轴向流中悬臂柔性板流固耦合动力特性研究

论文从理论分析和实验研究两方面对轴向流中悬臂柔性板流固耦合动力特性作了研究.基于板的轴向不可延伸假设,采用Hamilton变分原理,推导了轴向流中悬臂板非线性运动偏微分方程,通过面元法计算悬臂板上下面压力差.采用伽辽金法离散该非线性运动偏微分方程,通过无量纲化物理参数,研究了系统无量纲颤振临界速度,给定流速下悬臂板末端响应时程曲线及板的振动响应,并与风洞模型实验结果进行了对比.研究结果表明,系统发生Hopf分叉,流体流速大于颤振临界速度时,悬臂板发生稳定的极限环颤振,悬臂板振幅、频率随流速的增加而增大.     

宽翼缘梁温差自应力级数解

为了充分反映宽翼缘梁的温差自应力分布特点,克服按梁理论计算温差自应力时的不足,本文从弹性力学的分析方法入手,按平面应力状态分析翼缘板和腹板的温差应力.根据翼缘板与腹板连接处的变形协调及平衡条件建立补充方程,求解艾瑞应力函数中的积分常数,导出翼缘板与腹板的温差应力及位移的解析式.对一宽翼缘T梁的计算表明,当翼缘板相对于腹...     

宽翼缘T梁温差应力的弹性力学解法

为了充分反映宽翼缘梁的温差自应力分布特点,克服按梁理论计算温差自应力时的不足,从弹性力学的分析方法入手,按平面应力状态分析翼缘板和腹板的温差应力.根据翼缘板与腹板连接处的变形协调及平衡条件建立补充方程,求解艾瑞应力函数中的积分常数,导出翼缘板与腹板的温差应力及位移的解析式.对一宽翼缘T梁的计算表明,当翼缘板相对于腹板发生温差变化时,沿其宽度的纵向温度自应力分布很不均匀,在翼缘板根部自应力较大而在悬臂端则显著减小.     

Creep buckling and post-buckling analysis of the laminated piezoelectric viscoelastic functionally graded plates

The creep buckling and post-buckling of the laminated piezoelectric viscoelastic functionally graded material (FGM) plates are studied in this research. Considering the transverse shear deformation and geometric nonlinearity, the Von Karman geometric relation of the laminated piezoelectric viscoelastic FGM plates with initial deflection is established. And then nonlinear creep governing equations of the laminated piezoelectric viscoelastic FGM plates subjected to an in-plane compressive load are derived on the basis of the elastic piezoelectric theory and Boltzmann superposition principle. Applying the finite difference method and the Newmark scheme, the whole problem is solved by the iterative method. In numerical examples, the effects of geometric nonlinearity, transverse shear deformation, the applied electric load, the volume fraction and the geometric parameters on the creep buckling and post-buckling of laminated piezoelectric viscoelastic FGM plates with initial deflection are investigated.     

矩形板非线性蠕变损伤屈曲特性分析

基于Von Karman非线性板理论和Kachanov-Rabotnov损伤理论,建立了在横向和面内载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,采用有限差分法和时间增量算法对未知变量进行离散,对整个问题进行迭代求解,分析了几何非线性、荷载等因素对板非线性蠕变损伤特性的影响。     

Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid

A theoretical study on a linear hydroelastic vibration of two annular plates coupled with a bounded fluid is presented. The proposed method, based on the Rayleigh–Ritz method and the finite Hankel transform, is verified through a finite element analysis by using a commercial computer code, with an excellent accuracy. It is assumed that plates with an unequal thickness and with an unequal inner radius are clamped along their edges and an inviscid compressible fluid fills the space between the annular plates and the outer rigid vessel. When the two annular plates are identical, distinct in-phase and out-of-phase modes are observed. By increasing the difference in the plate thickness, the symmetric in-phase and out-of-phase modes with respect to the middle plane of the system are gradually shifted to pseudo in-phase and out-of-phase modes, and eventually they are changed to mixed modes. It is found that the natural frequencies decrease with an increase of the fluid compressibility, and additional modes due to a fluid concentration are observed when the plates are coupled with a compressible fluid. The fluid compressibility effect on the natural frequency is dominant in the out-of-phase modes and the higher modes. Also, the effects of the fluid thickness or the distance between the plates and the inner radius of the plates on the natural frequencies of the wet modes are investigated.     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大.     

Large deflection of rectangular sandwich plates

The governing differential equations and the boundary conditions for the large deflection of rectangular sandwich plates are derived using the principle of the complementary energy. The governing differential equations are transformed into systems of nonlinear algebraic equations using the finite difference method, and solved by successive iteration. For the purpose of illustration, deflection behavior of simply supported rectangular plates under uniform load is presented. The deflection behavior of plates with various values of shear rigidities and intensity of applied loads is studied. The change in the stress patterns of the face layers of the plate is also discussed.     

A Time Domain Method for Quasi-Static Analysis of Viscoelastic Thin Plates

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Bending of Composite Plates under Static and Dynamic Loading

The stationary bending of a two-dimensional elastic system of joined rectangular plates with different mechanical properties and boundary conditions is studied. A technique for solving the corresponding problem is proposed. It is based on approximate approaches in combination with a generalization of the force method. It is established that the static strain state of the system is essentially dependent on the difference between the elastic moduli of the constituent plates. It is also shown that with certain boundary conditions, the dependence of the first resonant frequency on the relative position of plates along the contact line is nonmonotonic__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 77–84, January 2005.     

