EMS磁浮列车车/轨耦合系统的分岔现象研究

通过分析EMS磁浮列车系统的Hopf分岔, 研究车轨耦合系统对应的轨道固有频率稳定范围. 采用串级控制悬浮控制器，给出控制器参数与特征频率的关系，在控制器稳定的前提下利用 数值算法计算在系统参数一定、轨道固有频率变化条件下所对应的Hopf分岔点，结合仿真方法 得出轨道固有频率的稳定范围，定性说明了系统载荷、控制器频率、二次系刚度与轨道固有 频率之间的变化关系.     

Cooling of liquid in the presence of natural convection

At present a large number of theoretical and experimental studies have been devoted to the problems of initiation and development of natural convection [1–4]. However, so far investigators have not paid much attention to the study of the damping characteristics of natural convection. In the present work the problem of cooling of a liquid in the presence of natural convection is solved by numerical methods.     

孤立波作用下细长港响应的数值研究

采用Boussinesq数值波浪模型,模拟了不同波高的孤立波分别对常水深和变水深细长港作用时港内的响应.对数值模型的结果进行小波分析和频谱分析并与现有的理论值比较.结果表明,孤立波传入一侧为开敞水域的细长港时,港内激发振荡的能量主要集中在细长港前三个自振模态上,港口的响应频率与理论固有频率非常接近,这为估算细长港池的固有频率提供了一种可行性方法.     

An efficient Legendre-Galerkin spectral method for the natural convection in two-dimensional cavities

An efficient numerical method is developed for solving the natural convection in two-dimensional cavities. The numerical scheme is proposed by using second-order projection scheme in time direction and Legendre-spectral in spatial variable of the incompressible flow. Finally, a series of numerical examples are presented to demonstrate the efficiency of our algorithm. The numerical strategies developed in this article could be readily applied to study other incompressible fluid problems.     

Calculation of higher natural frequencies of simply supported elastic composite beams using Riccati matrix method

A composite beam is composed of an upper slab and a lower beam connected at the interface by shear transmitting studs. In this paper, an improved and efficient numerical model for the calculation of higher natural frequencies of an elastic composite beam is presented. The numerical model uses the Riccati transfer matrix method. First, the exact field transfer matrix for an element of the beam is represented using the combination of the Analog Beam Method and the transfer matrix method. Second, applying Riccati method to the beam system, the natural frequencies can be easily calculated. The advantage of the present model is to overcome the numerical instabilities of the ordinary transfer matrix method, especially when calculating the higher natural frequencies of structures. A numerical example is given to illustrate and compare the results with those available from other methods. Finally, a parametric study is given to examine the effect of various parameters of the elastic composite beam on its free vibration behavior.     

A numerical study of the applicability of the Boussinesq approximation for a fluid-saturated porous medium

The regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid-saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water-saturated porous region.     

自然单元法研究进展

自然单元法是一种基于Voronoi图和Delaunay三角化几何结构,以自然邻点插值为试函数的一种新型数值方法.其既具有无网格方法和经典有限元方法的优点,又克服了两者的一些缺陷,是一种发展前景广阔的求解微分方程的数值方法.自然单元法的形函数满足插值性质,可以像有限元法一样直接施加本质边界条件,不存在基于移动最小二乘拟合的无网格方法不能直接施加本质边界条件的难题.由于自然单元法是无网格方法,可以方便处理有限元方法较难处理的一些问题,例如移动边界和大变形等问题.自然单元法与其他数值方法的最根本区别于其插值格式的不同.将自然邻点插值用于Galerkin过程,就得到基于Voronoi结构的自然单元Galerkin法.自然邻点插值有自然邻点Sibson插值和Laplace插值(非Sibson插值)两种.Laplace插值比Sibson插值在计算上要简单的多,并且不论对凸的或非凸的区域都能精确施加本质边界条件.以Laplace插值为试函数的自然单元法在数值实施上比以Sibson插值为试函数的自然单元法简单.本文对基于Voronoi结构的自然邻点插值和自然单元法的基本思想作了介绍,综述了国内外关于自然单元法的研究成果,总结了自然单元法的优点和尚需解决的问题.      

Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

The effect of the stiffness of ribs on the minimum natural frequencies and critical stresses of axially compressed open cylindrical shells reinforced with a quasiregular set of longitudinal ribs is analyzed by way of numerical examples. It is shown that the earlier discovered phenomenon of abrupt decrease in the minimum frequencies is independent of rib stiffness for certain modes and a small number of ribs     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板，考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况，应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件，利用伽辽金法得到了横向非线性固有振动方程，并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程，得出非线性固有频率表达式．通过算例，分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明，非线性固有频率随金属含量的增加而降低；随转速和圆板厚度的增大而升高；随功能梯度圆板表面温度的升高而降低．     

Numerical convergence studies of the mixed finite element method for natural convection flow in a fluid-saturated porous medium

This paper describes a numerical approximation scheme for the natural convection (NC) flow in a fluid-saturated porous medium. Our formulation of the problem is based on the mixed finite element method (FEM). Using the so-called consistent splitting scheme, a second-order accuracy in time and in space is verified by the numerical calculation. The resulting flow patterns and heat transfer for different Rayleigh numbers, Darcy numbers and porosities are numerically studied by the proposed scheme.     

