A two-dimensional theory for piezoelectric layers used in electro-mechanical transducers—I : Derivation

An Nth order two-dimensional theory is derived for strongly coupled piezoelectric layers that is suitable for use in analyzing electro-mechanical transducer response in circumstances where the field variations over the transducer face are important. Specific formulae are given for the widely used ceramic PZT-5.The first few branches of the dispersion curves for PZT-5 are obtained numerically for both the three-dimensional theory and the approximate two-dimensional theory. The correspondence of these curves at long wavelengths is used to determine a single correction factor. The face boundary conditions accommodate unknown traction and voltage so that the theory can be used in transducer applications.     

A two-dimensional model for linear elastic thick shells

In this paper, a two-dimensional model for linear elastic thick shells is deduced from the three-dimensional problem of a shell thickness 2ε, ε > 0. From different scalings on the tangent and normal components of the displacement u^ε as widely used in recent works, the limit displacement appears to be Kirchhoff–Love displacement of a different type. It contains additional terms to those found in the Reissner–Mindlin model and satisfies more general equations containing the classical terms found in the literature and some new terms related to the third fundamental form. Such terms could not be well handled in the usual framework. Shear stresses across the thickness are also computed. This model appears to be appropriate to handle stiffened shells which, in fact, cannot be considered uniformly as shallow shells. As a by-product it also lays the mathematical background to justify the Reissner–Mindlin model for plates and will probably contribute to a better understanding of the locking phenomenon encountered in computational mechanics.     

Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact

The dynamic response of a cracked piezoelectric ceramic under in-plane electric and anti-plane mechanical impact is investigated by the integral transform method. The electric and mechanical loads are assumed to be arbitrary functions of time. It is shown that the dynamic crack-tip stress and electric displacement fields still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. On the other hand, the dynamic response of the electric field is determined solely by the applied electric field. The electric field will promote or retard the propagation of the crack depending on the time elapsed since the application of the external electro-mechanical loads.     

Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact

By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation of the crack depending on the time elapse since the application of the external electro-mechanical loads. The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China     

Fracture of thick laminated composites

The fracture of thick laminated graphite/epoxy composites has been the subject of an extensive research program. The program was divided into three major areas of investigation which included laminate thickness, laminate stacking sequence, and part-through surface flaws. The results from this program are reviewed with emphasis placed on their applicability to the design of thick laminated composite structures. Paper was presented at 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas on June 9–14, 1985.     

Novel shear deformation model for moderately thick and deep laminated composite conoidal shell

This article presents a novel mathematical model for moderately thick and deep laminated composite conoidal shell. The zero transverse shear stress at top and bottom of conoidal shell conditions is applied. Novelty in the present formulation is the inclusion of curvature effect in displacement field and cross curvature effect in strain field. This present model is suitable for deep and moderately thick conoidal shell. The peculiarity in the conoidal shell is that due to its complex geometry, its peak value of transverse deflection is not at its center like other shells. The C¹ continuity requirement associated with the present model has been suitably circumvented. A nine-node curved quadratic isoparametric element with seven nodal unknowns per node is used in finite element formulation of the proposed mathematical model. The present model results are compared with experimental, elasticity, and numerical results available in the literature. This is the first effort to solve the problem of moderately thick and deep laminated composite conoidal shell using parabolic transverse shear strain deformation across the thickness of conoidal shell. Many new numerical problems are solved for the static study of moderately thick and deep laminated composite conoidal shell considering 10 different practical boundary conditions, four types of loadings, six different hl/hh (minimum rise/maximum rise) ratios, and four different laminations.     

非线性压电效应下压电弯曲执行器的弯曲

研究压电弯曲执行器在强电场作用下的非线性弯曲行为。考虑电致伸缩和电致弹性的非线性压电效应,导出了压电悬臂执行器自由端挠度或激励力和作用电场之间的非线性关系。结果表明,考虑非线性压电效应在很大的电场范围内都与实验结果吻合得很好,而线性压电效应只适合于低电场的情况。     

Nonlinear dynamic response and fatigue damage evolution for piezoelectric laminated plates with matrix cracks

Based on the Talreja’s damage model with tensor valued internal state variables, considering the effects of piezoelectricity, geometrical nonlinearity and the constitutive relations of the composite uni-ply plate with matrix cracks, the nonlinear dynamic equations of piezoelectric laminated plates with damage are established and the problems are solved by using the finite difference method. In numerical calculating examples, the nonlinear dynamics responses and the fatigue damage evolution curves of the plates are obtained, and the effects of piezoelectric materials, damage and external load on the nonlinear dynamic response and fatigue damage evolution of the plates are discussed.     

