L p-Perturbations of Invariant Subbundles for Linear Systems

We use Riccati's equations and the ordinary and exponential dichotomies to get simple recurrent formulae for the asymptotic integration of linear systems subjected to L _p -perturbations with arbitrary p 1. Moreover, we establish conditions which are necessary and sufficient for the persistence of one-dimensional invariant subbundles for the linear system under L _p -perturbations. In this way, we prove the sharp nature of the well known Levinson and Hartman–Wintner asymptotic theorems.     

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 ,　　 0 0 ,( 1 )withtheinitialandtheboundaryconditions　　　　　u(x,0 ) =f(x) ,　　 0 相似文献   

粘弹性几何非线性夹层梁动响应分析

本文选用考虑横向剪切效应的退化梁单元，引入几何非线性假设，对具粘弹性阻尼层的夹层梁动响应及其衰减效果进行了研究，得到了一些具有应用价值的结论。     

大型多支承变刚度回转窑支承载荷分配问题

回转窑是冶金、水泥、耐火材料生产中的核心设备，是一种重载、大扭矩、多支点、静不定运行系统，由于其载荷和刚度分布复杂、各支承存在偏移，作用在它托轮上的支承载荷分配严重不均。本文针对回转窑载荷和刚度分布的特点，建立支承载荷求解的力学模型和线性方程组，导出支承载荷分配与支承偏差的关系式；用该方法对现场回转窑进行计算，得出该窑支承载荷分配的线性公式和一些分析结论，为生产中回转窑的状态分析、优化调控提供依据。     

A SINGULAR VALUE DECOMPOSITION BASED TRUNCATION ALGORITHM IN SOLVING THE STRUCTURAL DAMAGE EQUATIONS

The structural damage identification through modal data often leads to solving a set of linear equations. Special numerical treatment is sometimes required for an accurate and stable solution owing to the ill conditioning of the equations. Based on the singular value decomposition (SVD) of the coefficient matrix, an error based truncation algorithm is proposed in this paper. By rejection of selected small singular values, the influence of noise can be reduced. A simply-supported beam is used as a simulation example to compare the results to other methods.Illustrative numerical examples demonstrate the good efficiency and stability of the algorithm in the nondestructive identification of structural damage through modal data.     

The relaxation of linear flexible polymers which are slightly poly-disperse

The relaxation of slightly poly-disperse linear flexible polymers has been expressed in a simplified blending rule which is presumed to be a weighted linear superposition of the relaxation spectra of mono-disperse components which constitute the blend. Discrete components are characterized by their molecular weight M _i,weight fraction w _i,and relaxation time spectrum H _i(). ). In contrast to broadly distributed blends in which the small molecules mobilize the large ones and vice versa, we introduce the term slightly polydisperse for blends with molecular weight distributions narrow enough to have very little change in the longest relaxation times of each molecular weight component. The properties of this blending rule are analyzed and dynamic data is calculated for slightly poly-disperse polystyrene. As an application, the blending rule is used to determine the characteristic mono-disperse parameters (BSW parameters) of two materials, poly (vinyl methyl ether) and polycarbonate, for which we could not determine their BSW parameters directly since they were not available in nearly monodisperse form. The proposed blending rule can only be applied to systems in which all components are above the entanglement molecular weight, i.e. M _iM _c.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Rheology/morphology/flow conditions relationships for polymethylmethacrylate/rubber blend

Viscoelastic behavior, phase morphology and flow conditions relationships in polymer/rubber blends have been investigated. The importance of such correlations is illustrated on polymethylmethacrylate (PMMA)/rubber blends subjected to different flow conditions both under small and large deformations. In small-amplitude oscillatory shear (the morphology does not change during the flow) the elastic modulus G of the concentrated blends shows a secondary plateau, G _p , in the low frequency region. This solid-like behavior appears for rubber particle contents beyond the percolation threshold concentration (15%). Morphological observations revealed that for concentrations higher than 15%, the particles are dispersed in a three-dimensional network-type structure.In capillary flow it was found that the network-type structure was destroyed and replaced by an alignment of particles in the flow direction. This morphological modification resulted in a decrease in both viscosity and post-extrusion swell of the blends. Morphological observations revealed that the ordered structure in the flow direction was concentrated only in the skin region of the extrudate, where the shear stress is higher than the secondary plateau, G _p . A simple kinetic mechanism is proposed to explain the observed morphology.Similarly, steady shear measurements performed in the cone-and-plate geometry revealed alignment of particles in the flow direction for shear stress values higher than G_p.Presented in part at the Symposium Recent Developments in Structured Continua Montréal (Canada) 26–28 May 1993 and at the 45th Canadian Chemical Engineering Conference, Quebec, October 15–18 (1995)     

Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening

Energy-coupled stress and strain measures are defined in Euler coordinates. They are used to analyze the relationship between the first invariants of the stress and strain tensors for linearity and to determine strains at which the plastic component of the first strain invariant can be neglected. It is established that this relationship remains linear within an engineering plastic-strain tolerance of 0.2% irrespective of the value of strain intensity, which depends on the type of material and its stress state __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 60–72, March 2007.     

On the analytic expression of the free energy in linear viscoelasticity

Two definitions of free energy for a linear viscoelastic material, due to Graffi and to Coleman and Owen, are considered, and the compatibility of these definitions with some expressions of the free energy proposed in the literature is examined. For the expressions of Staverman and Schwarzl and of Breuer and Onat, the two definitions are proved to be equivalent, and the set of all relaxation functions for which the two expressions are indeed free energies is determined. Two more expressions, proposed by Volterra and Graffi and by Morro and Vianello, are taken into consideration. For them, only the classes of relaxation functions for which they are free energies according to the first definition, is completely characterized. All results are established under regularity assumptions weaker than those usually made in the literature.     

Spatial Estimates for the Constrained Anisotropic Elastic Cylinder

This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone.