Modal Formulation of Segmented Euler-Bernoulli Beams

We consider the obtention of modes and frequencies of segmented Euler-Bernoulli beams with internal damping and external viscous damping at the discontinuities of the sections. This is done by following a Newtonian approach in terms of a fundamental response of stationary beams subject to both types of damping. The use of a basis generated by the fundamental solution of a differential equation of fourth-order allows to formulate the eigenvalue problem and to write the modes shapes in a compact manner. For this, we consider a block matrix that carries the boundary conditions and intermediate conditions at the beams and values of the fundamental matrix at the ends and intermediate points of the beam. For each segment, the elements of the basis have the same shape since they are chosen as a convenient translation of the elements of the basis for the first segment. Our method avoids the use of the first-order state formulation also to rely on the Euler basis of a differential equation of fourth-order and it allows to envision how conditions will influence a chosen basis

New Actuators for Aircraft, Space and Military Applications

Abstract: Actuation is used in all vehicles (aircraft, spacecraft, ground vehicles, etc) to control the position and/or attitude of the vehicle, and also to deploy or retract equipment, particularly for embedded optic instruments (cameras, telescopes). As such, the actuation is a safety critical system, particularly when humans could be catastrophically affected by failures within the system. Applications for actuation are flight controls, landing gear, rotors, suspension, antennae steering, valves, scanning, positioning using hydraulic, electromechanical, magnetic and piezo actuators. In aircraft there is a common goal to reduce the number of hydraulic actuators in vehicles and eventually to replace them completely by electric actuators. The interest for smart suspensions is pushing magnetorheological fluids (MRF) actuators. In UAV, MAV and microsatellites, actuators key drivers are often miniaturisation and low power. Embedded optic & space instruments are leading to improved piezo actuators and motors

Deep EST profiling of developing fenugreek endosperm to investigate galactomannan biosynthesis and its regulation

Galactomannans are hemicellulosic polysaccharides composed of a (1 → 4)-linked β-D-mannan backbone substituted with single-unit (1 → 6)-α-linked D-galactosyl residues. Developing fenugreek (Trigonella foenum-graecum) seeds are known to accumulate large quantities of galactomannans in the endosperm, and were thus used here as a model system to better understand galactomannan biosynthesis and its regulation. We first verified the specific deposition of galactomannans in developing endosperms and determined that active accumulation occurred from 25 to 38 days post anthesis (DPA) under our growth conditions. We then examined the expression levels during seed development of ManS and GMGT, two genes encoding backbone and side chain synthetic enzymes. Based on transcript accumulation dynamics for ManS and GMGT, cDNA libraries were constructed using RNA isolated from endosperms at four ages corresponding to before, at the beginning of, and during active galactomannan deposition. DNA from these libraries was sequenced using the 454 sequencing technology to yield a total of 1.5 million expressed sequence tags (ESTs). Through analysis of the EST profiling data, we identified genes known to be involved in galactomannan biosynthesis, as well as new genes that may be involved in this process, and proposed a model for the flow of carbon from sucrose to galactomannans. Measurement of in vitro ManS and GMGT activities and analysis of sugar phosphate and nucleotide sugar levels in the endosperms of developing fenugreek seeds provided data consistent with this model. In vitro enzymatic assays also revealed that the ManS enzyme from fenugreek endosperm preferentially used GDP-mannose as the substrate for the backbone synthesis

Expression Patterns of Genes Involved in Sugar Metabolism and Accumulation during Apple Fruit Development

