Critical Torsional Oscillations of a Rotating Accelerated Shaft

We assume that the forces applied to the shaft have a variable part which is a moment of constant amplitude M(x) per unit length, distributed along the shaft, and varying with a frequency proportional to the angular velocity. From the solution corresponding to the harmonic steady state vibration, we deduce, by using Heaviside's expansion, the motion due to a sudden application of the moment M(x). This enables us to compute the effect of the moment when applied with a linearly increasing frequency. In this analysis the damping will be neglected. In case of a viscous damping the linear character of the equations is not affected and the same method might be used. We did not carry this calculation for two reasons: 1. The exact result will be in general complicated, and involve viscous friction coefficients which will not be very accurately known. Besides, the effect of friction might be roughly taken into account by considering the steady state solution. 2. In most cases the damping is not viscous but due to the hysteresis or internal friction of the material. This is proved by the experimental fact that the energy absorbed in the vibration of elastic bodies is proportional to the frequency and not to its square. This effect might be taken roughly into account by energetic considerations

PERFORMANCE MANAGEMENT IN THE PUBLIC SECTOR:

Education supply in universities of most European countries has for the last ten years become a strategic matter. At present, French universities consider education supply as an investment. But they do not utilize all incentive mechanisms in order to drive their strategies. At the beginning of the year 2006, the public sector reform will tend to impose performance measurements of research and educational activities, in order to improve organizational efficiency. The aim of this reform in the French context is to provide driving elements to increase internal efficiency, social and economic impact of higher education system and to reinforce international attractiveness of public education institutions. The substitution of resources management by result management involves an agent's performance responsibility measurement. Evaluation becomes a central factor and is articulated with incentives system. The weakening of the property right system drives project bearers to maximize their utility instead of their incomes. In such a context, the understanding of individual strategies permits to understand constraints of management within universities, and to take into account the impact of stakeholders who take part in the value generation process. The major risk is to constraint the utility function of projects bearers by increasing their burden and their motivation. The result could be the limitation of the number of projects, and as well, the decreasing of university investments.performance, public sector, universities, efficiency, value generation

Nanoscale buckling deformation in layered copolymer materials

In layered materials, a common mode of deformation involves buckling of the layers under tensile deformation in the direction perpendicular to the layers. The instability mechanism, which operates in elastic materials from geological to nanometer scales, involves the elastic contrast between different layers. In a regular stacking of "hard" and "soft" layers, the tensile stress is first accommodated by a large deformation of the soft layers. The inhibited Poisson contraction results in a compressive stress in the direction transverse to the tensile deformation axis. The hard layers sustain this transverse compression until buckling takes place and results in an undulated structure. Using molecular simulations, we demonstrate this scenario for a material made of triblock copolymers. The buckling deformation is observed to take place at the nanoscale, at a wavelength that depends on strain rate. In contrast to what is commonly assumed, the wavelength of the undulation is not determined by defects in the microstructure. Rather, it results from kinetic effects, with a competition between the rate of strain and the growth rate of the instability. http://www.pnas.org/content/early/2011/12/23/1111367109.abstrac

Can one hear the shape of a saturation patch?

The theory of the acoustics of patchy-saturation in porous media is used to analyze experimental data on wave velocity and attenuation in partially water saturated limestones. It is demonstrated that the theory can be used to deduce the value of V/A, the ratio of the volume to area of the water patch, and l_f, the Poisson size of the water patch. One can ``hear'' the shape of a patch if the properties of the rock and the measurement frequencies are such as to satisfy the specific requirements for the validity of the theory

Scattering of a longitudinal wave by a circular crack in a fluid-saturated porous medium

Physical properties of many natural and man-made materials can be modelled using the concept of poroelasticity. Some porous materials, in addition to the network of pores, contain larger inhomogeneities such as inclusions, cavities, fractures or cracks. A common method of detecting such inhomogeneities is based on the use of elastic wave scattering. We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot's equations of dynamic poroelasticity. The problem is formulated in cylindrical co-ordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. It is found that the scattering that takes place is predominantly due to wave inducedfluid flow between the pores and the crack. The scattering magnitude depends on the size of the crack relative to the slow wave wavelength and has it's maximum value when they are of the same order

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio

Dynamic stability of bombs and projectiles

The four chapters comprising pages 1 to 123, inclusive, report were previously released in limited distribution with desigtions and dates as follows: Chapter I, CIT/JPC 4, January 2, 1943 Chapter II, CIT/JPC 5, January 2, 1943 Chapter III, CIT/JPC 6, January 2, 1943 Chapter IV, CIT/JPC 11, May 26, 1943 Chapters I and II were prepared as of July 1, 1942, Chapter III as of, September 1, 1942, and Chapter IV as of the publication date. The text is herewith reproduced from the original vellum copy by the photo-offset process, with mathematical notation in the author's hand. The references listed at the end of Chapter IV were originally contained in CIT/JPC 11 and since this list includes all references cited in JPC 4, 5, and 6, the lists originally contained in these reports are here omitted. The study as planned was intended to cover all aspects of the dynamic stability problems involved in solids moving through fluids. The chapters contained herein only partially cover the general subject. The results presented are immediately applicable to the ballistics of aerial bombs or the air trajectory of torpedoes. They also apply to the underwater ballistics of depth bombs and the underwater behavior of torpedoes in that phase of the trajectory where cavitation is absent