On stick-slip homoclinic chaos and bifurcations in a mechanical system with dry friction

In this paper we consider a self-excited mechanical system by dry friction in order to study the bifurcational behavior of the arisen vibrations. The oscillating system consists of a mass block-belt-system which is self-excited by static and Coulomb friction. We analyze the system behavior numerically through bifurcation diagrams, phase portraits, frequency spectra and Poincare maps, which show the existence of nonhomoclinic and homoclinic chaos and a route to homoclinic chaos. The homoclinic chaos is also analyzed analytically via the Melnikov prediction method. The system dynamic is characterized by the existence of two potential wells in the phase plane which exhibit rich bifurcational and chaotic behavior.

Friction losses in valves and fittings for power-law fluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Laminar flow of soursop juice through concentric annuli: Friction factors and rheology

Laminar axial flow of a pseudoplastic fluid food (soursop, juice) in annular ducts has been experimentally investigated. In the first part of the manuscript, the rheological behavior of soursop juice, being essential for the annular flow analysis, was completely determined from 9.3 to 49.4 degrees Brix and temperatures from 0.4 degrees C to 68.8 degrees C, using a rotational rheometer equipped with coaxial cylinders. In order to test the adequacy of the rheology results, pressure loss data in the laminar pipe flow were collected and then experimental and theoretical friction factors were compared, showing excellent agreement, which indicated the reliability of the Power-Law model for describing the soursop juices. In the second part, pressure loss in annular regions was measured and used to estimate friction factors, which were then compared to those resulted from analytical and semi-analytical equations. The principal contributions of this article are to provide a review on the determination of friction factors-Reynolds number of pseudoplastic fluids in annuli, and also supply extensive new experimental data on the rheological properties and pressure loss of an important shear-thinning fluid food, which is of particular interest for the food engineering process design. (c) 2006 Elsevier Ltd. All rights reserved.

Friction losses in valves and fittings for viscoplastic fluids

Data on pressure drop were obtained in stainless steel, sanitary fittings and valves during laminar and turbulent flow of aqueous suspensions of sucrose and bentonite. The rheological properties of these suspensions were determined and the Bingham model provided the best fitting with the experimental data. Friction losses were measured in fully- and partially-open butterfly and plug valves, bends and union. Values of loss coefficients (k(f)) were calculated and correlated as functions of the classical Reynolds number and the Reynolds number proposed by Govier and Aziz (1972) for viscoplastic fluids. The two-k method and a new proposed model presented the best adjustments for the Govier and Aziz Reynolds number, and Hedstrom and classical Reynolds numbers, respectively.

Friction factors and rheological properties of orange juice

The rheological behavior of Brazilian orange juice with different water content (0.34-0.73 w/w) was studied at a wide range of temperatures (0.5-62 degrees C) using a concentric cylinder viscometer. The results indicated that the juices behave as pseudoplastic fluids with yield stress, being represented by the Herschel-Bulkley model. The rheological parameters were fitted as functions of both temperature and water content in the tested range. Based on dimensional analysis it was proposed a modified Reynolds number (Re-M), which includes the Herschel-Bulkley parameters. Experimental data of friction factors during heating and cooling processes of orange juice in laminar flow through circular tubes could be well correlated as a function of Re-M. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

The carreau-yasuda fluids: a skin friction equation for turbulent flow in pipes and kolmogorov dissipative scales

In this work the turbulent flow of the Non-Newtonian Carreau-Yasuda fluid will be studied. A skin friction equation for the turbulent flow of Carreau-Yasuda fluids will be derived assuming a logarithmic behavior of the turbulent mean velocity for the near wall flow out of the viscous sub layer. An alternative near wall characteristic length scale which takes into account the effects of the relaxation time will be introduced. The characteristic length will be obtained through the analysis of viscous region near the wall. The results compared with experimental data obtained with Tylose (methyl hydroxil cellulose) solutions showing good agreement. The relations between scales integral and dissipative obtained for length, time, velocity, kinetic energy, and vorticity will be derived for this type of fluid. When the power law index approach to unity the relations reduces to Newtonian case.

