On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

Mixed-Ligand Complex Formation Equilibria of Copper(II) with 6-Methylpicolinic Acid and Some Amino Acids

In this work, the ternary complex formation among copper(II), 6-methylpicolinic acid (H6Mepic) as primary ligand, and the amino acids aspartic acid (H₂Asp), glutamic acid (H₂Glu) and histidine (HHis) as secondary ligands, were studied in aqueous solution at 25 °C using 1.0 mol·dm^?3 KNO₃ as the ionic medium. Analysis of the potentiometric data using the least squares computational program LETAGROP indicates formation of the species [Cu(6Mepic)]⁺, Cu(6Mepic)(OH), [Cu(6Mepic)(OH)₂]^?, Cu(6Mepic)₂ and [Cu(6Mepic)₃]^? in the binary Cu(II)–H6Mepic system. In the ternary Cu(II)–H6Mepic–H₂Asp system the complexes [Cu(6Mepic)(H₂Asp)]⁺, Cu(6Mepic)(HAsp), [Cu(6Mepic)(Asp)]^? and [Cu(6Mepic)(Asp)(OH)]^2? were observed. In the case of the Cu(II)–H6Mepic–H₂Glu system the complexes Cu(6Mepic)(HGlu), [Cu(6Mepic)(Glu)]^?, [Cu(6Mepic)(Glu)(OH)]^2? and [Cu(6Mepic)(glu)(OH)₂]^3? were detected. Finally, in the Cu(II)–H6Mepic–HHis system the complexes [Cu(6Mepic)(HHis)]⁺, Cu(6Mepic)(His) and [Cu(6Mepic)(His)(OH)]^? were observed. The species distribution diagrams as a function of pH are briefly discussed.     

Electrodes based on zeolites modified with cobalt and/or molybdenum for pesticide degradation: part II—2,4,6-trichlorophenol degradation

Journal of Solid State Electrochemistry - 2,4,6-trichlorophenol (TCP) is a persistent pollutant introduced in water by industrial processes and pesticides. We have studied the electrooxidation of...     

Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation

This paper develops a new procedure for evaluating the elastic forces, the elastic energy and the jacobian of the elastic forces in the absolute nodal coordinate formulation. For this procedure, it is fundamental to use some invariant sparse matrices that are integrated in advance and have the property of transforming the evaluation of the elastic forces in a matrix multiplication process. The use of the invariant matrices avoids the integration over the volume of the element for every evaluation of the elastic forces. Great advantages can be achieved from these invariant matrices when evaluating the elastic energy and calculating the jacobian of the elastic forces as well. The exact expression of the jacobian of the differential system of equations of motion is obtained, and some advantages of using the absolute nodal coordinate formulation are pointed out. Numerical results show that there is important time saving as a result of the use of the invariant matrices.     

Comparison of surface coverage values of tungsten-alumina catalysts determined by different methods

Apparent surface coverage (ASC) of a series of tungsten-alumina catalysts was determined by the electrophoretic migration method (EM). A linear increase in W coverage with increasing W loading (up to 13.1 wt.% W) was observed. The results were in close agreement with those obtained previously by ion scattering spectroscopy (ISS) and low temperature CO adsorption.     

HPLC with inductively coupled plasma optical emission spectrometric detection for the analysis of inositol phosphates

The use of inductively coupled plasma optimal emission spectroscopy as a detector for the high-performance liquid chromatographic analysis of inositol phosphates is studied. It is found that separation of different inositol phosphates with a mobile phase consisting of tetraethylammonium (0.14%, w/v), methanol (5%, v/v), and formic acid (0.18%, w/v) may be obtained on a PRP-1 column with an analysis time of 18 min. In addition, high specificity and sensitivity of the detection system used permits detection of the inositol phosphates from bi- to hexaphosphate free from interference of other chromatographic peaks, which could be from the sample or mobile phase. Additionally, it is possible to use less sample because of the high sensitivity of the detection system.     

Processability of a metallocene‐catalyzed linear PE improved by blending with a small amount of UHMWPE

The processability of a metallocene‐catalyzed polyethylene blended in the melt with low amounts of ultra‐high molecular weight polyethylene was evaluated. Our morphological and thermal studies revealed that the blends were structurally heterogeneous, formed by a matrix of metallocene polyethylene and homogeneously distributed particles of ultra‐high molecular weight material. The visible particles were smaller than those of the reactor powder. Also observed was some degree of interaction between both phases. Rheological data indicated an intense effect of morphology on viscoelastic functions, beyond that expected for a system composed of noninteractive phases. Collectively, our findings suggest the existence, to some extent, of a homogeneous phase at the molecular level composed of a fraction of ultra‐high molecular weight species and metallocene polyethylene. This gives rise to a striking behavior during processing in that the blends show improved extrusion performance the higher their ultra‐high molecular weight polyethylene content. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2963–2971, 2005     

On semiperfect associative pairs

It is known [8] that a semiperfect ring is characterized by the existence of a frame, i.e, a complete set of local orthogonal idempotents. We prove in this paper that a similar behaviour occurs when dealing with an associative pair A, namelyAis semiperfect if and only if Acontains a frame and ā=A/Rad Ais unital. Moreover, we show that, when ā is unital, the existence of a frame for Ais equivalent to the condition that every irreducible right A-module is isomorphic to _e A/e(RadA) for some idempotent e of A.