Development of generalized Iwan model to simulate frictional contacts with variable normal loads

Most friction models are originally proposed to predict restoring forces in mechanical contacts with constant normal load. In practice the contact interface kinematics may involve normal motion in addition to the tangential displacements, leading to variation of the contact normal load. This phenomenon is observed most strongly in contacts with high lateral vibration amplitudes and is known as slap. The current study establishes a general friction model to account for variation in the normal load and enables one to predict the behavior of a contact more precisely. Iwan model (1966) [5] is a suitable candidate for contact interface modeling and is able to represent the stick-micro/macro slip behavior involved in a friction contact. This physical based model is employed in the current work and its physical parameters are generalized to include the normal load variation effects. The model is characterized by a slippage distribution density function and a linear stiffness at stick state. Both these parameters, defined in presence of constant normal load in the original model, are derived considering normal load variation leading to generalization of the contact model. Conventional models with constant normal loads produce symmetric contact interface hysteresis loops, but the developed generalized Iwan model is capable of generating asymmetric hysteresis loops similar to those frequently seen in experiments. The generalized contact model is employed to simulate the measured behavior of a beam with frictional support observed in an experimental test set-up. The contact slippage distribution function is first identified in a constant normal load condition. Next in low levels of contact preloads where variation of the normal load is significant, the identified distribution function in generalized form is employed to predict the experimental observations.     

Specific Features of Finite Mixtures of Normal Distributions

Properties of finite mixtures of normal distributions are considered. Their behavioral similarities and differences relative to normal distributions are studied. A practical application of finite mixtures of normal distributions for the simulating the noise of neurophysiological signals is described. It is shown that the Aitken estimate can be used for the source amplitudes in the considered model.     

Decision problems in the space of Dehn fillings

Normal surface theory is used to study Dehn fillings of a knot-manifold. We use that any triangulation of a knot-manifold may be modified to a triangulation having just one vertex in the boundary. In this situation, it is shown that there is a finite computable set of slopes on the boundary of the knot-manifold, which come from boundary slopes of normal or almost normal surfaces. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely those manifolds obtained by Dehn filling of a given knot-manifold that: (1) are reducible, (2) contain two-sided incompressible surfaces, (3) are Haken, (4) fiber over S¹, (5) are the 3-sphere, and (6) are a lens space. Each of these algorithms is a finite computation.Moreover, in the case of essential surfaces, we show that the topology of each filled manifold is strongly reflected in the combinatorial properties of a triangulation of the knot-manifold with just one vertex in the boundary. If a filled manifold contains an essential surface then the knot-manifold contains an essential normal vertex solution which caps off to an essential surface of the same type in the filled manifold. (Normal vertex solutions are the premier class of normal surface and are computable.)     

Sequences of elliptical distributions and mixtures of normal distributions

Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distributions sharing the same mixing distribution function. Some examples are shown as applications of these concepts, showing the way of finding the mixing distribution function.     

均值混合正态分布统计量的性质

这篇文章基于基因遗传背景,提出了一类均值混合正态分布,它不同于通常所讨论的方差混合正态分布. 作者研究了这类均值混合正态分布统计量的性质,给出了平移变换群下不变量的稳健性,即它与正态分布下该统计量有相同的性质, 并且讨论了其它统计量的分布.     

On the Structure of Nilpotent Normal Form Modules

The set of vector fields that are in normal form with respect to a given linear part has the structure of a module and is best described by giving the Stanley decomposition of that module. An algorithm is presented that produces a Stanley decomposition for the module of equivariants of the flow of a nilpotent linear vector field, given a Stanley decomposition for the ring of invariants. This reduces the study of nilpotent normal forms to classical invariant theory plus this one additional algorithm. Both the inner product normal form (Elphick) and the sl(2) normal form (Cushman-Sanders) are covered within a single theory, and simplified (non-equivariant) versions of each normal form are presented.     

两自由度非对称三次系统非线性模态的奇异性质

利用非线性模态子空间的不变性和摄动技术,研究两自由度非对称三次系统在奇异条件下系统的性质.重点考虑子系统之间线性耦合退化时的奇异性质.对于非共振情形,所得到的解析结果表明,系统出现单模态运动以及振动局部化现象,这种现象的强弱不但与非线性耦合刚度有关,而且与非对称参数有关.并解析地得到了参数的门槛值;对于1:1共振情形,模态随非线性耦合刚度和非对称参数的变化会出现分岔,得到了参数分岔集以及模态的分岔曲线.     

