The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.

导电压头作用下的多层功能梯度压电材料涂层二维接触问题研究

考虑了材料参数可按照任意函数形式变化的功能梯度压电材料(FGPM)涂层在不同形状导电压头作用下的接触问题,研究了梯度系数对功能梯度压电涂层接触力学行为的影响.建立了多层功能梯度压电材料涂层模型,运用了Fourier积分变换和传递矩阵将多层功能梯度压电材料涂层的接触问题转化为奇异积分方程.利用Gauss-Chebyshev数值计算方法,得到了多层功能梯度压电材料涂层-基底结构在刚性导电平压头和圆柱形压头作用下的表面应力分布和电荷分布.利用数值解,分析了材料参数按照不同变化形式的FGPM涂层对最大压痕和电势的影响,还分析了功能梯度压电涂层内部的应力和电位移分布.研究结果表明,功能梯度压电材料参数的不同变化形式对结构的接触性能具有重要的影响.

含缺陷功能梯度压电材料的动态断裂行为分析

与传统的压电材料相比,功能梯度压电材料(functionally graded piezoelectric material,FGPM)具有力学性质(如压电常数、介电常数、弹性模量、密度等)沿某一方向连续变化的特点,从而可以避免应力集中,有效延长所构成元器件的使用寿命。在实际工程中,材料中的界面结构常常含有裂纹、空穴等多种形式的缺陷,在外载荷作用下缺陷附近的区域易发生应力集中甚至断裂。目前,对于功能梯度压电材料断裂问题的研究仅限于单一形式的缺陷,即在材料界面处仅存在空穴或仅存在裂纹,对于复合型缺陷的研究还很少。针对反平面剪切波作用下的含孔边激发界面裂纹缺陷的双相FGPM,提出一种分析其裂尖场动应力集中问题的计算方法。通过采用Green函数法、坐标变换法、裂纹“切割”与“契合”技术构建力学模型,将裂纹问题转化为第一类Fredholm型积分方程的求解,从而得到动应力强度因子(dynamic stress intensity factor,DSIF)的理论表达式。最后,给出数值算例,分析了缺陷的几何形状、入射波特性以及材料的非均匀性等因素对DSIF的影响,结果的正确性则通过与Griffith裂纹模型对比来验证。

Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere

Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material （FGPM） solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter β can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis

The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded(FG),the material properties vary along the thickness direction as one innovation of this study.Applying the first-order shear deformation theory(FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations(PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material(FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Due to the increasing interests in using functionally graded piezoelectric materials(FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then,a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained.Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.

Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads

This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material （FGPM） and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson＇s ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.

Peculiarities of surface acoustic waves,propagation in structures with functionally graded piezoelectric materials,coating from different ceramics on the basis of PZT

A model of a piezoelectric structure with an inhomogeneous coating is considered.The structure is a homogeneous half-space made of PZT-5H ferroelectric ceramics with a functionally graded coating.The properties of coating vary continuously in thickness from parameters of one material to parameters of another material in a continuously nonmonotonic or piecewise-continuous manner.As coating materials,various combinations of ceramics of different stiffness based on PZT are considered.Using the example of the problem of the propagation of sh-waves in a piezoelectric structure,we studied the influence of the ratio of the physical parameters of the coating materials,the localization region,and the size of the transition zone of one material to another on the propagation features of surface acoustic waves(SAWs)and the structure of the wave field.

Specific features of SH-waves propagation in structures with prestressed inhomogeneous coating made of piezoceramics based on LiNbO_(3)

Within the framework of the linearized theory of electroelastic wave propagation,a model of a piezoelectric structure with a prestressed functionally graded coating made of piezoceramics of a trigonal system with a symmetry class of 3m is considered.The ferroelectric LiNbO_(3) is used as the main material of the structure.The initial deformed state of the coating material is homogeneous,induced by the action of initial mechanical stresses and an external electrostatic field,the properties of the coating continuously change in thickness.By the example of the problem of the propagation of SH-waves from a remote source for structures with an inhomogeneous prestressed coating in the case of an electrically free and short-circuited surface,the influence of the nature and localization of the inhomogeneity of the coating on the features of SAW propagation is studied.The separate and combined effects of initial actions on changes in the physical properties of the structure,the transformation of the surface wave field,and the change in the SAW velocities in a wide frequency range is studied.The results obtained in this work are useful for understanding the dynamic processes in prestressed piezoelectric structures,in the optimization and design of new structures and devices on SAW with high performance characteristics.