Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 2: random excitation

Non linear dynamic behaviour of a normally excited preloaded Hertzian contact (including possible contact losses) is investigated using an experimental test rig. It consists on a double sphere plane contact loaded by the weight of a rigid moving mass. Contact vibrations are generated by a external Gaussian white noise and exhibit vibroimpact responses when the input level is sufficiently high. Spectral contents and statistics of the stationary transmitted normal force are analysed. A single-degree-of-freedom non linear oscillator including loss of contact and Hertzian non linearities is built for modelling the experimental system. Theoretical responses are obtained by using the stationary Fokker-Planck equation and also Monte Carlo simulations. When contact loss occurrence is very occasional, numerical results shown a very good agreement with experimental ones. When vibroimpacts occur, results remain in reasonable agreement with experimental ones, that justify the modelling and the numerical methods described in this paper. The contact loss non linearity appears to be rather strong compared to the Hertzian non linearity. It actually induces a large broadening of the spectral contents of the response. This result is of great importance in noise generation for a lot of systems such as mechanisms using contacts to transform motions and forces (gears, ball-bearings, cam systems, to name a few). It is also of great importance for tribologists preoccupied to prevent surface dammage

Le marais doux endigué de Bourgneuf-Machecoul (Pays de Loire) Premier éléments de connaissance du peuplement piscicole. Relation ichtyofaune-habitat et problèmes majeurs de gestion (Maroc)

