric plane is obtained through introduction of two generalized stress functions. The solution for a screw dislocation in a functionally graded piezoelectric half-plane is derived by using the method of image. It is also found that the interaction between a piezoelectric screw dislocation and a circular insulating hole in the functionally graded piezoelectric material can be solved by using series expansion method.     

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.     

Analysis of a crack in a half-plane piezoelectric solid with traction-induction free boundary

In this paper, the problem of a crack embedded in a half-plane piezoelectric solid with traction-induction free boundary is analyzed. A system of singular integral equations is formulated for the materials with general anisotropic piezoelectric properties and for the crack with arbitrary orientation. The kernel functions developed are in complex form for general anisotropic piezoelectric materials and are then specialized to the case of transversely isotropic piezoelectric materials which are in real form. The obtained coupled mechanical and electric real kernel functions may be reduced to those kernel functions for purely elastic problems when the electric effects disappear. The system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors for transversely isotropic piezoelectric materials.     

Domain switching effect on fracture of piezoelectric solids

Rational design of smart sensors and actuators that consist of piezoelectric solids requires a thorough understanding of the constitutive behavior of this material under mechanical and electrical loading. Domain switching is the cause of significant nonlinearity in the constitutive behavior of piezoelectric solids, which may be enhanced in the presence of cracks. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The corresponding finite element equations are derived and applied in the solution of the piezoelectric center crack problems. The effects of domain switching are evaluated on the near tip stress intensity factors.