The analysis of the orientation effect of non-linear flexible systems on performance of the pendulum absorber

In practical applications, many vibration absorbers are used to absorb oscillation of a structure, one of which is pendulum-type vibration absorbers. They are widely used in engineering applications where oscillations of a structure are constrained within a prescribed envelope. In this study, the primary structure consists of a flexible beam which has a single degree of freedom, and is subjected to a vertical sinusoidal base excitation. Non-linearity in the primary structure is due to large deflections. The rotation point of the pendulum-type absorber is attached to the tip of the primary structure. The primary structure and absorber together constitute a couple systems with two degrees of freedom. The primary objective of this study is to determine the effectiveness of pendulum-type passive vibration absorber attached to a primary structure whose orientation varies. In this study, the orientation at which the absorber is effective is established, and the factors that affect performance of the absorber are determined. The results are in good agreement with the experimental ones given in the literature.     

On the effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics

The effect of the nonparallelism of the boundary layer flow over a flat plate on its stability characteristics has been investigated by several authors, and it was claimed that the results of the theoretical calculations are already in good agreement with the experimental observations. However, this is not true. In this paper, this problem is reinvestigated, using two different methods. It is found that within the framework of linear theory, the theoretical results are in fact not in good agreement with the experimental observations. To settle this problem, nonlinear effect must be taken into consideration. Projects Supported by the Science Fund of the Chinese Academy of Sciences     

捷联式惯性导航系统惯性元件的设置与可靠性

本文对惯性元件的最佳冗余设置及其在飞行器上的布局与可靠性之间的关系进行了研究，建立了相应的可靠性数学模型，探讨了３／６（Ｇ）冗余惯性元件出现第三个故障时故障的检测与识别的方法。所得结果可供惯性导航系统可靠性分析及工程上应用。     

转轴上裂纹开闭模型的研究

本文提出了一种新的描述转轴裂纹开闭状态的数学模型,此模型描述了裂纹开、闭及过渡状态的持续过程,它将开裂纹、方波和余弦模型统一于同一模型中,它的使用不受动、静挠度关系的限制.用这个模型算得的裂纹轴刚度变化曲线与实验结果吻合程度比余弦和方波模型好.文中还以Jeffcott裂纹转子为例,对各模型进行了理论探讨.结果表明:当研究非同步运动时,本文模型与方波和余弦模型所得的解差别较大,且轴心位移矢量的方向角在静平衡位置处的波动,影响到所得响应的特性.而对同步运动,这种差别及影响都很小.     

数值模型内力影响面分析的机动法

本文提出并证明了普遍适用于以广义位移为独立变量的各种数值模型的内力影响面分析的机动算法原理。这一原理把内力影响面分析归结为求解在一个等价荷载作用下的结构位移场,并给出了得到等价荷载的方法。用本文方法得到的是结构某一点的内力的影响面,而且对数值模型来说,是精确解。作为本文原理的应用,用机动法分析了采用有限条模型的薄板的内力影响面,并给出了若干数值例子。     

On the role of nonlinearities in the Boussinesq-type wave equations

Longitudinal mechanical waves in biomembranes are described by a Boussinesq-type wave equation. It is shown that in this case the nonlinearities are of a different type compared with conventional models of solids. The governing equation analysed in this paper is the improved Heimburg–Jackson model with two dispersive terms. The soliton-type solutions of such a wave equation are found and analysed. The existence of solitons depends on the ratio of nonlinear terms and the width of solitons is governed by dispersive terms.     

On the Controllability of the Hydrostatic Stokes Equations

This paper is devoted to present some results on the controllability of the hydrostatic Stokes equations. The first main result of this paper states that the approximate null controllability of this system holds. This is proved whatever the boundary conditions are. Then, we extend this result to an exact null controllability result when the boundary conditions are ∂ _z u = 0 (the vertical derivative of the horizontal velocity) at the bottom.      