Le peuplement ichtyologique d'un marais littoral endigué, géré en eau douce, a été étudié sur une zone de 2 700 ha, située au nord du marais Breton-Vendéen (Loire-Atlantique, France). Le réseau hydraulique, qui représente près de 16 % de cette surface, se compose, d'environ 91 m de linéaire de fossés par ha (en tout 234 km) et de bassins présents uniquement dans la partie d'origine salicole du marais. Les hauteurs d'eau, l'envasement et le recouvrement par la végétation aquatique dépendent de la gestion humaine et sont très variables (moyennes respectives : 42 cm; 43 cm; 70 %). Cela se traduit par un morcellement spatial de l'habitat pour les poissons. La stratégie d'échantillonnage adoptée, qui tient compte de cette hétérogénéité, a permis de décrire un peuplement comportant 21 espèces. Dominé par les poissons-chats et par les anguilles, ce dernier est caractéristique de la zone à brèmes des cours d'eau. Les abondances sont relativement élevées (en moyenne 315 kg/ha et 11 460 poissons/ha), mais elles sont très hétérogènes. L'évolution qualitative et quantitative de la répartition spatio-temporelle est décrite à l'aide d'une analyse factorielle des correspondances portant sur 74 échantillons prélevés par pêche électrique entre 1987 et 1989. Bien que l'approche de ce milieu soit complexe et les références bibliographiques relativement rares, l'analyse des premières données permet d'ores et déjà d'identifier quelques problèmes de gestion ayant des répercussions directes sur le peuplement piscicole de cette zone.The dammed up marshes of the French Atlantic coast cover about 200 000 ha between River Vilaine and the « Bassin d'Arcachon ». Eighty eight % are managed with freshwater. They constitute original environments initially created for agriculture or for salt production, and they are now threatened by land abandonment within the next decade. Concurrently to aquaculture (in created or existing ponds), exploitation of the fish stocks in the ditchweb is likely to encourage a diversification of agricultural activities. Unfortunately, bibliographic analysis reveals the relative scarceness of research about sampling methods and qualitative or quantitative characteristics of these fish communities. This is quite surprising considering the importance of the ditchwed of this kind of environment outlined by several authors. In the Netherlands, BELTMANN (1984) assessed that there is a total of 400 000 km of ditches. In France, the littoral dyked marshes of the Atlantic coast couid comprise 20 000 km of ditches and about 24 000 ha of open water. The present work provides for the first data on the fish community of Bourgneuf marsh.The northern part of the marsh of Bourgneuf, 2 700 ha provided whith f reshwater, contains nearly every kind of landscapes found throughout the whole Breton-Vendéen marsh. The pattern of the ditch network strongly changes from a zone to another (fig.1) : presence of former salt pans in the western part, regular geometric shapes in the recently created polders next to the River Falleron, irregular ditchweb pattern in the eastern part. The average density of the ditch network is 91 m of ditches per ha, totalizing 234 km in the study area. The total surface of open water, composed of ditches and basins (former salt pans), covers 411 ha (over 15 % of the study site). Diversity of ditch types occurs at fine scales (<1 000 m2), they vary according to their widths (0,3 to 7 m), depths (average, 42 cm; SD, 20,4), thickness of silt layer (average, 43 cm; SD, 42) and their hydrophyte vegetation cover (average, 70 %; SD, 60 %). As a consequence of this heterogeneity, available habitats are scattered over the marsh (mosaïc distribution). A nested sampling (FRONTIER, 1983) was carried out to take into account this high heterogeneity : 5 sampling areas were selected randomly. In each one, 3 to 5 ditches were chosen according to their characteristics (see above). Sampling stations were delimited by 2 stop nets (5 mm mesh) settled 30 m apart, in order to avoid fish migration. Field work was conducted using « Heron » electric fishing material (see LAMARQUE et al., 1978). In each ditch-section, we carried out as many successive catches as necessary to apply the maximum likelihood weighted estimation method of CARLE and STRUB (1978). Nine to 19 stations were sampled at 5 periods, between 1987 and 1989. A total of 74 samples were collected.The fish community was composed of 21 species (table 1) and corresponded to the bream zone of Verneaux's classification (1977). The densities and biomass were quite high (on average 315 kg/ha and 11 460 fishes/ha) but very variable (0 to 2 120 kg/ ha and 0 to 39 300 fishes/ha). The catfish, Ictalurus nebulosus (170 kg/ha), the eel, Anguilla anguilla (47 kg/ha) and the tench, Tinca tinca (28 kg/ha), represented on average 77,5 % of the standing crop, but their spatial distribution was very irregular. These estimates are assumed to be reliable considering that the data used for the calculations were provided by a sampling design which permits to respect the basic assumptions of the removal method. (f) The population size could only change because of the fishings (no migration because of the stop nets; no recruitment/death because of the short duration of the fishing sequences). (ii) The standard sampling design permitted to reduce the variations of the catch probabilities between the successive removals. Several studies have shown that this removal method under-estimates by about 20 % the true size of the fish populations (e. g. BOHLIN and SUNDSTROM, 1977; MAHON, 1980). But they were based on Zippin's method, and the estimator of CARLE and STRUB (1978), that we used, was shown to be more robust (COWX, 1983; GERDEAUX, 1987). Nevertheless, we assume that the values presented in this paper provide for an approached information on the sizes of the studied fish populations.To assess the fish-habitat relationship, a correspondence analysis (fig. 2) was performed on the 74 samples X 17 species matrix (excluding the sticklebacks, Gaslerosteus aculeatus and Pungitius pungitius, which population size estimations failed because of their low catchabilities). Four groups of samples were ordinated according to their specific richness and the species they contained. Several habitat parameters were projected on F1-F2 factorial map (fig. 3). Hydrophyte cover, thickness of silt layer, water depth (fig. 3 and 4), which are directly controlled by human maintenance, appeared to be the major structuring habitat parameters for the fish community. In the deepest and less silted stations, the communities were rich (on average 11 species; group 4, fig. 2). Predators such as pike-perch, Stizostedion lucioperca, and perch, Perca fluviatilis, occurred, and cold water species were found, such as minnow, Phoxinus phoxinus, or chub, Leuciscus cephalus. When the silt layer was thicker and the water level was intermediate, the specific richness decreased (average, 6,2 species) and the community was either dominated by the cattish (group 2, fig. 2) or by the rudd, Scardinius erythrophtalmus (group 3, fig. 2), according to the importance of the aquatic vegetation cover. Habitats with thickest silt layers, shallowest waters and maximum aquatic vegetation cover contained the poorest communities (average 3,9 species) dominated by eel (group 1, fig. 2). There is also evidence that the diversity of the community has progressively decreased since 1987 (fig. 5). The most stenothermous species disappeared, and the importance of the catfish increased : it doubled between May 1987 and September 1989 (fig. 6). Although the eel is the species most adapted to this environment, we emphasize the diminution of its biomass (fig. 7). These phenomena could be partly due to the climate (cold winter in 1987, important swelling in January 1988 and 2 droughts in summers 1988 and 1989). But they are mainly caused by the water management policy which is intended to favour agriculture by keeping stable water levels (evacuation of swellings) and by preventing the freshwater part from the marine influence (collective sluice gates). This does mot permit an optimal breeding of the species that have to spawn on flooded meadows, neither a proper colonisation of the marsh by elvers

Response of an impacting hertzian contact to an order-2 subharmonic excitation : theory and experiments

Response of a normally excited preloaded Hertzian contact is investigated in order to analyze the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain the non-trivial steady state solutions, their stability, and the frequency-response curves. To this end, a third order Taylor series of the elastic Hertzian contact force is introduced over the displacement interval where the system remains in contact. A classical time integration method is also used in conjunction with a shooting method to take into account losses of contact. The theoretical results show that the subharmonic resonance constitutes a precursor of dynamic responses characterised by loss of contact, and consequently, the resonance establishes over a wide frequency range. Finally, experimental validations are also presented in this paper. To this end, a specific test rig is used. It corresponds to a double sphere-plane contact preloaded by the weight of a moving mass. Experimental results show good agreements with theoretical ones

Forced oscillations dynamic tribometer with real-time insights of lubricated interfaces

This paper presents an innovative forced oscillations dynamic tribometer, the CHRONOS tribometer, with a lubricated ball-on-flat contact configuration fitted out with an in situ optical visualization system and a triggered high-speed camera. The CHRONOS tribometer generates controlled oscillating kinematics by means of a shaker with a range of strokes from 5 μm to 2.5 mm and an oscillation frequency which can be adjusted from 5 Hz to 250 Hz. Displacement and velocity are measured using a vibrometer. The ball-on-flat mean contact pressure is set between 200 MPa and 600 MPa. During motion, the instantaneous normal and friction forces and the interfacial film thickness distribution (in the nanometer scale) are simultaneously measured. In addition to this instantaneous approach, a more macroscopic approach is developed in terms of moving averages of friction and velocity. Another parameter, the friction-velocity tilt angle, is also introduced. This last parameter may give information on the friction-velocity dependence. Eventually, the experiments performed on the CHRONOS device lead to the representation of synchronized temporal signals of displacement/velocity, friction, and lubricant central film thickness. This superimposition of key parameters reveals time effects introduced by the periodical fluid squeeze and flow in the contact

The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR

A large fraction of the present-day stellar mass was formed between z=0.5 and z~3 and our understanding of the formation mechanisms at work at these epochs requires both high spatial and high spectral resolution: one shall simultaneously} obtain images of objects with typical sizes as small as 1-2kpc(~0''.1), while achieving 20-50 km/s (R >= 5000) spectral resolution. The obvious instrumental solution to adopt in order to tackle the science goal is therefore a combination of multi-object 3D spectrograph with multi-conjugate adaptive optics in large fields. A partial, but still competitive correction shall be prefered, over a much wider field of view. This can be done by estimating the turbulent volume from sets of natural guide stars, by optimizing the correction to several and discrete small areas of few arcsec2 selected in a large field (Nasmyth field of 25 arcmin) and by correcting up to the 6th, and eventually, up to the 60th Zernike modes. Simulations on real extragalactic fields, show that for most sources (>80%), the recovered resolution could reach 0".15-0".25 in the J and H bands. Detection of point-like objects is improved by factors from 3 to >10, when compared with an instrument without adaptive correction. The proposed instrument concept, FALCON, is equiped with deployable mini-integral field units (IFUs), achieving spectral resolutions between R=5000 and 20000. Its multiplex capability, combined with high spatial and spectral resolution characteristics, is a natural ground based complement to the next generation of space telescopes.Comment: ESO Workshop Proceedings: Scientific Drivers for ESO Future VLT/VLTI Instrumentation, 10 pages and 5 figure

Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 1: harmonic excitation

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analysed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated. Linearised resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated. Resonance peak is confined in a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. Forced response spectrum exhibits several harmonics because of nonlinear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results. For higher input amplitude, system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibroimpacting contact and leads to a wide frequency range softening resonance. Spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency versus input amplitude allows the identification of the nonlinear damping law during intermittent contact. Simulations of the vibroimpacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results

Purification and Reconstitution of the Glutamate Carrier GltT of the Thermophilic Bacterium Bacillus stearothermophilus

An affinity tag consisting of six adjacent histidine residues followed by an enterokinase cleavage site was genetically engineered at the N-terminus of the glutamate transport protein GltT of the thermophilic bacterium Bacillus stearothermophilus. The fusion protein was expressed in Escherichia coli and shown to transport glutamate. The highest levels of expression were observed in E. coli strain DH5α grown on rich medium. The protein could be purified in a single step by Ni2+-NTA affinity chromatography after solubilization of the cytoplasmic membranes with the detergent Triton X100. Purified GltT was reconstituted in an active state in liposomes prepared from E. coli phospholipids. The protein was reconstituted in detergent-treated preformed liposomes, followed by removal of the detergent with polystyrene beads. Active reconstitution was realized with a wide range of Triton X100 concentrations. Neither the presence of glycerol, phospholipids, nor substrates of the transporter was necessary during the purification and reconstitution procedure to keep the enzyme in an active state. In B. stearothermophilus, GltT translocates glutamate in symport with protons or sodium ions. In membrane vesicles derived from E. coli cells expressing GltT, the Na+ ion dependency seems to be lost, suggesting a role for the lipid environment in the cation specificity. In agreement with the last observation, glutamate transport catalyzed by purified GltT reconstituted in E. coli phospholipid is driven by an electrochemical gradient of H+ but not of Na+.