On the motion stability of an airplane on a runway under wind loading

A nonlinear mathematical model is constructed for an airplane in high-speed plane-parallel motion along a runway when the airplane's weight exceeds slightly the lift of its wings in the presence of a cross wind. The airplane is considered a two-weight mechanical object. A system of second-order equations is obtained that describes the airplane's behavior. A system of three phase variables is suggested in which the dynamics of transverse motion is described by a set of three second-order equations. A stationary solution of this system is obtained. A stability criterion for the plane-parallel motion of the airplane is established using the Routh-Hurwitz criterion. Analysis of the data of other authors indicates that the mathematical model is adequate for some objects of aviation technology. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 101–107, October, 1999.     

Bingham Viscoplastic as a Limit of Non-Newtonian Fluids

A new formulation is proposed for the equations of the Bingham viscoplastic. Global existence of x--periodic solutions is proved. A uniqueness theorem is established in the two-dimensional case. A relation with the G. Duvaut--J. L. Lions variational inequality is discussed, and a result on equivalence is obtained. The question of interaction between fluid-rigid phases is studied when the initial state is rigid. A free-boundary problem that describes two-phase one-dimensional flows is considered.     

气泡在液体中运动过程的数值模拟

本文用数值方法预测气泡在液体中的百定常运动。运用位标函数进行界面的隐含跟踪并且与有限体积法相结合构成一种可行的计算方法。本文方法允许在界面处存在很大的物性差，而且较容易将表面张力引入控制方程。我们对气液两相流中单个气泡的运动进行了计算，得到了与实验结果符合很好的数值结果。     

Correlation of finite strain measures

A numerical scheme for correlating any two finite strain measures is given, and situations in which such a scheme might be used are introduced. A check is established by comparison with the Reiner-Hanin solution of the Almansi-to-Hencky conversion. A numerical example is provided.     

Development of an initially localized perturbation in the interaction of a cold beam with a dielectric

A homogeneous dielectric with a cold beam of charged particles passing through at a velocity greater than the velocity of the electromagnetic waves in the dielectric is considered. A smallperturbation instability in the form of a plane wave is built up. The structure of the perturbed state being developed from a small region of space is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 123–128, May–June, 1978.The author is grateful to A. G. Kulikovskii and A. A. Barmin for valuable comments and remarks about this research.     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.     

Selection of prestress for optimal dynamic/control performance of tensegrity structures

This paper concerns prestress optimization of a tensegrity structure for its optimal LQR performance. A linearized dynamic model of the structure is derived in which the force-density variables that parameterize the prestress of the structure appear linearly. A feasible region for these parameters is defined in terms of the extreme directions of the prestress cone. A numerical method for computing this basis for a structure prestress cone is proposed. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.     

The exponential asymptotic solution of differential equation

In this paper, the exponential asymptotic solution (E.A.S.) of differential equation is discussed. Firstly, E.A.S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E.A.S. are found out. Next, E.A.S. in matched asymptotic method is discussed. Finally, some examples are given.     

Stress analysis of a flexible ring plate with circumferentially varying stiffness in a magnetic field

A problem of magnetoelasticity for a ring plate of variable stiffness is solved. A governing system of nonlinear differential equations is derived. It describes the stress–strain state of flexible conductive plates in nonstationary mechanical and electromagnetic fields. A numerical example is given. The stress state of a flexible plate of variable stiffness in a magnetic field is analyzed     

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated.A new stability condition is presented based on the Lyapunov-Krasovskii method,which is dependent on the amount of delay.A result is given in the form ofa linear matrix inequdlity,and the admitted upper bound of the delay can be easily obtained.The time delay dependent and independent results can be obtained,which include flome previously published resultS.A numerical example is given to show the effectiveness of the main results.     

Uncoupled finite element solution of biharmonic problems for vector potentials

A method for the uncoupled solution of three-dimensional biharmonic problems for the vector potential in viscous incompressible flow is presented. The strategy applied in a previous work on vector Poisson equations is employed to reduce the vector fourth-order problem to a sequence of scalar biharmonic problems. A finite element aimed at the implementation of the method in a discrete version is considered. A conjugate gradient algorithm which is particularly efficient for the uncoupled solution method is also described.     

