Thin-Film Piezoelectric Actuators of Nonuniform Thickness and Nonhomogeneous Material Properties for Modulating Actuation Stress

The effects of the thickness variation and the material property variation of thin-film piezoelectric actuators on the actuation shear stress when the actuators are attached to an elastic plate are studied. A system of 2D equations for the flexure and shear of an elastic plate with symmetric piezoelectric actuators on the plate surfaces is derived. The equations are reduced to the case of elementary flexure without shear as a special case. The effects of the actuator thickness variation and material property variation on the actuation stress are examined using the equations obtained. It is shown that the distribution of the actuation stress depends on the thickness and material property variations of the actuators, and that actuators with varying thickness or varying material properties can be used to make modal actuators for producing a particular deformation or exciting a particular vibration mode.     

Pure-mode loci in piezoelectric plate resonators: application to materials evaluation in class 4 mm

The accuracy of piezoelectric material evaluations can be enhanced by the use of pure-mode orientations, provided that exact analytic expressions for the pure-mode eigenvalues are known. The accuracy is enhanced by eliminating the need to extract constants from the differences in sums and products of measured quantities. It is necessary to adopt an approach for determining pure-mode loci in piezoelectric crystals which yields simple analytic expressions for the stiffness eigenvalues and provides a convenient engineering methodology for pure-mode sample set selection. The theory of simple thickness modes in piezoelectric plate vibrators is reviewed. The determination of pure-mode loci and its application to pure-mode sample set selection for dilithium tetraborate are presented. Thickness- and lateral-field excitation considerations are discussed.     

基于不同压电材料作动机制的压电层厚度研究

研究了压电材料复合板的3种作动机制,弯曲作动机制、剪切作动机制、混合作动机制,针对粘贴在纤维板上不同厚度的压电作动层,具体分析了复合板的端部位移,研究结果对噪声和振动的主动控制中的模态控制和智能结构静态形状控制提供了一定的参考。     

层合板中压电作动器最优厚度和嵌入位置研究

研究了压电结构中压电片厚度和嵌入深度的优化问题。首先给出了压电层合板的高阶耦合分析模型;然后以不受约束的含压电铺层复合材料板为代表,在压电层厚度方向施加电场时板自由变形,假设板任意微元横截面上内力为零,以其弯(扭)曲曲率最大为优化目标,建立了求解压电片最优厚度和嵌入深度问题的约束优化模型。最后分别以各向同性板中嵌入各项同性压电片和复合材料板中嵌入各向异性压电片为例进行了分析,绘出了目标函数的三维曲面图及等高线图,结果表明压电片的作动效能与其厚度和嵌入位置密切相关,而最优厚度和嵌入位置是由压电片和基体的材料特性决定的。     

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.     

基于等几何方法的压电功能梯度板动力学及主动振动控制分析

针对表面粘贴有压电层的功能梯度板的动力学及主动振动控制问题，建立了一种基于三阶剪切变形理论的等几何分析求解方法。其中，功能梯度板的材料属性为板厚方向的幂函数分布，并假设电势沿着压电层的厚度方向呈线性变化。利用线性压电本构方程以及哈密顿变分原理，推导了压电功能梯度板的相关等几何分析有限元方程。通过分析压电智能结构的静态弯曲行为验证了该方法的有效性与精确性。运用模态叠加技术与Newmark-β直接积分法分析了两种不同结构的压电功能梯度板的动力学响应与主动振动控制问题。在主动振动控制分析中，引入了物理中面的概念避免当传感器与驱动器分别粘贴于功能梯度的上、下表面时，由拉伸-耦合效应引起的控制不稳定的问题，并着重分析了振动控制过程中两种结构传感器层和驱动器层的电压响应。     

Fracture of a finite piezoelectric layer with a penny-shaped crack

This paper studies a penny-shaped crack in a finite thickness piezoelectric material layer. The piezoelectric medium is subjected to a thermal flux on its top and bottom surfaces. Both thermally insulated crack and heated crack are considered. Numerical solution for the finite layer thickness is obtained through the solution of a pair of dual integral equations. The result reduces to the closed form solution when the thickness of the piezoelectric layer becomes infinite. Exact expressions for the stress and electric displacement at the crack border are given as a function of the stress intensity factor, which is determined by the applied thermal flux. This paper is useful for the reliability design of piezoelectric materials in thermal environments.     