Hybrid determination of equivalent characteristics of perforated plates

In this paper, we have adopted the hybrid method, which combines experimental and numerical methods, to investigate the dynamic behavior of perforated plates. It was found that the modal assurance criterion is a useful criterion to judge the degree of similarity between experimental and numerical models. The difference between the experimental and numerical models can be reduced via sensitivity testing and by checking the correlation coefficient. The equivalent material properties of the perforated plates were also obtained by the hybrid method. In addition, the curve-fitting technique was utilized to find the relationship of the mass remnant ratio with the parameter ratio. The functions obtained from the curve fitting can be used to predict accurately the equivalent material properties and resonant frequencies of perforated plates of the diagonal array.     

Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system

Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.     

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.     

Experimental and theoretical analysis of the deformation of transversely isotropic plates under creep conditions

This paper describes the results of calculations and experiments on the torsion of plates made of isotropic and transversely isotropic VT-20 and 1163T alloys with low resistance to creep strain in the direction perpendicular to the median surface. The numerical simulation results for plates of different thicknesses related to the class of rigid and flexible plates are compared using the pure bending theory and the finite element method. It is found that the curvature values are smaller in the case of deformation of a plate made of anisotropic material into a sign-variable saddle surface than in the case of a plate of isotropic material. The calculation in the assumption of pure bending provides an upper bound of the curvature difference in the deformation of plates made of transversely isotropic and isotropic materials.     

Elasto-plastic buckling and post-buckling analysis of sandwich plates with functionally graded metal-metal face sheets and interfacial damage简

Based on the elasto-plastic theory, considering the effect of spherical stress tensor on the elasto-plastic deformation and using the slicing treatment to deal with the plasticity of functionally graded coatings, the elasto-plastic increment constitutive equations of the sandwich plates with functionally graded metal-metal face sheets can be derived. Applying the weak bonded theory to the interfacial constitutive relation and taking into account the geometric nonlinearity, the nonlinear increment differential equilibrium equations of the sandwich plates with functionally graded metal-metal face sheets are obtained by the minimum potential energy principle. The finite difference method and the iterative method are used to obtain the post-buckling path. When the effect of geometrical nonlinearity of the plate is ignored, the elasto-plastic critical buckling load of the sandwich plates with functionally graded metal-metal face sheets can be solved by the Galerkin method and the iterative method. In the numerical examples, the effects of the interface damages, the induced load ratio, the functionally graded index, and the geometry parameters on the elasto-plastic post-buckling path and the elasto-plastic critical buckling load are investigated.     

ANALYSIS OF INTER-LAMINAR STRESSES FOR COMPOSITE LAMINATED PLATE WITH INTERFACIAL DAMAGE

A constitutive model for composite laminated plates with the damage effect of the intra-layers and inter-laminar interface is presented. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement on the interfaces are depicted by three shape functions, which are formulated according to solutions satisfying three equilibrium equations, By using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated plates with two different damage models are derived. Then, considering a simply supported laminated plate with damage, an analytical solution is presented using finite difference method to obtain the inter-laminar stresses.     

Vibration and stability of hybrid plate based on elasticity theory

The governing equations of elasticity theory for natural vibration and buck- ling of anisotropic plate are derived from Hellinger-Reissner＇s variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions. Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations.     

单箱双室箱梁的剪力滞效应分析

针对单箱双室箱梁,考虑各翼板间剪力滞翘曲的差异,并结合全截面轴力自平衡条件,定义了箱梁各翼板的剪滞翘曲位移函数. 利用最小势能原理,建立了双室箱梁考虑剪力滞效应的控制微分方程. 对一典型的单箱双室简支箱梁,利用空间板壳数值方法和本文解析解方法,研究了满跨均布载荷和跨中集中力作用下截面的剪力滞分布规律. 结果表明,本文提出的剪力滞翘曲位移模式能够反映双室箱梁各翼板间剪力滞翘曲的差异,本文解析解与有限元数值解吻合良好. 双室箱梁中腹板部位顶、底板处的剪力滞效应与边腹板部位有一定差异,对算例结构,中腹板部位的顶、底板应力小于边腹板部位的应力.     

EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES

IntroductionRecently,compositestructureshavereceivedwideapplicationsinmodernindustriesincludingastronavigation ,aviation ,petroleumandchemicalindustry ,etc.However,thiskindofmaterialsgenerallyhavethepropertiesofviscoelasticitywiththeapparentcreepphenomenonandrelaxationbehaviors.Moreover,variousdamagewillemergeinthestructuresundertheactionofloading ,temperatureandenvironment.Damagemakesthemechanicalbehaviorsdeteriorategraduallybeforethefailure .Damageeffectswillsoftenthestiffnessofthestructure…     

Axisymmetric buckling of the circular annular nanoplates using finite difference method

In recent years nanostructures have been used in a vast number of applications, so the study of the mechanical behavior of such structures could be of interest. In the present study, the buckling behavior of circular annular plates and solid disks under uniform compression has been surveyed for several combinations of boundary conditions using the finite difference method. The affects of nonlocal parameter and the plate size have been studied for each combination of boundary conditions. The obtained results are in good agreement with the other studies and the reality. The results also convince that the finite difference method is a powerful method for solving the problems corresponding to nanoplate mechanical behaviors.