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。     

四边简支载流矩形薄板的磁弹性动力屈曲分析

在载流薄板的磁弹性非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上,导出四边简支载流矩形薄板在电磁场与机械载荷共同作用下的磁弹性动力屈曲方程.应用Galerkin原理将该屈曲方程整理为Mathieu方程的标准形式,并利用Mathieu方程解的稳定区域与非稳定区域的分界,即方程系数的本征值关系,得出磁弹性问题屈曲临界状态的判别方程.通过具体算例,给出四边简支矩形板的磁弹性动力屈曲方程以及屈曲临界状态与相关参量之间的关系曲线,并对计算结果及其变化规律进行分析讨论.     

大挠度四边固定矩形薄板的磁弹性混沌运动

针对大挠度四边固定矩形薄板,研究其在机械载荷、电磁场耦合作用下的混沌运动。在板壳与磁弹性力学理论的基础上,推导出薄板在横向稳恒磁场和机械载荷共同作用下的非线性磁弹性耦合振动方程。利用Melnikov函数法,求出该动力系统Smale马蹄变换意义下出现混沌运动的条件,并对该系统振动方程进行数值模拟。通过具体算例,得到系统的分岔图、位移波形图、相图以及庞加莱截面图。讨论机械载荷、电磁场参数对系统混沌运动的影响,由仿真结果可知,通过变化机械载荷、电磁场参数,可以控制系统的振动特性。     

横向磁场中载流薄板模态截断问题研究

根据板壳理论与磁弹性理论,在不考虑感应电场,仅考虑机械场与磁场的相互耦合作用情况下,在薄板非线性运动方程、物理方程、几何方程、洛仑兹力表达式及电动力学方程的基础上,建立在横向磁场和机械载荷共同作用下的大挠度载流矩形薄板的非线性运动方程.以三边简支一边自由矩形薄板为例,给出板的单模态运动方程和双模态运动方程.利用数学计算软件,采用四阶Ronger-Kuta数值方法,模拟非线性系统在单、双模态位移模式下的时程图、庞加莱截面图、相轨迹图.讨论电磁参数和外载荷参数对板在单、双模态位移模式下的非线性行为的影响及差异.结果表明,这些参数对薄板的运动有较大的影响,通过调整电磁参数可控制系统的混沌运动,以实现对系统运动特性的控制.     

载流条形薄板的非线性应力与变形分析

在所建立的载流条形薄板的非线性磁弹性基本方程--运动方程、几何方程、物理方程和电动力学方程的基础上,通过变量代换,整理成含有10个基本未知函数的标准柯西型方程.采用差分及准线性化方法,将含有10个基本未知函数的偏微分方程组,变换成能用离散正交法编程求解的准线性微分方程组.由此计算分析两边简支条形薄板在电磁场和机械载荷耦合作用下的应力与变形,研究侧向电流和外磁场强度对载流条形薄板的磁弹性效应.     

热、力、磁耦合作用下大挠度矩形薄板的分岔与混沌特性

针对大挠度三边简支一边自由矩形薄板,研究其在热、力、磁耦合作用下的分岔与混沌运动特性。在板壳与磁弹性力学理论的基础上,导出薄板在耦合场共同作用下的非线性控制方程,利用伽辽金原理得到薄板的非线性热磁弹性耦合振动方程。由次谐轨道Melnikov函数法,求出该动力系统Smale马蹄变换意义下出现混沌运动的阈值条件,并对该系统振动方程进行数值模拟,得到系统随机械载荷、电磁场以及温度场的参数变化的分岔图及相应的位移波形图、相平面轨迹图及庞加莱截面图。由仿真结果可知,在热、力、磁耦合作用下的大挠度矩形薄板系统的振动方程具有明显的非线性,运动特性比较复杂,呈现出非常丰富的混沌与分岔现象。通过变化机械载荷、电磁场和温度场参数,可以控制系统的振动特性。     

四边简支载流矩形薄板在磁场中的随机分岔

根据板壳力学与磁弹性力学理论,建立了在横向磁场与机械载荷共同作用下的四边简支载流矩形薄板的非线性随机振动模型,利用Galerkin变分法将其化简为非线性微分动力学方程。其次使用拟不可积Hamilton系统的随机平均理论将方程等价为一个一维的It随机微分方程,并通过计算该系统的最大Lyapunov指数来判断该系统的局部稳定性,同时利用奇异边界理论判断其系统的全局稳定性。最后通过稳态概率密度函数的变化研究了系统参数对发生的随机Hopf分岔的影响。并采用数值模拟对理论分析进行了验证。     

周边固定载流壳体的热磁弹性分析

针对磁场环境中周边固定载流壳体的热磁弹性问题进行研究。通过运动方程、几何方程、物理方程及电动力学方程,给出了载流壳体在机械场、电磁场、温度场作用下的基本方程。建立了包含10个基本未知量的非线性偏微分方程组,采用Newmark稳定有限等差式,获得可以利用离散正交法求解的标准型。对于周边固定壳体,导出了Lorentz力表达式、温度场和温度场积分特征值。分析了载流壳体应力、温度及变形随外加电磁参量的变化规律,通过实例计算,证实了改变电场、磁场、力场的参数能够实现对板壳应力、应变、温度的控制。为改变在电磁场环境中板壳结构的工作状态及强度研究提供理论分析和数值计算方法。     

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。     

横向磁场中导电圆柱壳体的超谐波共振

研究磁场环境中受机械载荷作用圆柱薄壳的三阶超谐波共振问题.在给出横向磁场和机械动载共同作用下圆柱薄壳的振动方程基础上,应用伽辽金积分法,并进行无量纲化处理,进一步导出相应的非线性磁弹性振动微分方程.采用多尺度法对三阶超谐波共振问题进行求解,得到稳态运动下的幅频响应方程与解的稳定性判别式.通过算例,给出几种情况下反映振幅...     

