Space-time perturbation modes for non-linear dynamic analysis of beams

In this work an attempt is made at bridging the powerful perturbation methods of analytical dynamics to the versatile finite element techniques which can readily handle arbitrarily complex structures. The proposed analysis methodology has two distinguishing features. First, a space-time finite element formulation is used, and hence the concept of modes is here naturally extended to that of space-time modes, where the time dependency is implied in the assumed modes. As a result, the partial differential equations of motion are directly reduced to purely algebraic non-linear simultaneous equations. Second, perturbation modes, rather than the usual vibration mode shapes are used and shown to be an appropriate basis for non-linear dynamic analysis. These modes bring information about the non-linearities of the system through the higher order derivatives of the strain and kinetic energies. The procedure is illustrated on non-linear beam problems and the results are compared with those of a full finite element model, i.e., when all the degrees of freedom are considered, as well as with analytical results, when available.     

The Vectorial Parameterization of Rotation

The parameterization of rotation is the subject of continuous research and development in many theoretical and applied fields of mechanics, such as rigid body, structural, and multibody dynamics, robotics, spacecraft attitude dynamics, navigation, image processing, and so on. This paper introduces the vectorial parameterization of rotation, a class of parameterization techniques encompassing many formulations independently developed to date for the analysis of rotational motion. The exponential map of rotation, the Rodrigues, Cayley, Gibbs, Wiener, and Milenkovic parameterization all are special cases of the vectorial parameterization. This generalization parameterization sheds additional light on the fundamental properties of these techniques, pointing out the similarities in their formal structure and showing their inter-relationships. Although presented in a compact manner, all of the formulae needed for a complete implementation of the vectorial parameterization of rotation are included in this paper.     

Double-sided laser heating system for in situ high pressure–high temperature monochromatic x-ray diffraction at the esrf

A new double-sided laser heating system optimized for monochromatic X-ray diffraction at high pressure and high temperature has been developed at beamline ID27 of the European Synchrotron Radiation Facility (ESRF). The main components of this system including optimized focusing optics to produce a large and homogenous heated area, optimized mirror optics for temperature measurements and a state-of-the-art diffraction setup are described in details. Preliminary data collected at high pressure and high temperature on tungsten and iron are presented.     

In situ viscometry of high-pressure melts in the Paris–Edinburgh cell: application to liquid FeS

Knowledge of the viscosity of high-pressure melts is important in various domains of research, such as geosciences or materials science. Experimentally, the viscosity of liquids can be determined using the falling sphere technique. This method has been developed at high pressures and high temperatures at Beamline ID27 of the European Synchrotron Radiation Facility (ESRF), combining a Paris–Edinburgh cell with in situ X-ray radiography. The press is interfaced to Soller slits and imaging systems to measure high-quality diffraction patterns and high-resolution X-ray images of the sample. The viscosity of the liquid is derived from the velocity of a dense sphere falling through the pressurized melt and the Stokes law. An optimized two-circle diffractometer allows for moving the press upside down in order to perform a series of measurements on a single sample. The simultaneous collection of X-ray diffraction data on liquids offers the unique opportunity of investigating the relations between viscosity and the structure of melts. The potential of this new equipment is illustrated on the example of FeS melt viscosity and its implications for the Earth's core.     

Modeling of unilateral contact conditions with application to aerospace systems involving backlash, freeplay and friction

This paper describes an analysis procedure for the modeling of backlash, freeplay and friction in flexible multibody systems. The first two effects are formulated in a general manner as unilateral contact conditions in multibody dynamics. The incorporation of the effects of friction in joint elements is also discussed, together with an effective computational strategy. These non-standard effects are formulated within the framework of finite element based multibody dynamics that allows the analysis of complex, flexible systems of arbitrary topology. The versatility and generality of the approach are demonstrated by presenting applications to aerospace systems: the flutter analysis of a wing-aileron system with freeplay, the impact of an articulated rotor blade on its doop stop during engagement operation in high wind conditions, and the dynamic response of a space antenna featuring joints with friction.