Microstructural and electrochemical characterization of friction stir welded duplex stainless steels

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Local order and magnetic field effects on the electronic properties of disordered binary alloys in the quantum site percolation limit

Electronic properties of disordered binary alloys are studied via the calculation of the average Density of States (DOS) in two and three dimensions. We propose a new approximate scheme that allows for the inclusion of local order effects in finite geometries and extrapolates the behavior of infinite systems following finite-size scaling ideas. We particularly investigate the limit of the Quantum Site Percolation regime described by a tight-binding Hamiltonian. This limit was chosen to probe the role of short range order (SRO) properties under extreme conditions. The method is numerically highly efficient and asymptotically exact in important limits, predicting the correct DOS structure as a function of the SRO parameters. Magnetic field effects can also be included in our model to study the interplay of local order and the shifted quantum interference driven by the field. The average DOS is highly sensitive to changes in the SRO properties and striking effects are observed when a magnetic field is applied near the segregated regime. The new effects observed are twofold: there is a reduction of the band width and the formation of a gap in the middle of the band, both as a consequence of destructive interference of electronic paths and the loss of coherence for particular values of the magnetic field. The above phenomena are periodic in the magnetic flux. For other limits that imply strong localization, the magnetic field produces minor changes in the structure of the average DOS. © World Scientific Publishing Company.

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.

Permeability, overburden stress and friction coefficients of ODP Hole 190-1173A and 190-1174B

Permeability measured on three samples in a triaxial cell under effective confining pressure from 0.2 to 2.5 MPa ranges from 10**-18 to 10**-19 m**2. Overall, results indicate that permeability decreases with effective confining pressure up to 1.5 MPa; however, measurements at low effective pressure are too dispersed to yield a precise general relationship between permeability and pressure. When the effective pressure is increased from 1.5 to 2.5 MPa, permeability is roughly constant (~1-4 x 10**-19 m**2). Samples deformed in the triaxial cell developed slickenlined fractures, and permeability measurements were performed before and after failure. A permeability increase is observed when the sample fails under low effective confining pressure (0.2 MPa), but not under effective pressure corresponding to the overburden stress. Under isotropic stress conditions, permeability decrease related to fracture closure occurs at a relatively high effective pressure of ~1.5 MPa. Coefficients of friction on the fractures formed in the triaxial cell are ~0.4.

Measurements of velocity-dependent and slip-dependent frictional strength in laboratory friction experiments on natural samples from IODP Expedition 316 and ODP Hole 190-1174B

Slowslip forms part of the spectrum of fault behaviour between stable creep and destructive earthquakes. Slow slip occurs near the boundaries of large earthquake rupture zones and may sometimes trigger fast earthquakes. It is thought to occur in faults comprised of rocks that strengthen under fast slip rates, preventing rupture as a normal earthquake, or on faults that have elevated pore-fluid pressures. However, the processes that control slow rupture and the relationship between slow and normal earthquakes are enigmatic. Here we use laboratory experiments to simulate faulting in natural rock samples taken from shallow parts of the Nankai subduction zone, Japan, where very low-frequency earthquakes - a form of slow slip - have been observed.We find that the fault rocks exhibit decreasing strength over millimetre-scale slip distances rather than weakening due to increasing velocity. However, the sizes of the slip nucleation patches in our laboratory simulations are similar to those expected for the very lowfrequency earthquakes observed in Nankai. We therefore suggest that this type of fault-weakening behaviour may generate slow earthquakes. Owing to the similarity between the expected behaviour of slow earthquakes based on our data, and that of normal earthquakes during nucleation, we suggest that some types of slow slip may represent prematurely arrested earthquakes.

Percolation in soils at Different Bulk Densities: Porosity, Connectivity and Grey Threshold.

To improve percolation modelling on soils the geometrical properties of the pore space must be understood; this includes porosity, particle and pore size distribution and connectivity of the pores. A study was conducted with a soil at different bulk densities based on 3D grey images acquired by X-ray computed tomography. The objective was to analyze the effect in percolation of aspects of pore network geometry and discuss the influence of the grey threshold applied to the images. A model based on random walk algorithms was applied to the images, combining five bulk densities with up to six threshold values per density. This allowed for a dynamical perspective of soil structure in relation to water transport through the inclusion of percolation speed in the analyses. To evaluate separately connectivity and isolate the effect of the grey threshold, a critical value of 35% of porosity was selected for every density. This value was the smallest at which total-percolation walks appeared for the all images of the same porosity and may represent a situation of percolation comparable among bulks densities. This criterion avoided an arbitrary decision in grey thresholds. Besides, a random matrix simulation at 35% of porosity with real images was used to test the existence of pore connectivity as a consequence of a non-random soil structure.