MAGNETIC-ELASTIC BUCKLING OF A THIN CURRENT CARRYING PLATE SIMPLY SUPPORTED AT THREE EDGES

The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin＇s method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients 2 and r/ in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.     

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.     

Inertia effects in magnetohydrodynamic porous conducting thrust bearings

The effects of fluid inertia in an externally pressurized porous conducting thrust bearing in the presence of a transversely applied magnetic field are theoretically analysed. The load capacity increases and the flow flux decreases as the fluid inertia term, the applied magnetic field or the conductivity of the plate increases. Both the load capacity and the flow flux increase with increasing permeability of the plate.     

机械载荷作用下单边裂纹电热止裂的实验研究

采用实验分析和数值分析的方法，研究分析了在等值拉伸机械载荷作用下的、对带有单边裂纹导电薄板进行电热止裂的止裂效果。并且与文献[1]给出的通电瞬间由温度产生的应力场与机械载荷产生的应力场叠加的理论计算结果进行了比较。通过算例比较，表明了理论分析、数值计算和实验研究结果有较好的一致性。     

横向磁场中轴向运动条形导电板的组合共振

给出了磁场中轴向运动条形导电薄板的动能、应变能以及电磁力表达形式,应用哈密顿变分原理,推导出了轴向运动导电板的非线性磁弹性振动微分方程。通过位移函数的设定并应用伽辽金积分法,得到横向磁场中对边简支边界约束轴向运动条形板的达芬型磁弹性振动方程。利用多尺度法进行求解,得到组合共振发生时确定共振幅值的幅频响应方程,并给出定常稳定解的判定条件。通过数值算例,得到轴向运动速度、磁感应强度、激励力和轴向拉力等参量不同时的振幅变化规律曲线图以及系统振动的时程响应图和相图,分析了不同参量对共振幅值和非线性特征的影响,并对系统呈现的概周期和混沌运动行为变化规律进行了分析。     

Effect of Using Current-Carrying-Wire Models in the Design of Hydrodynamic Journal Bearings Lubricated with Ferrofluid

Based on the momentum and continuity equations for ferrofluid under an applied magnetic field, a modified Reynolds equation has been obtained. Assuming linear behavior for the magnetic material of the ferrofluid, the magnetic force was calculated. The magnetic pressure resulting from the magnetic force was incorporated into the Reynolds equation and it was not separately treated. The derived Reynolds equation can be applied for any magnetic field distribution model. Using different magnetic field models, the equation has been solved numerically by the finite difference technique with an appropriate iterative technique and pressure distributions have been obtained. The boundary shapes of the load-carrying active regions and cavitation regions could be then determined. The solution gives the bearing performance characteristics, namely; load-carrying capacity, attitude angle of the journal center, friction coefficient and bearing side leakage. The displaced current-carrying infinitely long wire gives a field distribution with a gradient in the circumferential direction. Two novel field models are introduced. The concentric finite current-carrying-wire model gives an axially symmetric magnetic field with a gradient in the axial direction. Axial and circumferential gradients are obtained using displaced finite wire model. The effect of these magnetic models and their design parameters on the overall bearing performance characteristics has been studied. The results concluded that the magnetic lubrication provides a higher load capacity and a reduced friction coefficient, compared with a conventional lubricated bearing. The other bearing characteristics depends on the applied field model. An axially symmetric applied field, with its sealing magnetic force, leads to a decrease in the side leakage, such that the bearing may operate without side leakage by appropriate design of the field.     

轴向运动矩形板的谐波共振与稳定性分析

针对轴向运动矩形薄板的非线性振动问题,在给出薄板运动的动能和应变能的基础上,应用哈密顿变分原理,推得几何非线性下轴向运动薄板的非线性振动方程。通过位移函数和应力函数的设定,并应用伽辽金积分法,得到四边简支边界约束条件下受横向激励载荷作用轴向运动薄板的达芬型振动方程。利用多尺度法对系统的非线性谐波共振问题进行求解,得到稳态运动下关于共振幅值的幅频响应方程。依据李雅普诺夫运动稳定性理论对定常解的稳定性进行分析,得到解的稳定性判别式。通过数值算例,得到不同横向载荷和轴向速度下共振幅值的变化规律曲线图以及对应的相图,讨论分岔点变化以及倍周期运动规律,分析横向激励载荷和轴向运动速度对系统非线性动力学行为的影响。     

Nonlinear resonance of the rotating circular plate under static loads in magnetic field

The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.     

Characterization of magnetic field rotation of steel sheet under uniaxial stress

The rotation of magnetic field strength on a steel plate caused by uniaxial stress has been known for years. However, previous study investigated this phenomenon rather experimentally using hall plates and searching coils. This paper presents a fundamental study of magnetic anisotropy based on an analytic model using magnetic scalar potential. The magnetic field strength of the steel sheet can be solved mathematically by performing a special coordinate transformation. The calculated angular displacement due to stress induced magnetic anisotropy was later found to be highly consistent with FEM simulation results. Finally, the quantization of magnetic field rotation of an electrical sheet (ES) under variable tension stress was performed. Using 50CS470 ES sheet as the testing sample, it was discovered the rotation as much as 25° occurred when 50 MPa tension load was applied, corresponding to a permeability ratio of 2.8.