Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis

In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory.     

Rainbow refractrometry on particles with radial refractive index gradients

The rainbow refractrometry, under its different configurations (classical and global), is an attractive technique to extract information from droplets in evaporation such as diameter and temperature. Recently a new processing strategy has been developed which increases dramatically the size and refractive index measurements accuracy for homogeneous droplets. Nevertheless, for mono component as well as for multicomponent droplets, the presence of temperature and/or of concentration gradients induce the presence of a gradient of refractive index which affects the interpretation of the recorded signals. In this publication, the effect of radial gradient on rainbow measurements with a high accuracy never reached previously is quantified.     

Model identification and FE simulations: Effect of different yield loci and hardening laws in sheet forming

The bi-axial experimental equipment [Flores, P., Rondia, E., Habraken, A.M., 2005a. Development of an experimental equipment for the identification of constitutive laws (Special Issue). International Journal of Forming Processes] developed by Flores enables to perform Bauschinger shear tests and successive or simultaneous simple shear tests and plane strain tests. Flores investigates the material behavior with the help of classical tensile tests and the ones performed in his bi-axial machine in order to identify the yield locus and the hardening model. With tests performed on one steel grade, the methods applied to identify classical yield surfaces such as [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic materials. Proceedings of the Royal Society of London A 193, 281–297; Hosford, W.F., 1979. On yield loci of anisotropic cubic metals. In: Proceedings of the 7th North American Metalworking Conf. (NMRC), SME, Dearborn, MI, pp. 191–197] ones as well as isotropic Swift type hardening, kinematic Armstrong–Frederick or Teodosiu and Hu hardening models are explained. Comparison with the Taylor–Bishop–Hill yield locus is also provided. The effect of both yield locus and hardening model choices is presented for two applications: plane strain tensile test and Single Point Incremental Forming (SPIF).     

A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate

In this paper, we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress–strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.     

Peripheral spectrum of positive quasi-compact operators onC 0(X)

LetX be a locally compact space, andT, a quasi-compact positive operator onC ₀(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r) ^p and ker(T ^*-r) ^p , and finally the dimension of the algebraic eigenspace associated to each peripheral pole.     

Constructing Robust Feedback Laws by Set Oriented Numerical Methods

In [8, 6] a numerical method for the construction of optimally stabilizing feedback laws was proposed. The method is based on a set oriented discretization of phase space in combination with graph theoretic algorithms for the computation of shortest paths in directed weighted graphs. The resulting approximate optimal value function is piecewise constant, yielding an approximate optimal feedback which might not be robust with respect to perturbations of the system. In this contribution we extend the approach to the case of perturbed control systems. Based on the concept of a multivalued game we show how to derive a directed weighted hypergraph from the original system and generalize the corresponding shortest path algorithm. The resulting optimal value function yields a robustly stabilizing approximate optimal feedback law. This note is an abbreviated version of [5]. For the proofs of the statements here we refer to the full paper. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Monte Carlo method for the Broadwell model with relaxation

A Monte Carlo method is proposed for numerical solution of the Broadwell model. Developing a probabilistic interpretation of the equations, the transport and collision parts are treated separately in the method. Particles are advected according to their velocities and collisions are performed between randomly chosen particles. We numerically test the algorithm for a variety of examples. In particular we are interested in situations which generate structures that have nonsmooth fronts. Our simulations show that this Monte Carlo method is capable of capturing the nonlinear regime in presence of shocks and interactions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adsorption of nucleic acid bases on clays: an investigation using Langmuir and Freundlich isotherms and FT-IR spectroscopy

In the present paper, the adsorption of nucleic acid bases (A, adenine; C, cytosine; U, uracil; and T, thymine) on clays (bentonite, kaolinite, and montmorillonite) was studied at different pH (2.00 and 7.20). It should be pointed out there is no reported study of adsorption of nucleic acid bases on clays using seawater (with the major elements), and a wide range of pH. The main finding of this study was that the ratio of A and T adsorbed on clays ranged from 4.68 to 25.1, much higher than the ratio of their occurrence in organisms ranging from 0.95 to 1.05. The weaker adsorption of U and T on clays raises the question of the possibility of a genetic code based on purines only. The FT-IR spectra at pH 2.00 showed that the interaction of A, C, T, and U with the clays occurs through positively charged, protonated groups. Correspondence: Dr. Dimas A. M. Zaia, Departamento de Química-CCE, Universidade Estadual de Londrina, 86051-990 Londrina-PR, Brazil.     

Synthesis of a novel amphiphilic GdPCTA-[12] derivative as a potential micellar MRI contrast agent

A novel amphiphilic contrast agent, a GdPCTA-[12] derivative containing a dodecyl chain as lipophilic moiety, has been prepared. A convergent synthetic route from commercially available diethylene triamine and 3-hydroxypyridine is described. The target amphiphilic gadolinium complex was obtained in nine steps in 22% overall yield. Physicochemical properties and relaxivity measurements of this new contrast agent are described.