STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

A note on the Sarmanov bivariate distributions

We investigate the maximum correlation for Sarmanov bivariate distributions with fixed marginals and strengthen the existing results in the literature. The improvement in the maximum correlation is significant. A characterization of the Sarmanov distribution via chi-square divergence is also given. This extends Nelsen [13] result about the Farlie-Gumbel-Morgenstern (FGM) distribution.     

ON THE FREE VIBRATION OF A SUBMERGED FGM HOLLOW SPHERE

The free vibration of a functionally graded material hollow sphere submerged in a compressible fluid medium is exactly analyzed. The sphere is assumed to be spherically isotropic with material constants being inhomogeneous along the radial direction. By employing a separation technique as well as the spherical harmonics expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial coordinate. Numerical examples are finally given to show the effect of the material gradient on the natural frequencies. The project is supported by the National Natural Sciences Foundation of China(No. 19872060).     

线性分布荷载作用下梯度功能压电悬臂梁的解

采用逆解法求解了上表面受线性分布荷载作用的压电悬臂梁执行器，其中体积力$F_z$ 呈非线性分布. 首先确定了应力函数和电位移函数的多项式表达式，进而研究了该问题的 通解，以及体积力的不同分布对解答的影响. 常体积力和无体力情况下的解可以由上述 解直接得到. 本文为研究其它类型的压电梯度微观结构提供了一种可行的方法.     

Using a pseudo-functionally graded interlayer in order to improve the static and dynamic behavior of wind turbine blade T-bolt root joints

The large wind turbines blades with multi-ton composite structures are mostly connected to the peach-bearings flanges using T-bolt joints which induce shear and bearing stress fields around the cross bolts. The significant differences between the modulus of elasticity of metallic bolts and composite surrounding materials cause stress concentration around interfaced zones and, also, limit the load capacity of the joints. In the present research, a pseudo functionally graded material (PFGM) as an interlayer is used around the cross bolts to examine the reduction of the stress concentration. Some radial variation of the mechanical properties would be considered for this interlayer. The finite element method is used to analyze the structures. Loadings are applied to the center of the cross bolts analogous to the real cases. Both the static and dynamic loadings are studied. For the finite element of the functionally graded material interlayer, a multilayer alternative material with constant properties in each layer is used. The results show that using an isotropic single layer with an average modulus of elasticity and specific thickness decreases the stress concentration of the composite part up to 47%. The various property models for the interlayer also show that an appropriated model can decrease the stress concentration up to 55%. Dynamic transient analyses would be implemented over the joint structure and improved considering to the practical cases. Using the PFGM interlayer decreases the constant and variable parts of the stresses up to 55% and also causes significant increasing of the joint fatigue life.     

热荷载作用下Timoshenko功能梯度夹层梁的静态响应

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦合变形的影响,并给出温度函数在夹层梁厚度方向的具体分布形式.     

基于脉冲电铸技术Ni-ZrO2纳米梯度功能材料的制备工艺

研究了在脉冲复合电铸过程中,当其它工艺参数一定时,镀液中纳米ZrO2颗粒含量、脉间、脉宽和阴极电流密度对复合电铸层中ZrO2复合量和沉积速率以及脉冲参数对复合电铸层表面形貌的影响,并对所制备复合电铸层的横截面进行了SEM观察和组成成分测定.结果表明,通过控制脉冲复合电铸过程中的工艺参数可以制备出由纳米颗粒复合量变化而导致其组织成分呈梯度分布的纳米功能梯度材料.