Parametric study of a two degree-of-freedom cylinder subject to vortex-induced vibrations

This numerical work is an attempt to build accurate and continuous response surfaces of two degree-of-freedom vortex-induced vibrations (VIV) of flexibly mounted cylinders for a wide range of transverse and in-line natural frequencies. We consider both the structure and the flow to be two-dimensional. The structure has a low mass damping, with the transverse and in-line mass ratios as well as the transverse and in-line damping coefficients being equal. The goal is to capture the sensitivity of the response to the change in the natural frequencies of the structure. The system is studied for a wide range of transverse natural frequency within the synchronization region. The extent of variation of the in-line natural frequency is chosen to be larger than the one of the transverse natural frequency in order to favor multi-modal responses. No preferred frequencies are emphasized within the intervals of study. The numerical technique uses a multi-element stochastic collocation method coupled to a spectral element based deterministic solver.     

Vibrations and Stability of Shallow Ribbed Shells with a Rectangular Planform

A technique is developed to determine the critical stresses and natural frequencies of shallow ribbed shells with a rectangular planform and the corresponding buckling wave and natural modes. The effect of discrete rib arrangement on these characteristics is studied by numerical examples.     

Difference scheme and numerical simulation based on mixed finite element method for natural convection problem

ntroductionLetΩ R2 beaboundeddomain .Weconsiderthefollowingnon_stationarynaturalconvectionproblem :Problem (Ⅰ )　Findu =(u1,u2 ) ,p ,andTsuchthat,foranyt1>0 ,ut- μΔu +(u· )u + p=λjT　　 ((x ,y ,t) ∈Ω× (0 ,t1) ) ,divu =0　　　　　　　　　 ((x ,y,t) ∈Ω× (0 ,t1) ) ,Tt-ΔT +λu· T =0　　 ((x,y,t) ∈Ω× (0 ,t1) ) ,u =0 ,T =0　　　　　　 ((x,y,t)∈ Ω× (0 ,t1) ) ,u(x ,y ,0 ) =0 ,　T(x,y,0 ) =f(x,y)　　 ((x,y) ∈Ω) ,whereuisthefluidvelocityvectorfield ,pthepressurefield ,Tthet…     

A two-phase,two-component model for natural convection in a porous medium

A numerical study of natural convection in a two-phase, two-component flow in a porous medium heated from below is presented. Interphase mass and energy transfer, latent heat and bouyancy effects are major physical features. This study extends earlier studies of natural convection based on single-phase, saturated porous medium models. The appearance of two-phase heat pipe zones in the flow has a marked effect on the fluid and heat flows as well as on the performance of the numerical methods. The numerical techniques for handling phase change, Jacobian construction and time step selection are discussed.     

Upper-bound limit analysis based on the natural element method

The natural element method (NEM) is a newly-developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic theorem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nonsmoothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.     

Free vibrations of square elastic tubes with a free end

The localized vibrations of a thin-walled square tube with a free end are studied. By means of asymptotic methods, an expression for the natural frequency is found. The asymptotic results agree well with the numerical results obtained using the Finite Element Method. The dependence of the natural frequency on the tube length is analyzed.     

固有频率法评估损伤的阈值研究

通过分析损伤可测性的影响因素,对固有频率法判断损伤阈值的估算方法进行了研究,并以 悬臂梁模型为例,应用该方法研究了悬臂梁的损伤阈值. 数值及理论计算的结果表明：在已 知频率测量精度及方法偏差时,该方法可以判别固有频率法损伤识别的阈值,在早期损伤阶 段,该方法判别的阈值与数值模拟结果吻合良好.     

封闭方腔内空气和水自然对流每一次分岔数值预报

采用二阶全展开ETG分裂步有限元方法,通过对流动拓扑的详细分析,在排除网格密度影响的基础上,结合二分法给出封闭方腔内空气和水两种典型流体自然对流发生第一次分岔时的临界Rayleigh数。计算结果表明,该方法可用于进行不同Prandtl数条件下方腔内自然对流流动第一次分岔的数值预报,可作为后续各阶分岔及转捩数值预报研究的基础。在相应的条件下,封闭方腔内空气比水更容易发生分岔,且空气的流动结构相对于水表现出一定的倾斜性。     

Natural frequencies of nonlinear vibration of axially moving beams

Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform of a series of data samples by means of digital computers. The governing equations of coupled planar of an axially moving beam are reduced to two nonlinear models of transverse vibration. Numerical schemes are respectively presented for the governing equations via the finite difference method under the simple support boundary condition. In this paper, time series of the discrete Fourier transform is defined as numerically solutions of three nonlinear governing equations, respectively. The standard FFT scheme is used to investigate the natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results are compared with the first two natural frequencies of linear free transverse vibration of an axially moving beam. And results indicate that the effect of the nonlinear coefficient on the first natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results also illustrate the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters.     

A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape

This paper deals with the static and dynamic analyses of multi-layered plates with discontinuities. The two-dimensional first-order shear deformation theory is used to derive the fundamental system of equations in terms of generalized displacements. The fundamental set, with its boundary conditions, is solved in its strong form. A new method termed strong formulation finite element method is considered in the present paper to solve this kind of plates. This numerical methodology is the cohesion of derivative evaluation of partial differential systems of equations and a domain sub-division. The numerical results in terms of natural frequencies and maximum deflections are compared to literature and to the same results obtained with a finite element code. The stability, accuracy and reliability of the present methodology is shown through several numerical applications.