On use of the Dirac delta function in the vibration analysis of elastic structures

The Dirac delta function has often been employed to represent the amplitude of concentrated harmonic forces in the analysis of vibration of elastic structures such as beams and plates. It is known that this function, as represented by a truncated Fourier series, does not provide a true representation of a concentrated force, nevertheless, it is frequently employed and good convergence is usually, though not always, encountered in solutions thereby obtained. In this paper, the nature of the function is discussed and for illustrative purposes it is used to obtain series solutions for some selected beam and plate free vibration problems. In some cases problems are chosen for which exact solutions are already obtainable by analytical means. This permits powerful checks to be made on rates of convergence experienced when the series solutions are investigated. Rates of convergence are discussed in detail and it is explained why convergence is to be expected when analyzing certain families of problems when employing this function and a lack of convergence is to be expected in others.     

Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini??s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb??s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.     

On the criteria of the absolute convective stability for compressible fluids

The conditions under which natural convection is absent from compressible fluids are investigated. It is shown that in the parameter “Rayleigh number-given temperature difference” plane there is a domain in which convection occurs for neither Rayleigh numbers. It is proposed to refer to this domain as the absolute convective stability region and to name the criterion determining the boundary of this region the absolute convective stability criterion. The necessary, sufficient, and necessary and sufficient conditions of the absolute convective stability for a viscous compressible fluid are derived. It is shown that in the particular case in which the thermal properties of the fluid and the adiabatic gradient are constant, these conditions coincide with the Schwarzschild criterion.     

分流河道淤积与洞庭湖萎缩对长江洪灾的影响

1998年长江流域的特大洪水灾害表明，目前长江流域防洪体系在面临特大洪水时仍然显得比较脆弱．以长江中下游荆江洞庭湖地区为背景，运用有限体积计算方法建立了一维河道和二维湖泊交错的复杂水系洪水演进数值模型，细致分析了由于分流河道淤积以及洞庭湖萎缩对长江洪灾的影响．得出长江分流河道和洞庭湖由于泥沙淤积产生的萎缩将造成长江干流河道洪水期间水位抬升，从而加重长江的洪水灾害．其结论可为长江中下游地区的洪水治理提出建设性意见．     

Solution of the connection problems between a finite holed plate and a stiffener by using the partitioning concept of the generalized variational method

In this paper a new finite element method is presented, in which complex functions are chosen to be the finite element model and the partitioning concept of the generalized variational method is utilized. The stress concentration factors for a finite holed plate welded by a stiffener are calculated and the analytical solutions in series form are obtained. From some computer trials it is demonstrated that the problem of displacement compatibility and continuity of tractions between the holed plate and the stiffener is successfully analysed by using this method. Since only three elements need to be formulated, relatively less storage is required than the usual finite element methods. Furthermore, the accuracy of solutions is improved and the computer time requirements are considerably reduced. Numerical results of stress concentration factors and stresses along the welded-line which may be referential to engineers are shown in tables.     

On the formulation of the planar ANCF triangular finite elements

In this paper, new planar isoparametric triangular finite elements (FE) based on the absolute nodal coordinate formulation (ANCF) are developed. The proposed ANCF elements have six coordinates per node: two position coordinates that define the absolute position vector of the node and four gradient coordinates that define vectors tangent to coordinate lines (parameters) at the same node. To shed light on the importance of the element geometry and to facilitate the development of some of the new elements presented in this paper, two different parametric definitions of the gradient vectors are used. The first parametrization, called area parameterization, is based on coordinate lines along the sides of the element in the reference configuration, while the second parameterization, called Cartesian parameterization, employs coordinate lines defined along the axes of the structure (body) coordinate system. The fundamental differences between the ANCF parameterizations used in this investigation and the parametrizations used for conventional finite elements are highlighted. The Cartesian parameterization serves as a unique standard for the triangular FE assembly. To this end, a transformation matrix that defines the relationship between the area and the Cartesian parameterizations is introduced for each element in order to allow for the use of standard FE assembly procedure and define the structure (body) inertia and elastic forces. Using Bezier geometry and a linear mapping, cubic displacement fields of the new ANCF triangular elements are systematically developed. Specifically, two new ANCF triangular finite elements are developed in this investigation, namely four-node mixed-coordinate and three-node ANCF triangles. The performance of the proposed new ANCF elements is evaluated by comparison with the conventional linear and quadratic triangular elements as well as previously developed ANCF rectangular and triangular elements. The results obtained in this investigation show that in the case of small and large deformations as well as finite rotations, all the elements considered can produce correct results, which are in a good agreement if appropriate mesh sizes are used.     

Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient

In this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values. Geometrically, this can be interpreted as finding a minimal Lipschitz extension. Due to the weak convexity of the functional associated to this problem, solutions are generally nonunique. By adopting G. Aronsson's notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation. In fact, we actually prove a weak maximum principle for this partial differential equation, which in some sense is the Euler equation for the minimization problem. This is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity. To overcome this difficulty we use the weak solutions of M. G. Crandall and P.-L. Lions, also known as viscosity solutions, in conjunction with some arguments using integration by parts.     

A theory of the adaptive growth of biological materials

Summary In this paper, a new theory of the adaptive growth of biological materials is presented. The theory is derived from the basic laws of continuum mechanics. The material is described as a classical mixture of solid material and fluid. It will be shown that several well-known models of the adaptive growth are embedded in this more general theory. In addition, it is clarified on which material assumptions these models are based. Finally, a solution procedure for the new theory is developed, and several examples are given. Received 31 March 1999; accepted for publication 1 June 1999     

On the problem of the number of bifurcation solutions at singular point

I.IntroductionConsiderthenonlinearequationF(x,A)=o(l.l)whereF:XXR-R"isaC'function,andxCX=R".Pseudo-arclenthmethodIl'2l(i.e.,homotopymethod),asoneofthemostefficientmethodsforsolvingEq.(l.l),hasbeengreatlydevelopedinrecent2Oyears.AndSard'sTheoremisthefundam…     

Study of the effect of capillary pressure on the permeability of porous media embedded with a fractal-like tree network

In this paper, the analytical expressions for permeability of (both saturated and unsaturated) porous media embedded with a fractal-like tree network are presented based on fractal theory and technique when the capillary pressure is taken into account. Both the dimensionless effective permeability and the relative permeability of the composites, which are defined as porous media embedded with a fractal-like tree network in this work, are derived and found to be a function of saturation, the capillary pressure and microstructural parameters of the networks. The relative permeabilities predicted by the present fractal model are compared with the available experimental data and a fair agreement between them is found.     

Qualitative behaviors of the continuous-time chaotic dynamical systems describing the interaction of waves in plasma

In this paper, a new Lorenz-like chaotic system describing the interaction of three resonantly coupled waves in plasma is studied. Explicit ultimate boundedness and global attraction domain are derived according to stability theory of dynamical systems. The innovation of the paper is that this paper not only proves this chaotic system is globally bounded for the parameters of this system but also gives a family of mathematical expressions of global exponential attractive sets for this system with respect to the parameters of this system. Furthermore, the exponential rate of the trajectories is also obtained. Finally, numerical localization of attractor is presented.     

连续体结构屈曲约束的ICM方法拓扑优化

基于ICM(独立、连续、映射)方法解决具有屈曲约束的连续体拓扑优化问题。建立以结构重量为目标,以屈曲临界力为约束的拓扑优化模型;采用独立的连续拓扑变量,借助泰勒展式将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将约束化为近似显函数,避免了灵敏度的计算;将优化模型转化为对偶规划,并利用序列二次规划求解,减少了设计变量的数目,缩小了模型的求解规模。给出三个算例,结果表明:该方法可有效地解决屈曲约束的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。