On the Nonlinear Development of Small Three-Dimensional Perturbations in Plane Poiseuille Flow: Single-Mode Approach

Nonlinear aspects of developing three-dimensional perturbations in plane Poiseuille flow have been elucidated at the primary, instead of the conventional secondary, level. Three-dimensional perturbation velocities generate normal vorticity by stretching and tilting the basic-flow vorticity. The amplitude of the induced normal vorticity, and hence that of the streamwise perturbation velocity, can grow temporally to significant peak values before the exponential decay predicted by the linear theory sets in. These growths, according to the linear theory, do not influence the amplitudes of the normal perturbation velocity that are monotonically decaying with time. It is shown in this study that the normal velocity continues to be oblivious to the development of induced normal vorticity, even in the nonlinear regime, if the perturbation velocities are described by waves traveling in a single oblique direction. Also, the Reynolds number dependence of the amplitude of the normal vorticity is discussed.     

Fuzzy蕴涵代数的MP理想与正规MP理想

在Fuzzy蕴涵代数(简称FI代数)上引入了MP理想与正规MP理想的概念并给出了它们的等价刻画;探讨了FI代数的MP理想、偏序理想和正规MP理想间的多种关系, 证明了一个正则FI代数是可交换FI代数当且仅当它的每个MP理想都是正规理想,也当且仅当{0}是正规MP理想.     

模糊商群的推广

引入关于一个子群的正规模糊子集概念，研究正规模糊子集的一些性质，并在此基础上将模糊商群做了自然推广，最后建立群同态下正规模糊子集的对应定理。     

Noncentral quadratic forms of the skew elliptical variables

In this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution.     

多项式组的特征分解

任一多项式理想的特征对是指由该理想的约化字典序Grobner基G和含于其中的极小三角列C构成的有序对(G,C).当C为正则列或正规列时,分别称特征对(G,C)为正则的或正规的.当G生成的理想与C的饱和理想相同时,称特征对(G,C)为强的.一组多项式的(强)正则或(强)正规特征分解是指将该多项式组分解为有限多个(强)正则或(强)正规特征对,使其满足特定的零点与理想关系.本文简要回顾各种三角分解及相应零点与理想分解的理论和方法,然后重点介绍(强)正则与(强)正规特征对和特征分解的性质,说明三角列、Ritt特征列和字典序Grobner基之间的内在关联,建立特征对的正则化定理以及正则、正规特征对的强化方法,进而给出两种基于字典序Grobner基计算、按伪整除关系分裂和构建、商除可除理想等策略的(强)正规与(强)正则特征分解算法.这两种算法计算所得的强正规与强正则特征对和特征分解都具有良好的性质,且能为输入多元多项式组的零点提供两种不同的表示.本文还给出示例和部分实验结果,用以说明特征分解方法及其实用性和有效性.     

Factor normal wedges of semi-ordered spaces

A concept of a factor normal cone in a linear topological space is introduced and basic properties of semiordered spaces possessing a positive factor normal cone are studied. The main aim of the paper is to investigate topologies of semiordered spaces whose dual positive cone in the conjugate space is factor normal.     

Protomodular aspect of the dual of a topos

The structure of the dual of a topos is investigated under its aspect of a Barr exact and protomodular category. In particular the normal monomorphisms in the fibres of the fibration of pointed objects are characterized, and the change of base functors with respect to this same fibration are shown to reflect those normal monomorphisms.     

Wreath products and enlargements of groups

To take care of the fact that a normal subgroup of a normal subgroup need not be normal in the original group, the concept of group extensions is generalized to the concept of group enlargements. This is related to wreath products. Applications are made to the calculation of algebraic fundamental groups.     

Principally normal matrices

Normal matrices in which all principal submatrices are normal are said to be principally normal. Various characterizations of irreducible matrices in this class of are given. Notably, it is shown that an irreducible matrix is principally normal if and only if it is normal and all of its eigenvalues lie on a line in the complex plane. Such matrices provide a generalization of the Cauchy interlacing theorem.     

Completely normal matrices

Normal matrices in which all submatrices are normal are said to be completely normal. We characterize this class of matrices, determine the possible inertias of a particular completely normal matrix, and show that real matrices in this class are closed under (general) Schur complementation. We provide explicit formulas for the Moore–Penrose inverse of a completely normal matrix of size at least four. A result on irreducible principally normal matrices is derived as well.     

Classification of surfaces with planar normal sections

A surface in E^m is said to have planar normal sections if normal sections of M are planar curves. In this paper we completely classify surfaces in E^m with planar normal sections. Consequently, a new characterization of the Veronese surface is obtained.