An exact analytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory

Based on third-order shear deformation plate theory of Reddy, the authors aim to provide an exact analytical solution for free vibration analysis of thick circular/annular plates, both upper and lower surfaces of which are in contact with a piezoelectric layer. Natural frequencies are determined by the solution of the coupled electromechanical governing equations for a combination of free, soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the plate. The electrodes on each piezoelectric layer are assumed to be short-circuited. The Maxwell electrostatics equation is satisfied by adopting a half-sine distribution of the electric potential in the transverse direction of the piezoelectric layers. A comparison of the present exact natural frequencies for piezoelectric coupled circular/annular plates with different boundary conditions is made with previously published results obtained by the Mindlin plate theory and 3-D modified finite element method. The effects of plate parameters such as host thickness to radius ratios, inner to outer radius ratios and piezoelectric to host thickness ratios on the natural frequencies of laminated circular/annular plates are investigated for different combinations of boundary conditions. Results obtained by the present exact closed-form solutions can be served as benchmark data for investigators to validate their numerical and analytical methods in the future.     

Vibration analysis of a circular thin polymeric piezoelectric diaphragm with fluid interaction

This paper presents vibration analysis of a circular piezoelectric micro-plate in fluidic environment. PVDF film is used as the piezoelectric material. PVDF is a material with asymmetric matrix of piezoelectric constants and shows different piezoelectric properties in different directions. The governing equations, which are more complicated compared to piezo-ceramics, are derived. The boundary conditions for the plate are assumed fully clamped at outer edge, as is the case in many micro devices. Liquid is modeled as a damping foundation under the plate. The equations of motion are solved using generalized differential quadrature method to obtain Eigen frequencies and mode shapes of the plate. The results are compared by developed finite element analysis.     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.     

基于三阶剪切变形理论的压电功能梯度板静力学等几何分析

针对压电功能梯度板的静力学问题,建立了一种基于三阶剪切变形理论的等几何分析求解方法.其中,定义功能梯度板的材料属性为板厚方向的幂函数分布,并假设压电功能梯度板中的机械位移场与电势场相互独立.利用压电材料的第二类本构方程以及哈密顿变分原理,推导出压电功能梯度板的相关等几何有限元方程.在压电功能梯度板的自由振动分析中,研究...     

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     

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.     

Active aeroelastic flutter suppression of a supersonic plate with piezoelectric material

The active aeroelastic flutter properties of supersonic plates are investigated by using the piezoelectric material. The piezoelectric material has been extensively used for the active vibration control of engineering structures. In this paper, the piezoelectric material is further used to improve the flutter characteristics of the supersonic plates. The equation of motion of the plate and piezoelectric material system is obtained by Hamilton’s principle with the assumed mode method. The supersonic piston theory is used to evaluate the aerodynamic load. By applying an appropriate external control voltage to activate the piezoelectric material, a displacement and acceleration feedback control strategy is used to obtain the active stiffness and active mass. Solving the eigenvalue problem of the equation of motion, the natural frequencies and damping ratios of the structural system are obtained. Furthermore, the aeroelastic flutter bounds are calculated, and the effects of feedback control gains on the active aeroelastic flutter characteristics of the structure are analyzed in detail. From the numerical results it is seen that the active stiffness and active mass have prominent effects on the flutter characteristics of the supersonic plates. The aeroelastic flutter properties can be greatly improved by introducing the active stiffness and active mass into the supersonic plate with the piezoelectric patch. With the increase of the feedback control gains, the active aeroelastic flutter properties for the lower order modes of the supersonic plate are gradually improved.     

