Structure and stability of annular sheared channel flows: effects of confinement,curvature and inertial forces – waves

The structure and stability of the flows in an annular channel sheared by a rotating lid are investigated experimentally, theoretically and numerically. The channel has a square section, and a small curvature parameter: the ratio Γ of the inter-radii to the mean radius is 9.5%. The sidewalls and the bottom of the channel are integral and can rotate independently of the lid, permitting pure shear, co-rotation and counter-rotation cases. The basic flows obtained at small shear are characterized. In the absence of co-rotation, the centrifugal force linked with the curvature of the system plays an important role, whereas, when co-rotation is fast, the Coriolis force dominates. These basic flows undergo some instabilities when the shear is increased. These instabilities lead to supercritical traveling waves in the pure shear and co-rotation cases, but to weak turbulence in the counter-rotation case. The Reynolds number for the onset of instabilities, constructed with the velocity difference between the lid and bottom at mid-radius, and the height of the channel, increases from 1000 in the counter-rotation case to 1260 in the pure shear case and higher and higher values when co-rotation increases, i.e., when the Coriolis effect increases. The relevance of uni-dimensional Ginzburg-Landau models to describe the dynamics of the waves is studied. The domain of validity of these models turns out to be quite narrow.     

Optimal Forms of Shallow Arches with Respect to Vibration and Stability

Shallow, linearly elastic arches of unspecified form but with given uniform cross section and material are considered. For given span and length of the arch, two different optimization problems are formulated and solved. In the first, we determine the form of the arch which maximizes the fundamental vibration frequency. The corresponding vibration mode turns out to be either symmetric or antisymmetric. In the second, a static load with given spatial distribution is considered, and the critical value of the load magnitude for snap-through instability is maximized. This instability may occur at a limit point or a bifurcation point. Optimal forms are determined for sinusoidal loading, uniform loading, and a central concentrated load. In both types of problems, arches with simply supported or clamped ends are considered, and the maximum frequencies and critical loads obtained are compared to those for a circular arch with similar end conditions. In all the cases with simply supported ends, it is found that a circular arch is almost optimal. For clamped ends, however, it turns out that the optimal arches have zero slope at the ends and that they are much more efficient than a circular arch.     

Sensitivity Analysis and Optimal Design of Nonlinear Beams and Plates

A uniform formulation of sensitivity analysis for beams and plates is presented in terms of generalized stresses and strains. Both physical and geometric nonlinearities can be treated within this formulation. Next, optimal design problems for stress and deflection constraints are formulated and the relevant optimality conditions are derived using the concept of a linear adjoint structure. Finally, several numerical solutions of optimal design problems of beams are presented.     

Rapid Manufacturing of Non-Assembly Complex Micro-Devices by Microstereolithography

This paper introduces a non-assembly manufacturing case with microstereolithography technology. The design and manufacturing process of a pneumatic thrust bearing is described, and a special tessellation method is developed to further improve the capability of the manufacturing system thus bigger products can also be easily manufactured. Implemented in a layer-by-layer fashion, stereolithography has been used for the rapid manufacturing of complex devices, and it avoids the expensive assembly process in the traditional manufacturing. This paper presents that microstereolithography can produce high-resolution products with intricate details, small openings, and smooth surfaces. The potential of the microstereolithograhy technique is explored for the rapid manufacturing of small and complex objects.     

Snap loads and torsional oscillations of the original Tacoma Narrows Bridge

In 1940, the original Tacoma Narrows Bridge was completed on June 10 and opened to traffic on July 1. On November 7, the deck collapsed. Before that day, significant vertical oscillations had occurred, but no torsion. The bridge as built was stable with respect to torsional motion under the winds of November 7 and previous winds with higher speeds. However, snap loads in the diagonal ties attached to the north midspan cable band helped to loosen the band, and the frictional resistance between the band and the north suspension cable passing through it was overcome. The cable began to slip through the band. For this new structural system, with longitudinal motion of the north cable, the wind speed was higher than the critical speed for torsional flutter, and torsional motion was initiated. Approximately 700 cycles of torsional oscillations occurred during the hour prior to the collapse. In the present study, the snap loads on the cable band are discussed first. Then a continuum model of the central span (deck, cables, and hangers) is formulated. The longitudinal motions of the cables are included, so that the slippage can be incorporated. Known information from the observed steady-state torsional motion is utilized with assumed forms of the vertical cable displacements, and the governing equations provide the horizontal cable displacements, the dynamic tensions in the cables, the vertical and torsional motions of the deck, and the resultant lift force and pitching moment (including damping) acting on the deck during its final hour.     

FLUORESCENCE OF THE COENZYME ANALOG NICOTINAMIDE FORMYCIN DINUCLEOTIDE

Abstract— Emission spectra of unbound reduced nicotinamide formycin dinucleotide (NFDH) revealed the presence of two major conformations of the coenzyme in solution: when examined at excitation wavelengths at or below 307 nm, emission spectra contained peaks at 343 and 447 nm; when excited above 307 nm, an additional maximum appeared at 355 nm and the peak of the dihydronicotinamide emission band shifted from 447 to 440 nm. Both conformers are probably detected at the longer wavelengths since the emission peak at 343 nm was retained. Identical changes occurred in the emission spectra of NFD⁺, however, the dihydronicotinamide emission between 440 and 447 nm was absent. Several mechanisms which may account for the presence of these conformers have been considered. The choice has been narrowed to conformations with ring-ring interactions of the formycin and nicotinamide moieties resulting from (a) formycin tautomerization or (b) heterogeneity of glycosidic bond angles in the structures. The efficiency of intramolecular energy transfer from the formycin to the dihydronicotinamide moiety for free NFDH in aqueous solution was 84% and declined slightly (to 77%) when measured in 1,2-propanediol. NFD⁺ has coenzyme activity for NAD-specific isocitrate dehydrogenase (Plaut et al. , 1979). The emission spectrum of enzyme bound NFDH was altered markedly in the presence of manganese isocitrate; emission intensity at 343 and 355 nm decreased while the emission from the dihydronicotinamide ring at 433 nm increased, when NFDH was excited at 310 nm. This shift in emission intensity was indicative of an increase in energy transfer within the NFDH molecule, caused by a change in coenzyme conformation upon binding to the enzyme-substrate complex.     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: II. Experiments

We study experimentally the evolution of thermoconvection in a laterally extended planar nematic layer, at zero or weak stabilizing magnetic field. As the applied thermal gradient is increased, a cascade of symmetry breakings occurs, towards structures of increasing spatial complexity, and ultimately towards oscillating states. The patterns are characterized optically, and simple models for the distortion of the vertical (out of plane) component of the director field are proposed. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998