Gyroscopic behaviour of stressed rotating shafts

An analysis is presented of the secondary effects due to deformation as a result of the shearing force, to the kinetic energy of rotation, and to the gyroscopic coupling, on the linearized equation of a straight shaft turning at a constant angular velocity and which is subjected to an axial torque and a compressive force. The local equations of motion of a section of shaft are derived and the magnitudes of the coupling terms are studied, non-dimensional variables being used. Results obtained by different authors in certain particular cases are rediscovered, and, in particular, the case of a shaft on short bearings is studied. Some comparisons of the theoretical results with those from experiments are given.     

Ultrasonic energy input influence οn the production of sub-micron o/w emulsions containing whey protein and common stabilizers

Ultrasonication may be a cost-effective emulsion formation technique, but its impact on emulsion final structure and droplet size needs to be further investigated. Olive oil emulsions (20 wt%) were formulated (pH ～ 7) using whey protein (3 wt%), three kinds of hydrocolloids (0.1–0.5 wt%) and two different emulsification energy inputs (single- and two-stage, methods A and B, respectively). Formula and energy input effects on emulsion performance are discussed. Emulsions stability was evaluated over a 10-day storage period at 5 °C recording the turbidity profiles of the emulsions. Optical micrographs, droplet size and viscosity values were also obtained. A differential scanning calorimetric (DSC) multiple cool–heat cyclic method (40 to ?40 °C) was performed to examine stability via crystallization phenomena of the dispersed phase.Ultrasonication energy input duplication from 11 kJ to 25 kJ (method B) resulted in stable emulsions production (reduction of back scattering values, dBS ～ 1% after 10 days of storage) at 0.5 wt% concentration of any of the stabilizers used. At lower gum amount samples became unstable due to depletion flocculation phenomena, regardless of emulsification energy input used. High energy input during ultrasonic emulsification also resulted in sub-micron oil-droplets emulsions (D₅₀ = 0.615 μm compared to D₅₀ = 1.3 μm using method A) with narrower particle size distribution and in viscosity reduction.DSC experiments revealed no presence of bulk oil formation, suggesting stability for XG 0.5 wt% emulsions prepared by both methods. Reduced enthalpy values found when method B was applied suggesting structural modifications produced by extensive ultrasonication. Change of ultrasonication conditions results in significant changes of oil droplet size and stability of the produced emulsions.     

Combined operando studies of new electrode materials for Li-ion batteries

The performances of Li-ion batteries depend on many factors amongst which the important ones are the electrode materials and their structural and electronic evolution upon cycling. For a better understanding of lithium reactivity mechanism of many materials the combination of X-Ray Powder Diffraction (XRPD) and Transmission Mössbauer Spectroscopy (TMS) providing both structural and electronic information during the electrochemical cycling has been carried out. Thanks to the design of a specific electrochemical cell, derived from a conventional Swagelock cell, such measurements have been realised in operando mode. Two examples illustrate the greatness of combining XRPD and TMS for the study of LiFe_0.75Mn_0.25PO₄ as positive electrode and TiSnSb as negative electrode. Different kinds of insertion or conversion reactions have been identified leading to a better optimization and design of performing electrodes.     

Thermoset modified with polyethersulfone: Characterization and control of the morphology

Thermoset (TS) epoxy resins can be toughened with a thermoplastic (TP) for high-performance applications. The final structure morphology has to be controlled to achieve high mechanical properties and high impact resistance. Four polyethersulfone-modified epoxy resins are considered. They consist of different epoxy monomer structure (TGAP, triglycidyl-p-aminophenol and TGDDM, tetraglycidyl diaminodiphenylmethane) and a fixed amount of thermoplastic, and they are cured with two different amounts of curing agent. A reaction-induced phase separation occurs for all formulations generating morphologies, different in shapes and scales. The aim is to control the final morphology and in particular its dominant length scale. This morphology depends on the phase separation process, from the initiation to its final stage. The initiation relies on the relative miscibility of the components and on the stoichiometry between epoxy and curing agent. The kinetics depends on the viscosity of the systems. The different morphologies are characterized by electron microscopy or neutron scattering. Dynamic mechanical analysis allows confirming the presence of a phase separation even when it is not observable by electron microscopy. Vermicular morphologies with few hundreds nanometer width are obtained for the systems containing the TGAP as epoxy monomer. Systems formulated with TGDDM presents morphologies on much smaller scale of order a few tens of nanometers. We interpret the different sizes of the morphologies as a consequence of a larger viscosity for the TGDDM systems as compared to the TGAP ones rather than by a latter initiation of phase separation.     

Cycloisomerization of (arene)chromium complexes with enyne by gold(I) catalyst for axially chiral biaryls

Planar chiral arene chromium complexes with enyne bond gave stereoselectively axial biaryl chromium complexes by gold(I) catalyzed cycloisomerization in good yields. Arene chromium complexes with enyne bonds were treated with triphenylphosphine gold bis(trifluoromethanesulfonyl)imidate in methylene chloride to give anti-biaryl monochromium complexes without formation of stereoisomers.     

Decomposition for adjustable robust linear optimization subject to uncertainty polytope

We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to polytope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row generation or column-and-row generation algorithms. The novelty of our approach lies in formulating the separation problem as a feasibility problem instead of a max–min problem as done in recent works. Applying the Farkas lemma, we can reformulate the separation problem as a bilinear program, which is then linearized to obtained a mixed-integer linear programming formulation. We compare the two algorithms on a robust telecommunications network design under demand uncertainty and budgeted uncertainty polytope. Our results show that the relative performance of the algorithms depend on whether the budget is integer or fractional.     

Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced

In this paper, the dynamics of a system composed of a harmonically forced single-degree-of-freedom linear oscillator coupled to a vibro-impact nonlinear energy sink (VI-NES) is experimentally investigated. The mass ratio between the VI-NES and the primary system is about \(1\%\). Depending on the external force’s amplitude and frequency, either a strongly modulated response (SMR) or a constant amplitude response (CAR) is observed. In both cases, an irreversible transfer of energy occurs from the linear oscillator toward the VI-NES: process known in the literature as passive targeted energy transfer. Furthermore, the problem is analytically studied by using the method of multiple scales. The obtained slow invariant manifold shows the existence of a stable and of an unstable branch of solutions, as well as of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently, the fixed points of the problem are calculated. When a stable fixed point is reached, the system is naturally drawn to it and a CAR is established, whereas when no stable point is attained, the system exhibits a SMR regime. Finally, a good correlation between the experimental and the analytical results is presented.     

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.