Both sorbitol and sucrose are imported into apple fruit from leaves. The metabolism of sorbitol and sucrose fuels fruit growth and development, and accumulation of sugars in fruit is central to the edible quality of apple. However, our understanding of the mechanisms controlling sugar metabolism and accumulation in apple remains quite limited. We identified members of various gene families encoding key enzymes or transporters involved in sugar metabolism and accumulation in apple fruit using homology searches and comparison of their expression patterns in different tissues, and analyzed the relationship of their transcripts with enzyme activities and sugar accumulation during fruit development. At the early stage of fruit development, the transcript levels of sorbitol dehydrogenase, cell wall invertase, neutral invertase, sucrose synthase, fructokinase and hexokinase are high, and the resulting high enzyme activities are responsible for the rapid utilization of the imported sorbitol and sucrose for fruit growth, with low levels of sugar accumulation. As the fruit continues to grow due to cell expansion, the transcript levels and activities of these enzymes are down-regulated, with concomitant accumulation of fructose and elevated transcript levels of tonoplast monosaccharide transporters (TMTs), MdTMT1 and MdTMT2; the excess carbon is converted into starch. At the late stage of fruit development, sucrose accumulation is enhanced, consistent with the elevated expression of sucrose-phosphate synthase (SPS), MdSPS5 and MdSPS6, and an increase in its total activity. Our data indicate that sugar metabolism and accumulation in apple fruit is developmentally regulated. This represents a comprehensive analysis of the genes involved in sugar metabolism and accumulation in apple, which will serve as a platform for further studies on the functions of these genes and subsequent manipulation of sugar metabolism and fruit quality traits related to carbohydrates

MODÉLISATION DE TRANSDUCTEURS MAGNÉTOSTRICTIFS À L'AIDE DU CODE ÉLÉMENTS FINIS ATILA

Un modèle mathématique tridimensionnel a été développé pour prendre en compte le phénomène physique de la magnétostriction. Il utilise une formulation variationnelle basée sur un potentiel magnétique scalaire réduit. Cette approche permet de modéliser des transducteurs magnétostrictifs en régime statique ou harmonique, dans l'air ou rayonnant dans un fluide, par la méthode des éléments finis. Cet article décrit brièvement le modèle mathématique, puis son application à l'étude d'un dispositif de caractérisation, pour lequel on dispose d'un modèle d'ondes planes ainsi que de mesures.New magnetostrictive rare earth - iron alloys offer an attractive opportunity for the design of high-power low-frequency transducers. In order to optimize the design of this particular class of transducers, a model based on a new variational principle has been derived, following a classical finite element method approach. This model describes the three-dimensional dynamic behavior of heterogeneous electromechanically coupled structures, in air or acoustically radiating in a surrounding fluid domain. Using a reduced scalar potential formulation of the magnetic field, the model has been implemented within the ATILA finite element code. In this paper, a general view of the method is given and results of the computation on a characterization device are compared to plane-wave model and experimental results

ANALYSE D'UN MOTEUR ULTRASONORE PIÉZOÉLECTRIQUE À L'AIDE DE LA MODÉLISATION

Ultrasonic motors use a frictional force produced by high frequency vibrations created by the piezoelectric effect of the stator, to drive the rotor. These devices have been widely studied especially in Japan. A stator of a piezoelectric ultrasonic rotating motor, which uses Lamb waves vibrations, has been modelled using the finite element code ATILA. It takes into account three dimensional piezoelectric effects and electrical excitations. ATILA permits the computation of the resonance frequency and the effective coupling coefficient of each vibrational mode, the electrical impedance and the elliptical displacement field. The governing electromechanical coupling has been determined. Consequently, the selection of active material and stator geometry may be optimized to provide an improved transduction efficiency

Forced oscillations with continuum models of atomic force microscopy

The dynamics of the AFM-atomic force microscope follows a model based in a Timoshenko cantilever beam with a tip attached at the free end and acting with the surface of a sample. General boundary conditions arise when the tip is either in contact or non-contact with the surface. The governing equations are given in matrix conservative form subject to localized loads. The eigenanalysis is done with a fundamental matrix response of a damped second-order matrix differential equation. Forced responses are found by using a Galerkin approximation of the matrix impulse response. Simulations results with harmonic and pulse forcing show the filtering character and the effects of the tip-sample interaction at the end of the beam. © 2012 American Institute of Physics

Closed-Form Solution for the Solow Model with Constant Migration

ABSTRACT. In this work we deal with the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss' Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining