铁电薄膜在红外辐射作用下的动力响应

本文研究了红外探测器中红外焦平面列阵的象元———铁电薄膜微桥在红外辐射作用下的输出信号。用层合板壳作为微桥结构的力学模型,中间一层为压电材料,上下两层为金属材料电极。采用了力-电-热耦合的控制方程和变分原理,考虑了铁电薄膜的惯性力,推导出了基于Mindlin假设的压电材料层合板有限元公式。以红外探测器在夜间从飞机上探测地面的坦克为例,用有限单元法模拟了铁电薄膜微桥在红外辐射作用下的力、热、电输出信号,并对结果作了分析比较。     

铁电薄膜在红外辐射作用下的响应

研究了红外探测器中红外焦平面列阵的象元———铁电薄膜微桥在红外辐射作用下的输出信号。用层合板壳作为微桥结构的力学模型,中间一层为压电材料,上下两层为金属材料电极。采用了力-热-电耦合的控制方程和变分原理,推导出了基于Mindlin假设的压电材料层合板有限元公式。以红外探测器在夜间从飞机上探测地面的坦克为例,用有限单元法模拟了铁电薄膜微桥在红外辐射作用下的力、热、电输出信号,并对结果作了分析比较。     

Behavior of a Semi-Infinite Ice Cover Under a Uniformly Moving Load

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener–Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated.     

考虑表面效应的双层圆板的自由振动分析

考虑微生化传感器中谐振器的结构特点,基于Kirchhoff薄板理论与表面弹性理论推导了考虑表面效应的双层圆板的自由振动方程.使用伽辽金法得到了近似解.分析了硬化与软化表面效应与表面残余应力对双层圆板固有频率的影响.结果表明,与已有简化的单层圆板模型相比,现有考虑表面效应的双层板模型会得到与之不同的固有频率.随着板厚与上...     

边界膜剪切弹性模量对于微接触性能的影响

建立接触模型,理论分析了微接触中边界膜剪切弹性模量对于接触性能的影响. 接触区由两平行平面形成,属一维接触. 上接触表面为粗糙表面,具有矩形微凸体. 下接触表面为光滑平面. 两接触表面均处理成刚性表面. 微接触区中充满流体. 它分成两个子区,在微接触的出口区由于极小的接触间隙充满边界膜,在微接触的入口区由于接触间隙较大充满流体膜. 边界膜和流体膜行为决定整个微接触性能. 当膜厚较大时,这里边界膜可看成纳米级薄膜. 由于上接触表面处有限的剪应力承受能力,边界膜可于上接触表面滑移. 设下接触表面处剪应力承受能力很大而边界膜在下接触表面不滑移. 由于边界膜-接触表面间相互作用,边界膜黏度、密度和剪切弹性模量均沿膜厚变化,在理论分析中使用它们的等效值,这些值与边界膜厚度有关. 流体膜在两个接触表面均不发生滑移,分析中不考虑流体膜剪切弹性模量. 流体膜采用传统分析法. 给出了理论分析和若干变工况参数下的计算结果.      

Finite element analysis of smart functionally graded plates

This paper deals with the derivation of a finite element model for the static analysis of functionally graded (FG) plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material. The layer of PFRC material acts as the distributed actuator of the FG plates. The Young’s modulus of the FG plate is assumed to vary exponentially along the thickness of the plate while the Poisson’s ratio is assumed to be constant over the domain of the plate. The finite element model has been verified with the exact solutions for both thick and thin plates. Emphasis has been placed on investigating the effect of variation of piezoelectric fiber angle in the PFRC layer on its actuating capability of the FG plates. The finite element solutions also revealed that the activated PFRC layer is more effective in controlling the deformations of the FG plates when the layer is attached to the surface of the FG plate with minimum stiffness than when it is attached to the surface of the same with maximum stiffness.     

Size-dependent response of ultra-thin films with surface effects

A modified continuum model of elastic films with nano-scale thickness is proposed by incorporating surface elasticity into the conventional nonlinear Von Karman plate theory. By using Hamilton’s principle, the governing equations and boundary conditions of the ultra-thin film including surface effects are derived within the Kirchhoff’s assumption, where the effects of non-zero normal stress and large deflection are taken into account simultaneously. The present model is then applied to studying the bending, buckling and free vibration of simply supported micro/nano-scale thin films in-plane strains and explicit exact solutions can be obtained for these three cases. The size-dependent mechanical behavior of the thin film due to surface effects is well elucidated in the obtained solutions.     

轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论,研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先,考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后,忽略温度梯度在面内的变化,建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法,将变系数热传导方程转化为一系列常系数的微分方程,利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程,得到了包含热弹性阻尼的复频率,从而获得了反映热弹性阻尼水平的逆品质因子．最后,针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板,定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．     

Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field

This paper studies the two dimensional flow of an electrically conducting fluid which is an optically thin gray gas past a stationary vertical infinite plate in the presence of radiation. It is assumed that the temperature of the plate and the suction at the plate are constant. The presence of the induced magnetic field is also taken into account. Numerical solutions for the velocity and the induced magnetic field are derived and the effects of the radiation parameter are discussed.     

功能梯度材料明德林矩形微板的热弹性阻尼

功能梯度材料微板谐振器热弹性阻尼的建模和预测是此类新型谐振器热?弹耦合振动响应的新课题. 本文采用数学分析方法研究了四边简支功能梯度材料中厚度矩形微板的热弹性阻尼. 基于明德林中厚板理论和单向耦合热传导理论建立了材料性质沿着厚度连续变化的功能梯度微板热弹性自由振动控制微分方程. 在上下表面绝热边界条件下采用分层均匀化方法求解变系数热传导方程, 获得了用变形几何量表示的变温场的解析解. 从而将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的偏微分方程. 然后,利用特征值问题在数学上的相似性,求得了四边简支条件下功能梯度材料明德林矩形微板的复频率解析解, 进而利用复频率法获得了反映谐振器热弹性阻尼水平的逆品质因子. 最后, 给出了材料性质沿板厚按幂函数变化的陶瓷?金属组分功能梯度矩形微板的热弹性阻尼数值结果. 定量地分析了横向剪切变形、材料梯度变化以及几何参数对热弹性阻尼的影响规律. 结果表明, 采用明德林板理论预测的热弹性阻尼值小于基尔霍夫板理论的预测结果, 而且两者的差别随着相对厚度的增大而变得显著.      

Vibrations of Circular Sandwich Plates under Resonance Loads

The paper studies axisymmetric resonance vibrations of an elastic circular sandwich plate under local periodic surface loads of rectangular, sinusoidal, and parabolic forms. The hypotheses of broken normal are used to describe the kinematics of the plate, which is asymmetric in thickness. The core is assumed to be light. The initial–boundary-value problems are solved analytically. The solutions are analyzed     

任意边界条件下双模量矩形薄板的弯曲

将双模量板等效为两个各向同性小矩形板组成的层合板,假定该层合板的中性面即为两个小矩形板的交界面。根据中性面上应力为零且薄板全厚度上应力的代数和为零,推导了双模量矩形薄板的中性面位置。本文采用严宗达提出的带补充项的双重正弦傅里叶级数通解,该通解可以适用于任意边界条件的矩形薄板且不需要叠加或者重新构造。联立边界条件和控制方程,求得通解中的待定系数并代入到通解中,即可得到任意边界条件下双模量矩形薄板的弯曲解析解。与有限元结果比较,本文结果符合工程精度要求。     

Unsymmetrical nonlinear bending problem of circular thin plate with variable thickness

Introduction Manystructuralelements(pole,plate,shell)withunevenandvariablethicknessarewidely usedinallkindsofengineeringfields.Engineerscansavematerialswhentheydesignbecause theseelementshavebetteroptimizedshapeofstructuralfeature,butthisaddsdifficultytotheanalysisoftheirmechanicalcapability.Manypreviouspapers[1-4]havesolvedtheproblemof symmetricalaxis,butnobodyhassolvedtheunsymmetricalnonlineardeformationproblemof circularthinplatewithvariablethicknessandunsymmetricalaxisuptonow,afewworkonly …     

Nonlinear analysis of a thin circular functionally graded plate and large deflection effects on the forces and moments

The dynamic von Karman equations are used for nonlinear analysis of a thin circular plate made of a functionally graded material. The thickness of the plate is constant and the properties of the functionally graded material depend on temperature and vary throughout the thickness. It is assumed that the plate oscillates with large amplitudes. The forces and moments in the plate are determined in solving the equations for harmonic vibrations. Relevant results are obtained in the case of stead-state free vibrations. These results indicate that the volume fraction has a strong effect on the forces, moments, and material properties Published in Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 134–144, June 2008. An erratum to this article can be found at     

Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations

A simple isoparametric finite element formulation based on a higher-order displacement model for flexure analysis of multilayer symmetric sandwich plates is presented. The assumed displacement model accounts for non-linear variation of inplane displacements and constant variation of transverse displacement through the plate thickness. Further, the present formulation does not require the fictitious shear correction coefficient(s) generally associated with the first-order shear deformable theories. Two sandwich plate theories are developed: one in which the free shear stress conditions on the top and bottom bounding planes are imposed and another, in which such conditions are not imposed. The validity of the present development(s) is established through, numerical evaluations for deflections/stresses/stress-resultants and their comparisons with the available three-dimensional analyses/closed-form/other finite element solutions. Comparison of results from thin plate. Mindlin and present analyses with the exact three-dimensional analyses yields some important conclusions regarding the effects of the assumptions made in the CPT and Mindlin type theories. The comparative study further establishes the necessity of a higher-order shear deformable theory incorporating warping of the cross-section particularly for sandwich plates.     