基于高阶位移模式的压电层合板动力有限元模型

建立了含压电片层合板的有限元动力学模型。以位于压电层上下表面处的电场强度和层间电压为未知量,给出了三次函数的电势分布模式,采用Reddy的高阶剪切理论描述板的位移场,假设板厚度方向的正应力为零给出了减缩的本构方程,采用有限元方法,基于Hamilton原理导出结构的动力学方程,然后用静态缩聚的方法压缩掉电场自由度和次要的位移自由度。最后用四边形矩形单元求解了一对称铺层和非对称铺层悬臂板的固有频率,并与ANSYS结果对比验证了本文模型的精确性。     

Accurate equations for laminated composite deep thick shells

This paper derives accurate equations of elastic deformation for laminated composite deep, thick shells. The equations include shells with a pre-twist and accurate force and moment resultants which are considerably different than those used for plates. This is due to the fact that the stresses over the thickness of the shell have to be integrated on a trapezoidal-like cross-section of a shell element to obtain the stress resultants. Numerical results are obtained and showed that accurate stress resultants are needed for laminated composite deep thick shells, especially if the curvature is not spherical. A consistent set of equations of motion, energy functionals and boundary conditions are also derived. These may be used in obtaining exact solutions or approximate ones like the Ritz or finite element methods.     

Analysis of laminated piezoelectric cylindrical shells

A new method is developed for three-dimensional stress analysis of laminated piezoelectric cylindrical shell with simple support. The shell can be subjected to various applied loadings, including distributed body force, inner and outer surface traction and potential. Each layer of the shell can be piezoelectric or elastic/dielectric, with perfect bonding assumed between each interface. The governing equations are solved by the state-space technique. Numerical results are presented to show the sensing and actuating effects of three-layered piezoelectric cylindrical shell. The project supported by the National Natural Science Foundation of China (19572027)     

Elastodynamic Green's functions for a laminated piezoelectric cylinder

Elastodynamic Green's functions for a piezoelectric structure represent the electro-mechanical response due to a steady-state point source as either a unit force or a unit charge. Herein, Green's functions for a laminated circular piezoelectric cylinder are constructed by means of the superposition of modal data from the spectral decomposition of the operator of the equations governing its dynamic behavior. These governing equations are based on a semi-analytical finite element formulation where the discretization occurs through the cylinder's thickness. Examples of a homogeneous PZT-4 cylinder and a two-layer cylinder composed of a PZT-4 material at crystal orientations of ±30° with the longitudinal axis are presented. Numerical implementation details for these two circular cylinders show the convergence and accuracy of these Green's functions.     

A new method for exactly solving the bending problem for a hingedly supported plate under the action of a piezoelectric actuator

The Navier solution is used to exactly solve the bending problem in the form of an eigenfunction series for a hingedly supported rectangular orthotropic Kirchhoff-Love plate under the action of a piezoelectric actuator.     

The exact solution for thick laminated cantilever cylindrical shell

Discarding any assumption regarding displacement or stress models, the state equation for orthotropy is established in a cylindrical system. The exact solution is presented for the statics of thick closed laminated cantilever cylindrical shells. Every equation of elasticity can be satisfied and all the elastic constants are taken into account. Arbitrary precision of a desired order can be obtained. Project supported by the National Natural Science Foundation of China     

非线性压电效应下压电弯曲执行器的动力分析

研究压电弯曲执行器在强电场作用下的非线性动力行为．考虑电致伸缩和电致弹性的非线性压电效应,导出了压电悬臂执行器变刚度的弯曲振动控制方程．利用非定常振动的渐近理论,讨论了弯曲压电执行器的动力特征．根据目前的非线性模型可以计算压电悬臂执行器的固有共振频率与电场的变化关系．结果表明压电执行器端头挠度谐振幅度随作用电场振幅的增大而增大,以及力学品质因数随电场振幅的增大而减少,并且与实验结果非常吻合．通过数值比较得到在电场频率随时间变化非常缓慢的情况下非定常振动问题可以近似地用定常振动来处理．     

压电智能复合材料层合梁的力电耦合模型及层间应力分析

由于非凡的物理性能,石墨烯纳米片(GPL)被认为是最有吸引力的复合材料增强材料之一.GPL增强材料可以明显提高聚偏氟乙烯(PVDF)压电性能和力学性能.在力电载荷作用下,对含均匀石墨烯薄片增强(GSR)智能压电复合材料层合梁层间应力预测至关重要.若对受到力电耦合作用且层与层之间材料性能突变的压电层合梁层间剪切变形预测有误,则其层间应力过大可能导致层间失效.因此,论文提出一种适于分析此类问题且满足层与层之间相容性条件的有效力电耦合模型,用于含GSR致动器的复合材料层合梁层间应力分析.应用Reissner混合变分原理(RMVT),可以提高考虑力电耦合效应的横向剪应力预测精度.三维(3D)弹性理论和所选模型计算结果将用于评估所提梁模型性能.此外,还从力电载荷、压电层厚度、石墨烯体积分数和长厚比等方面对含GSR致动器复合材料层合梁力学响应特性进行了系统的研究.     

双向变步长大位移压电作动器

提出一种基于蠕动式运动原理的新型双向变步长的大位移压电作动器,建立了该作动器的动力学模型。在30Hz作动频率下,采用MATLAB-SIMULINK软件进行了仿真。设计了含有高电压驱动器的作动器实验系统,作动器样机整体机构由嵌位部分、作动部分和轨道间距微调部分组成。研究结果表明,该作动器实际可提供±8mm的双向往返运动,实际作动曲线与计算机仿真结果在0.1μm级精度条件下吻合良好。