Well-posedness of the free boundary problem for incompressible elastodynamics

The free boundary problem for the three dimensional incompressible elastodynamics system is studied under the Rayleigh–Taylor sign condition. Both the columns of the elastic stress $\mathbf{F}{\mathbf{F}}^{?}?\mathrm{I}$ and the transpose of the deformation gradient ${\mathbf{F}}^{?}?\mathrm{I}$ are tangential to the boundary which moves with the velocity, and the pressure vanishes outside the flow domain. The linearized equation takes the form of wave equation in terms of the flow map in the Lagrangian coordinate, and the local-in-time existence of a unique smooth solution is proved using a geometric argument in the spirit of [19].     

DFT calculations as a powerful tool for ESR spin trapping experiments

A combined electron spin resonance (ESR) and density functional theory study has been carried out to obtain deeper insight in the reaction mechanism of the photorearrangement of 3‐hydroxyindolic nitrones. Also, in this case, the combination of these techniques constitutes a powerful tool when discriminating between different reaction pathways. In particular, density functional theory calculations played an important role for unraveling the overlapping of signals coming from different species in the ESR spin trapping experiments. In the present study, the computed energies and the corresponding ESR parameters of each possible isomer hypothesized have been considered, taking also into account their different possibilities of intramolecular H‐bond formation. However, the results obtained indicate that the possibility of intramolecular H‐bonding did not play a determinant role in this case. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterization of flow around rectangular bluff bodies at angle of attack

Using data present in the literature from wind tunnel testing of semi-infinite and infinite rectangular bluff bodies at angle of attack, we develop a simple relation to predict the range of angles of attack where the lift remains approximately constant. This prediction is useful for researchers attempting to develop simplified models of the forces on rectangular bluff bodies. Additionally, prior work has shown that this region of the lift curve is characterized by complex three-dimensional flow, which has consequences for computational simulations.     

Expedient synthesis of ialibinones A and B by manganese(III)-mediated oxidative free radical cyclisation

The tricyclic natural products ialibinone A and ialibinone B were prepared as a 41:59 mixture in four steps starting from phloroglucinol. The synthetic sequence involved (i) acylation of phloroglucinol under Friedel-Crafts conditions, (ii) double prenylation using phase-transfer methodology, (iii) dearomatising methylation, and (iv) oxidative free radical cyclisation using manganese(III) acetate.     

The restricted three body problem revisited

We present a new computation of the Birkhoff normal form for the Hamiltonian of the restricted three body problem near the Lagrangian libration points. This leads to a new proof of the Lyapunov stability of these points.     

Gyroscopic signal smoothness assessment by geometric jolt estimation

The present contribution focuses on the estimation of the geometric acceleration and of the geometric jolt (namely, the derivative of the acceleration) of a multidimensional, structured gyroscopic signal. A gyroscopic signal encodes the instantaneous orientation of a rigid body during a full three‐dimensional rotation that is regarded as a trajectory in the curved space SO(3) of the special orthogonal matrices. The geometric acceleration and jolt associated to a gyroscopic signal are evaluated through the rules of calculus prescribed by differential geometry. Such an endeavor is motivated by recent studies on the smoothness of human body movement in biomechanical engineering, sports science, and rehabilitation neuroengineering. Two indexes of smoothness are compared, namely, a normalized proper geometric acceleration index and a normalized proper geometric jolt index. Our investigation concludes that, in the considered experiments with measured signals, for relatively low values of the acceleration and of the jolt indexes, such indexes are strongly positively correlated. Copyright © 2017 John Wiley & Sons, Ltd.     

Free vibration of composite laminated plate with complicated cutout

Abstract

This paper presents the free vibration analysis of a composite laminated square plate with complicated cutout. The problem formulation is based on the higher order shear deformation plate theory HDST C⁰ coupled with a curved quadrilateral p-element. The elements of the stiffness and mass matrices are calculated analytically. The curved edges are accurately represented using the blending function method. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as the cutout shape, plate thickness, fiber orientation angle, and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New results for the fundamentals frequencies of a composite laminated plate with complicated cutout are presented.     

On impacts with friction

For modeling contacts or more specifically impacts we have two possible concepts. Either we discretize the contact zone by applying some continuum mechanical approach, or we use a rigid body model, where the impact behavior follows from complementarity rules. It depends on the problem itself, which approach might be more convenient, more contact details in the first and more system aspects in the second case. In the following we shall consider the second method and apply it to large industrial problems.