HSDT-layerwise analytical solution for rectangular piezoelectric laminated plates

The present paper develops a formulation for laminated plates with extensional distributed piezoelectric sensors/actuators. This formulation is based on linear electroelasticity, and an equivalent single layer is used for the mechanical displacement field, applying a Higher-Order Shear Deformation Theory (HSDT), whereas a layerwise discretization is used in the thickness direction for the electric potential. The electric and mechanical local equilibrium equations and local constitutive equations for the problem are identified. The Principle of Virtual Work is used to derive the dynamic equilibrium equations in terms of generalized forces and the consistent boundary conditions. The piezoelectric laminate constitutive equations are built and used to write the equations of motion in terms of generalized displacements. Finally, analytical solutions for simply supported square laminates with piezoelectric layers are developed. The entire laminate, composed of the base structure and piezoelectric layers, can be arbitrary orthotropic. The solution is adequate for an arbitrary number of piezoelectric layers and stacking positions. Moreover, the solution takes into account all material coefficients, whether mechanical, piezoelectric or dielectric. Analytical results are obtained for static bending, both in sensor and actuation modes, and for free vibration of symmetric cross-ply laminates with piezoelectric layers externally bonded to the plate.     

Flexural vibration behavior of piezoelectric heterogeneous bimorph beams

Bending oscillations of piezoelectric bimorph beams are effective sound sources in gases or fluids, and, therefore, of practical interest. On the basis of the piezoelectric constitutive relations and the elastodynamic equations, the differential equation of flexural vibrations of thin rectangular piezoelectric heterogeneous bimorph beams, consisting of a piezoelectric layer glued onto an elastic substrate, is derived. The piezoelectric layer is polarized in thickness direction and can be excited to thickness vibrations by an electric alternating current voltage applied to electrodes covering the upper and lower surface of the layer. This causes an oscillating transverse contraction in the piezoelectric layer but not in the substrate, and, thus, generates flexural vibrations of the beam. The differential equation is solved analytically for beams of finite length with both ends free, one clamped and one free end, as well as for both ends clamped. Their vibration behavior in viscous fluids is considered. For a piezo-ceramic composite layer joined to a steel plate vibrating in air and in water, the analytical results are evaluated numerically as function of frequency     

Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory

Here, free vibration analysis of functionally graded piezoelectric (FGP) plates with porosities is carried out based on refined four-unknown plate theory. The present plate theory captures shear deformation impacts needless of shear correction factor. A modified power-law model is adopted to describe the graded material properties of a functionally graded piezoelectric plate. Implementing an analytical approach, which satisfies different boundary conditions, governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. The impacts of applied voltage, porosity distribution, material graduation, plate geometrical parameters, and boundary conditions on vibration of porous FGP plate are discussed.     

Flextensional ultrasonic motor using the contour mode of a square piezoelectric plate

This paper presents the design, fabrication, and characterization of a new type of standing wave piezoelectric ultrasonic motor. The motor uses a metallic flextensional amplifier, or cymbal, to convert the contour mode vibrations of a square piezoelectric ceramic plate into flexural oscillations, which are further converted to produce rotary actuation by means of an elastic-fin friction drive. The motor operates on a single-phase electrical supply. A beryllium copper rotor design with three-fin configuration was adopted, and the geometry was varied to include different material thicknesses, fin lengths, and inclinations. The best stall torque and no load speed for a 25-mm square motor were 0.72 Nmm and 895 r/minute, respectively. The behavior of the stator structure was analyzed by ANSYS finite element software using harmonic and modal analyses. The vibration mode estimated by finite element modeling (FEM) was confirmed by laser Doppler vibration measurements.     

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.     

间隙波在功能梯度压电板和压电半空间结构中的传播

研究了间隙波在功能梯度压电板和压电半空间结构中的传播性质.功能梯度压电板的材料性能沿x2方向呈指数变化,首先推导了间隙波传播时的解析解,利用界面条件得到了间隙波的频散方程,基于推导的频散方程,结合数值算例分析了功能梯度压电材料的梯度、压电层厚度以及材料性能对间隙波相速度的影响,研究结果对功能梯度压电材料的覆层结构在声波器件中的应用具有重要的参考价值.