双同步混沌吸引子动力系统中的筛形域

解析证明耦合映射混沌同步系统中的两个同步混沌吸引子的吸引域是筛形域．在特定耦合参数区间中，解析证明这两个同步混沌吸引子的吸引域不仅被无穷远吸引子的吸引域筛形，还通过数值证明它们的吸引域彼此互相筛形，展示出类似于Wada性质的特征．但进一步的讨论表明这种复杂的被两个(或更多)吸引域共同筛形的结构并不是Wada域，而是由于筛形分岔和筛形域局部—全局分岔导致的．     

A fast and general upper-bound limit analysis approach for out-of-plane loaded masonry walls

A new general approach for the limit analysis of out-of-plane loaded masonry walls based on an upper bound formulation is presented. A given masonry wall of generic form presenting openings of arbitrary shape is described through its Non-Uniform Rational B-Spline (NURBS) representation in the three-dimensional Euclidean space. A lattice of nodes is defined in the parameters space together with possible fracture lines. An initial set of rigid elements initially subdividing the original wall geometry is identified accordingly. A homogenized upper bound limit analysis formulation, which takes into account the main characteristics of masonry material such as very low resistance in traction and anisotropic behavior is deduced. Moreover the effect of vertical loads and membrane stresses is considered, assuming internal dissipation allowed exclusively along element edges. A number of technically meaningful examples prove that a good estimate of the collapse load multiplier is obtained, provided that the initial net of yield lines is suitably adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism.     

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investi- gating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen＇s systems. A simulation example is presented to illustrate its effectiveness.     

Motion of the interface of two fluids with formation of a region of two-phase flow

A study is made of the problem of the displacement of one fluid by another with the formation of a region of combined flow in the case of an elastic flow regime in the region of the displaced fluid. A self-similar solution is constructed for the flow equations averaged with respect to the vertical coordinate. A numerical algorithm is developed for determining the saturation in the region of the mixture, the pressure, and also the position and shape of the interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 78–83, October–December, 1981.We thank A. A. Barmin for a helpful discussion of the work.     

On the approximate computation of extreme eigenvalues and the condition number of nonsingular matrices

From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determinedby the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a by-product in the computation of the conjugate gradient ifa computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on A~T A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.     

Space-time description of stationary and homogeneous turbulence

A system of two functional equations is derived, describing turbulence that is stationary in time and homogeneous in space. A theory of perturbations is formulated and the character of hypotheses concerning termination of the series involved is sharpened.     

板壳结构弹塑性稳定性的有限元分析

构造了20参数圆柱壳拟协调单元,同时采用分层模型的弹塑性稳定性分析.根据塑性屈曲的Stowell形变理论,用基于切线刚度矩阵的增量法和修正的Newton-Raphson方法,计算屈曲前的弹塑性内力分布,并用逆幂迭代法求解弹塑性屈曲荷载.     

A finite deformation theory for shear-strained prismatical bodies with non-linear stress-strain law

A finite deformation theory for the longitudinal shear is formulated for homogeneous and isotropic bodies with non-linear stress-strain law. A new set of simplified field equations, which is valid in the case of some deviations from Hooke's law. is derived systematically with the aid of the method of order estimation. A circular hole in an infinite body under uniform longitudinal shear is treated for illustration purposes.     

Intrinsic relationship of vorticity between modes A and B in the wake of a bluff body

The intrinsic physical relationship of vorticity between modes A and B in the three-dimensional wake transition is investigated.Direct numerical simulations for the flow past a square-section cylinder are carried out at Reynolds numbers of 180 and 250,associated with modes A and B,respectively.Based on the analysis of spacial distributions of vorticity in the near wake,characteristics of the vertical vorticity in modes A and B are identified.Moreover,the relationship of three vorticity components with specific signs is summarized into two sign laws,as intrinsic physical relationships between two instability modes.By the theory of vortex-induced vortex,such two sign laws confirm that there are two and only two kinds of vortex-shedding patterns in the near wake,just corresponding to modes A and B.In brief,along the free stream direction,mode A can be described by the parallel shedding vertical vortices with the same sign,while mode B is described by the parallel shedding streamwise vortices with the same sign.Finally,it is found out that the|-type vortex is a basic kind of vortex structure in both modes A and B.