电压激励下四边简支压电层合板的振动分析

以压电陶瓷-金属-压电陶瓷对称层合板为研究对象,依据小挠度弯曲理论,根据Hamilton原理和Rayleigh-Ritz法推导出了电压激励下压电层合薄板的振动方程。以四边简支的压电层合薄板为算例,用ANSYS软件建立有限元模型并对其进行模态分析、瞬态动力学分析,仿真结果与理论值基本相符,验证了本文理论的正确性;通过改变电压幅值的大小分析其对中心节点位移响应幅值以及x,y方向应力幅值的影响。通过改变阻尼大小分析其对薄板横向位移的影响。数值模拟了薄板中心处节点x,y方向应力随时间的变化规律,并分析了薄板最大应力出现位置及随时间的变化规律,所得结论可为压电振子的设计和分析提供一定的理论参考。     

平行四边形加肋板自由振动分析的无网格法

基于一阶剪切理论,提出一种求解平行四边形加肋板自由振动问题的无网格法,通过用一系列点来离散平板及肋条,得到加肋板的无网格模型。基于一阶剪切理论及移动最小二乘近似求出位移场,以梁模拟肋条,求出平行四边形加肋板总动能及总势能。再由Hamilton原理导出加肋板自由振动的控制方程,采用完全转换法引入边界条件,求解方程得出结构自振频率。以不同参数的加肋板为例,将该文解与ABAQUS有限元解进行比较分析。研究表明,该方法能有效地分析平行四边形加肋板自由振动问题,在肋条位置改变时,又避免了网格重构。     

含分层的压电材料层合板的自由振动分析

该文为含分层的压电材料层合板的自由振动分析提出了一种状态空间方法。首先通过压电材料的修正H-R (Hellinger-Reissner)变分原理和径向基函数推导了无网格状态空间列式。然后结合非线性弹簧层模型,导出了含分层压电材料层合板的三维模型。该模型的主要优点是:场节点数和背景网格数不随层合板的层数增加而增加;另一方面,通过设定弹簧的刚度值,非线性弹簧层既能保证非分层区域横向应力和位移的连续性,也能防止分层区域嵌入现象的发生。     

压电体的混合变分原理及叠层板的自由振动分析

建立了具有机一电耦合效应的压电材料修正后的Hellinger—Reissner(H—R)混合变分原理，并推导了压电材料的Hamilton正则方程，即压电材料自由振动的控制微分方程；根据矩阵分析理论给出了带有压电材料层的叠层矩形板自由振动的精确求解方法，文中没有引入任何位移模式或应力模式假设，实例分析得到了压电混合叠层板正逆效应两种情况自由振动的低阶频率，并与已有文献结果进行了比较。本文提出的压电材料修正后的H—R混合变分原理将有利于压电材料动力问题的有限元法或半解析法的推导。     

对称层合折板结构自由振动分析的移动最小二乘无网格法

提出了一种求解对称层合折板结构自由振动问题的移动最小二乘无网格法。以作者提出的折板无网格模型为基础,将对称层合折板结构视为由不同平面上对称层合板组成的复合结构。先基于一阶剪切变形理论,由移动最小二乘近似推导出各对称层合板的刚度和质量矩阵,再利用板与板间的位移协调条件,将各板的刚度和质量矩阵叠加得到整个结构的刚度和质量矩阵,推导出描述层合折板结构自由振动行为的控制方程。文末算例表明由本文方法得到的解与采用壳单元得到的ANSYS有限元解吻合良好,证明了本文方法的准确性。     

加层压电层硬币型裂纹断裂分析

研究粘接着弹性层的压电层内硬币型裂纹的断裂问题。压电层与弹性层均为横观各向同性材料,r轴方向无限长,z轴方向有限厚度。压电层沿z轴方向极化。考虑电不导通裂纹表面条件,利用Hankel积分变换将问题化为求解积分方程组,导出了场强度因子与能量释放率的表达式。给出了数值计算结果,并分析了弹性层厚度对场强度因子与能量释放率的影响。     

电压激励的压电层合悬臂梁横向振动分析

以压电陶瓷-金属-压电陶瓷对称层合结构为研究对象,基于能量法得到了等截面压电层合对称悬臂梁在横向激振电压下的强迫振动微分方程。用ANSYS软件对建立的相关有限元模型进行模态分析、谐响应分析及瞬态动力学分析,仿真结果与理论值基本吻合,验证了理论的正确性。进一步分析了阻尼对横向位移响应的影响,讨论了速度、加速度随时间的变化规律,分析了压电悬臂梁的最大应力出现位置及最大应力值随时间的关系。所得结论可为压电振子的设计和分析提供必要理论参考。     

转轴横向裂纹的振动分析诊断

从金属材料疲劳过程的特征出发，对具有横向裂纹转轴的运动情况进行了分析，研究了具有横向裂纹转轴在断裂过程中的振动频谱分布情况及其变化规律，给转轴横向裂纹的诊断提供了进一步的信息。     

无网格法模拟复合型疲劳裂纹的扩展

本文提出了用无网格Galerkin法模拟构件在复合变形作用下疲劳裂纹扩展路径并预估其疲劳寿命的方法。该法能够自然模拟疲劳裂纹的扩展,不需要网格重构,避免了裂纹扩展过程中的精度受损。应用无网格数值结果计算了J积分和应力强度因子K_I和K_Ⅱ;按照最大周向应力理论获得了裂纹扩展偏斜角。基于最小应变能密度因子理论,确定了裂纹扩展量Δa,并能获得疲劳载荷的循环周数ΔN。文末对数值模拟结果和实验拟合结果进行了对照。     

自感知压电层合梁的数值分析与数值模拟

从压电本构方程出发,借助Hamilton原理建立了压电层合结构的有限元方程,基于此理论,对一五层的压电梁运用ANSYS参数化设计语言(APDL)建模,采用二维四结点四边形耦合单元,分析了梁与压电层的几何参数对传感与致动性能的影响,比较了不同边界条件下梁的变形变化。得出的一些有效结论,对多层智能结构的设计具有一定的参考价值。     

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.     