An exact solution for transversely isotropic,simply supported and layered rectangular plates

Levinson's solution for the problem of a simply supported rectangular plate of arbitrary thickness by normal surface loads is extended to the transversely isotropic and layered case. The exact closed form solution is obtained by using the propagator matrix method in a system of vector functions. As a special case of the layered medium, the normal displacement or deflection of a homogeneous plate of arbitrary thickness by normal surface loads is also given. It is shown that it approaches the classical solution for the transversely isotropic thin plate as the thickness approaches zero on the one hand, and on the other hand reduces to the thick plate expression as given by Levinson when the medium is isotropic.     

Use of B-spline surface to model large-deformation continuum plates: procedure and applications

The absolute nodal coordinate formulation (ANCF) has been used in the analysis of large deformation of flexible multibody systems that encompass belt drive, rotor blade, and cable applications. As demonstrated in the literature, the ANCF finite elements are ideal for isogeometric analysis. The purpose of this investigation is to establish a relationship between the B-splines, which are widely used in the geometric modeling, and the ANCF finite elements in order to construct continuum models of large-deformation geometries. This paper proposes a simplified approach to map the B-spline surfaces into ANCF thin plate elements. Matrix representation of the mapping process is established and examined through numerical examples successfully. The matrix representation of the mapping process is used because of its suitability of computer coding and to minimize the calculation time. The error estimation is carried out by analyzing the gap between the points of each ANCF element and the corresponding points of the portion of the B-spline surface. The Hausdorff distance is used to study the effect of the number of control points, the degree of interpolation, and the knot multiplicity on the mapped geometry. It is found that cubic interpolation is recommended for optimizing the accuracy of mapping the B-spline surface to ANCF thin plate elements. It is found that thin plate element in ANCF missing a number of basis functions which considered a source of error between the two surfaces, as well as it does not allow to converting the ANCF thin plate elements model to B-spline surface. In this investigation, an application example of modeling large-size wind turbine blade with uniform structure is illustrated. The use of the continuum plate elements in modeling flexible blades is more efficient because of the relative scale between the plate thickness and its length and width and the high flexibility of its structure. The numerical results are compared with the results of ANSYS code with a good agreement. The dynamic simulation for mapped surface model shows a numerical convergence, which ensures the ability of using the proposed approach for applications of dynamics for design and computer-aided design.     

Stiffness and buckling optimization of thin plates with BEM

The thickness optimization is used to maximize the stiffness or the buckling load of a Kirchhoff plate having constant volume. The shape of the plate is arbitrary and it is subjected to any type of admissible boundary conditions. The optimization consists in establishing the thickness variation law, for which either the stiffness of the plate or the buckling load is maximized. Beside the equality constraint of constant volume, the thickness variation is subjected also to inequality constraints resulting from serviceability requirements (upper and lower thickness bounds) as well as from the condition that the Kirchhoff plate theory remains valid. The latter constraint is new and it is derived herein by approximating the plate with a three-dimensional prismatic elastic body having curved upper and lower surface. The optimization problem is solved using the sequential quadratic programming algorithm. The bending and the plane stress problem of a plate with variable thickness, required for the evaluation of the objective function, are solved using the analog equation method. The thickness is approximated using integrated radial basis functions that approximate accurately not only the thickness function but also its first and second derivatives involved in the plate equation and in the constraints. Several plate optimization problems have been studied giving realistic and meaningful optimum designs without violating the validity of the thin plate theory.     

石墨氧化物分子沉积膜的制备及其摩擦学行为研究

采用分子沉积技术制备了石墨氧化物（GO）－聚二丙烯二甲铵（PDDA）多层超薄膜，用紫外和红外光谱对超薄膜的结构进行了分析，用原了力显微镜考察了薄膜的表面形貌及纳米摩擦学行为。结果表明：石墨氧化物分子沉积膜可以降低玻璃表面的摩擦系数；其摩擦系数随载荷增大而降低；该分子沉积薄膜良好的润滑性能归因于其较低的表面剪切强度。     

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.