对边简支载流矩形薄板在电磁场中的稳定性分析

针对对边简支、另一对边固定载流矩形薄板,利用Mathieu方程解的稳定性,研究在电磁场与机械荷载共同作用下的磁弹性稳定性问题。在导出载流薄板在电磁场与机械荷载共同作用下的磁弹性动力稳定方程的基础上,应用Galerkin原理将稳定方程整理为Mathieu方程的标准形式,并将其归结为对Mathieu方程的求解问题。利用Mathieu方程系数、 的本征值关系,得出载流薄板磁弹性动力稳定临界状态的判别方程,并给出当 为小激励时的稳定区域图,以及Mathieu方程稳定解区域和非稳定解区域的分界。最后通过具体数值算例,给出该矩形薄板的磁弹性动力失稳临界状态与相关参量之间的关系曲线。研究结果表明,变化电磁场和通电电流的参数,可以改变电磁力的状态,从而达到控制载流薄板的变形,应力、应变状态及其稳定性的目的。     

三边简支载流薄板在交变磁场中的稳定性分析

针对三边简支、一边自由的载流矩形薄板,利用马丢方程解的稳定性,研究在交变磁场与机械载荷共同作用下的磁弹性稳定性问题.在导出载流薄板在电磁场与机械载荷共同作用下的磁弹性动力稳定方程的基础上,应用伽辽金原理将方程整理为马丢方程的标准形式.利用马丢方程系数的本征值关系,得出载流薄板磁弹性动力失稳临界状态的判别方程.通过具体算例,给出该矩形薄板在交变磁场中,动力失稳临界状态与相关参量之间的关系曲线及变化规律,并与均匀磁场中情形相比较.研究结果表明:变化电磁场的性质和大小,改变通电电流参数,均可改变电磁力的状态,从而达到控制载流薄板稳定性的目的.     

耦合场中弹性圆形薄板在混沌状态下的应力分析

在给出圆薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上,得到在横向稳恒磁场、环向电流和机械载荷共同作用下简支圆薄板的振动方程,并采用四阶Runge-Kutta法求解方程,得出圆板的弹性变形及应力状态.通过变化磁感应强度和电流密度,使系统由周期状态进入混沌状态;由分岔图与最大Lyaponov指数图判定系统是否进入混沌状态;并讨论磁场与电流对系统应力状态的影响.     

Dynamic stability of ferromagnetic plate under transverse magnetic field and in-plane periodic compression

The dynamic stability of a soft ferromagnetic rectangular and simply supported plate immersed in an applied transverse magnetic field, as well as subjected to an in-plane periodic compression is presented in this paper. The fundamental equations involving magnetoelastic interaction and magnetic damping effect for the ferromagnetic plate are developed. In the theoretical model, the expression of induced magnetic force is based on a generalized magnetoelastic variational model, and the magnetic damping is due to the Lorentz body force arising from eddy current in the ferromagnetic material. By means of a linearized magnetoelastic theory and perturbation technique, the motion equation of the ferromagnetic plate is reduced to a damped Mathieu's equation and solved. The dynamic stability of the magnetoelastic system without in-plane compression is theoretically analyzed first, to show that there exist two stable states: magnetic damped stable oscillation, and over-damped asymptotically stable motion before static divergence instability of the ferromagnetic plate occurs. The dynamic instability and stability regions for the parametric excitation of the ferromagnetic plate due to the harmonically excited in-plane compression are obtained next. The effects of magnetic damping and excitation frequency of the in-plane periodic compression on the stability regions are discussed in detail.     

Buckling of antisymmetric cross- and angle-ply laminated plates

A system of three well-known equations of equilibrium governing the buckling response of arbitrarily laminated composite plates is reduced to a single eighth order partial differential equation in terms of a displacement function. This equation is then solved in closed form to predict the buckling response of antisymmetric cross- and angle-ply plates for different boundary conditions. The effect of various plate parameters including the effect of coupling between inplane extension and out of plane bending upon the buckling response of composite plates is discussed. The results are presented in nondimensional graphical form.     

Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators

This paper deals with the nonlinear vibration and dynamic response of simply supported shear deformable cross-ply laminated plates with piezoelectric actuators subjected to mechanical, electrical and thermal loads. The material properties are assumed to be independent of the temperature and electric field. Theoretical formulations are based on the higher order shear deformation plate theory and general von Kármán-type equation, which includes thermo-piezoelectric effects. Due to the bending and stretching coupling effects, a nonlinear static problem is first solved to determine the pre-vibration deformation caused by temperature field and control voltage. By adding an incremental dynamic state to the pre-vibration state, the equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of hybrid laminated plates. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply laminated plates. The results presented show the effects of temperature rise, applied voltage and stacking sequence on the nonlinear vibration and dynamic response of the plates.     

Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method

In this paper, a finite element formulation is developed for analyzing the axisymmetric thermal buckling of FGM annular plates of variable thickness subjected to thermal loads generally distributed nonuniformly along the plate radial coordinate. The FGM assumed to be isotropic with material properties graded in the thickness direction according to a simple power-law in terms of the plate thickness coordinate, and has symmetry with respect to the plate midplane. At first, the pre-buckling plane elasticity problem is developed and solved using the finite element method, to determine the distribution of the pre-buckling in-plane forces in terms of the temperature rise distribution. Subsequently, based on Kierchhoff plate theory and using the principle of minimum total potential energy, the weak form of the differential equation governing the plate thermal stability is derived, then by employing the finite element method, the stability equations are solved numerically to evaluate the thermal buckling load factor. Convergence and validation of the presented finite element model are investigated by comparing the numerical results with those available in the literature. Parametric studies are carried out to cover the effects of parameters including thickness-to-radius ratio, taper parameter and boundary conditions on the thermal buckling load factor of the plates.     

载流圆板的磁弹性随机振动

分析载流圆板在磁场中的磁弹性随机振动问题。根据薄板、薄壳体的磁弹性运动方程和连续体的随机振动理论,导出在磁场环境中圆板的磁弹性随机振动方程。对磁场中的载流圆板进行随机响应分析,得到圆板位移响应的自相关函数、功率谱密度函数及均值函数等数字特征。通过具体算例,对处于外加磁场中通入平稳随机电流的导电圆板,计算其位移响应的功率谱密度函数。     

Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads

In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin's approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented.     

The field of a finite defect in a plate

An equation for determining the magnetic field of a plate inside which there is a cavity of finite dimensions with a smooth boundary has been obtained on the basis of the integro-differential equation of magnetostatics. A particular problem has been solved for a spherical cavity and an external uniform magnetizing field directed parallel to the plate surface.     

含裂纹板断裂韧度厚度效应的理论与应用

从理论角度对断裂韧度厚度效应进行了研究。在线弹性断裂力学与含裂纹板的二维位移场的基础上,给出分离变量型的具有待定函数的三维位移场的表达式,进而通过几何方程与物理方程获取三维应变场和三维应力场。进一步,通过虚位移原理,使用变分方法建立待定函数所应满足的支配方程与边界条件,从而确定待定函数。基于上述分析,建立一个断裂韧度与试样厚度关系的理论表达式。最后通过两种试验材料LY12CZ(L-T)与TC4(L-T)进行了验证。     

电磁弹性板中的Lamb波传播特性分析

用状态空间方法将电磁弹性材料中质点运动的广义位移和应力作为状态变量，结合本构方程和平衡方程，得到质点运动的状态方程；获得状态方程的通解后，利用Lamb波存在的边界条件，求出波传播的频散曲线及模态参数。所提方法推导过程简单直观，程序编制方便。以双层电磁弹性板为对象，计算了其频散曲线及模态，结果表明，电磁弹性耦合影响电势与磁势分布，而对频散特征和弹性位移影响很小。     