On free vibration of a functionally graded piezoelectric rectangular plate

Summary On the basis of three-dimensional theory equations of transversely isotropic piezoelasticity, two independent state equations with variable coefficients are derived. To this end, separation formulae for displacements and shear stresses are employed. A laminated approximation is used to transform the state equations to the ones with constant coefficients in each layer. The free vibration problem of a piezoelectric rectangular plate with a functionally graded property is then investigated. Discussion on the boundary conditions is presented.     

Experimental analysis of vibration characteristics of an edge- cracked composite plate by ESPI method

In this paper, the amplitude fluctuation (AF) electronic speckle pattern interferometry (ESPI) method was adopted to investigate the vibration characteristics of a composite plate containing an edge crack. The change of the modal shapes was discussed. In addition, the stress intensity factors (SIFs) induced by the resonant vibration were evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Generalized plane problem of a cracked piezoelectric layer bonded to dissimilar layers

Summary In this paper, we proposed a model to study the electro-elastic crack problem for a cracked piezoelectic layer bonded to two elastic layers of finite thickness. The crack is assumed to be through thez-direction and the crack faces perpendicular to they-direction. Fourier transforms technique is used to reduce the problem to the solution of singular integral equations. The model is general enough to account for arbitrary electrical polarized direction and material anisotropy, for any mechanical or electrical mode of loading. Numerical results are plotted to illustrate the influence of the crack face electrical boundary condition on crack tip fields for different layer thickness.     

Line-spring boundary element method for a surface cracked plate

In the published line-spring boundary element method, the effect of bending is not considered. Therefore it cannot be used to deal with the problem of a surface cracked plate. Taking the advantage of the line-spring model and the boundary element method the authors present a new line-spring boundary element method in which the effect of membrane force and bending moment in a Reissner plate is taken into account. The implementation of the method is discussed in detail. The stress intensity factors for several example problems concerning surface cracked plates are calculated. Comparisons are made with the Newman-Raju solutions. The results show that the proposed method is efficient.     

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.     

基于Chebyshev-变分法的复杂开口形状矩形薄板弯曲振动特性分析

针对复杂开口形状的矩形薄板弯曲振动问题,提出一种基于Chebyshev-变分原理的建模方法,建立弹性边界条件下不同开口形状矩形薄板弯曲振动模型。采用边界约束因子模拟弹性边界条件,视开口部分为一种物理属性为零的特殊薄膜。将板的横向位移展开成双重Chebyshev多项式级数形式,建立薄板的拉格朗日泛函,利用变分法推导薄板的特征方程并求得固有频率及对应振型。开展开口薄板模态试验研究,对比理论计算结果与试验结果及有限元结果,验证该方法及模型的准确性和有效性。研究边界约束和开口形状对弯曲振动特性的影响。结果表明:开口形状对结构低阶固有频率影响较小,对高阶固有频率影响较大;开口形状的改变对结构奇数阶固有频率的影响大于对偶数阶固有频率的影响。     

Flexural vibration of a lithium niobate piezoelectric plate with a ferroelectric inversion layer

Abstract

Two-dimensional equations for flexural motions of a lithium niobate piezoelectric plate are derived from three-dimensional equations. The plate has a ferroelectric inversion layer where the piezoelectric constants reverse signs. The equations show an unconventional behavior that a uniform electric field along the plate thickness can produce bending. This offers many possibilities for new designs of devices. Waves in unbounded plates are examined for the accuracy of the equations. A piezoelectric energy harvester based on such a plate is analyzed as an example of the application of the equations derived in vibrations of finite plates.     

Finite element method for piezoelectric vibration

A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.     

On free vibration of piezoelectric nanospheres with surface effect

Surface effect responsible for some size-dependent characteristics can become distinctly important for piezoelectric nanomaterials with inherent large surface-to-volume ratio. In this paper, we investigate the surface effect on the free vibration behavior of a spherically isotropic piezoelectric nanosphere. Instead of directly using the well-known Huang-Yu surface piezoelectricity theory (HY theory), another general framework based on a thin shell layer model is proposed. A novel approach is developed to establish the surface piezoelectricity theory or the effective boundary conditions for piezoelectric nanospheres employing the state-space formalism. Three different sources of surface effect can be identified in the first-order surface piezoelectricity, i.e. the electroelastic effect, the inertia effect, and the thickness effect. It is found that the proposed theory becomes identical to the HY theory for a spherical material boundary if the transverse stress components are discarded and the electromechanical properties are properly defined. The nonaxisymmetric free vibration of a piezoelectric nanosphere with surface effect is then studied and an exact solution is obtained. In order to investigate the surface effect on the natural frequencies of piezoelectric nanospheres, numerical calculations are finally performed. Our numerical findings demonstrate that the surface effect, especially the thickness effect, may have a particularly significant influence on the free vibration of piezoelectric nanospheres. This work provides a more accurate prediction of the dynamic characteristics of piezoelectric nanospherical devices in nano-electro-mechanical systems.