磁场中轴向运动导电板磁弹性主共振分析

给出轴向运动薄板动能、应变能以及电磁力虚功的表达形式。应用哈密顿变分原理,推得横向磁场中轴向运动条形导电薄板的非线性磁弹性振动方程。针对对边简支边界约束条件,通过位移函数的设定并应用伽辽金积分法,得到三阶位移展开形式下轴向运动板的非线性振动微分方程组。利用多尺度法对系统的主共振问题进行求解,分别得到三种频率关系条件下关于稳态解的幅频响应方程。依据李雅普诺夫稳定性理论对解的稳定性进行分析,得到相应的稳定性判别式。通过数值算例,得到轴向速度、磁感应强度、激励力幅值及板厚不同时的振幅变化规律曲线图,分析不同参量对共振幅值和非线性特征的影响,并对不同频率关系进行比较。     

含裂纹板断裂韧度厚度效应的理论研究

从理论角度对断裂韧度厚度效应进行研究。在线弹性断裂力学与含裂纹板的二维位移场的基础上，给出分离变量型的具有待定函数的三维位移场的表达式，进而通过几何方程与物理方程获取三维应变场和三维应力场。进一步，通过虚位移原理，使用变分方法建立待定函数所应满足的支配方程与边界条件，从而确定待定函数。基于上述分析，建立一个断裂韧度与试样厚度关系的理论表达式。最后通过两种试验材料LY12CZ（L-T）与TC4（L-T）进行验证。     

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NON- CONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.     

基于图像差分的精密畸变校正研究

图像畸变是影响视觉检测精度的关键因素.通过图像差分建立畸变场微分方程,提出了摄像机光学成像系统畸变场微分方程参数的理论计算方法,实现了基于图像差分的精密视觉检测.首先给出差分成像方式及图像畸变场微分方程建立方法,然后高精度标定摄像机确定畸变场微分方程理想平移量参数,改进Harris角点提取法使其达到亚像素精度,再采用SAD角点特征匹配法确定畸变场微分方程局部位移量参数,最后利用Nelder-Mead-Simplex优化策略实现畸变场微分方程求解,获得图像畸变完整精确的描述.在石油管螺纹梳刀上的实验表明,该方法检测精度高,且仅需要2个平移自由度,极大地简化了图像检测机械装置.     

Chaotic responses of curved plate under sinusoidal loading

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clampedfreeclampedfree plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK.-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. l) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.     

Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations

The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.     

控制棒驱动机构的分段非线性动态特性

控制棒驱动机构是核电厂中的重要安全设备,其动态特性是研究和设计该机构的关键.首先建立控制棒驱动机构的磁路和电路方程.然后基于控制棒驱动机构动态提升过程分析,将运动过程分为3个阶段,并分别推导出各阶段的磁路-电路-机械运动耦合方程.采用解析解和数值仿真两种方法相结合,求解了控制棒驱动机构分段的非线性方程.最终得出动态过程中电流、电磁力、衔铁速度、衔铁位移和衔铁加速度等一系列反应控制棒驱动机构动态特性的参数随时间的变化曲线,并得到了实验验证.     

Moving interfacial crack between two dissimilar soft ferromagnetic materials in uniform magnetic field

This paper presents the dynamic magnetoelastic stress intensity factors of a Yoffe-type moving crack at the interface between two dissimilar soft ferromagnetic elastic half-planes. The solids are subjected to a uniform in-plane magnetic field and the crack is opened by internal normal and shear tractions. The problem is considered within the framework of linear magnetoelasticity. By application of the Fourier integral transform, the mixed boundary problem is reduced to a pair of integral equations of the second kind with Cauchy-type singularities. The singular integral equations are solved by means of a Jacobi polynomial expansion method. For a particular case, closed-form solutions are obtained. It is shown that the magnetoelastic stress intensity factors depend on the moving velocity of the crack, the magnetic field and the magnetoelastic properties of the materials.