Stability analysis of a free falling pararotor

The pararotor is a decelerator device based on the autorotation of a rotating wing. When it is dropped, it generates an aerodynamic force parallel to the main motion direction, acting as a decelerating force. In this paper, the rotational motion equations are shown for the vertical flight without any lateral wind component and some simplifying assumptions are introduced to obtain analytic solutions of the motion. First, the equilibrium state is obtained as a function of the main parameters. Then the equilibrium stability is analyzed. The motion stability depends on two nondimensional parameters, which contain geometric, inertia, and aerodynamic characteristics of the device. Based on these two parameters a stability diagram can be defined. Some stability regions with different types of stability trajectories (nodes, spirals, focuses) can be identified for spinning motion around axes close to the major, minor, and intermediate principal axes. It is found that the blades contribute to stability in a case of spin around the intermediate principal inertia axis, which is otherwise unstable. Subsequently, the equations for determining the angles of nutation and spin of the body are obtained, thus defining the orientation of the body for a stationary motion and the parameters on which that position depends.

Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Avaliação de métodos numéricos de análise linear de estabilidade para perfis de aço formados a frio.

Para o projeto de estruturas com perfis de aço formados a frio, é fundamental a compreensão dos fenômenos da instabilidade local e global, uma vez que estes apresentam alta esbeltez e baixa rigidez à torção. A determinação do carregamento crítico e a identificação do modo de instabilidade contribuem para o entendimento do comportamento dessas estruturas. Este trabalho avalia três metodologias para a análise linear de estabilidade de perfis de aço formados a frio isolados, com o objetivo de determinar os carregamentos críticos elásticos de bifurcação e os modos de instabilidade associados. Estritamente, analisa-se perfis de seção U enrijecido e Z enrijecido isolados, de diversos comprimentos e diferentes condições de vinculação e carregamento. Determinam-se os carregamentos críticos elásticos de bifurcação e os modos de instabilidade globais e locais por meio de: (i) análise com o Método das Faixas Finitas (MFF), através do uso do programa computacional CUFSM; (ii) análise com elementos finitos de barra baseados na Teoria Generalizada de Vigas (MEF-GBT), via uso do programa GBTUL; e (iii) análise com elementos finitos de casca (MEF-cascas) por meio do uso do programa ABAQUS. Algumas restrições e ressalvas com relação ao uso do MFF são apresentadas, assim como limitações da Teoria Generalizada de Viga e precauções a serem tomadas nos modelos de cascas. Analisa-se também a influência do grau de discretização da seção transversal. No entanto, não é feita avaliação em relação aos procedimentos normativos e tampouco análises não lineares, considerando as imperfeições geométricas iniciais, tensões residuais e o comportamento elastoplástico do material.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Linear transient analysis.

Includes bibliographies.

Embankment stability analysis. Pere Marquette Railroad (main line)-Detroit Industrial Expressway crossing. Project: X-7 of 82-22-10.

Mode of access: Internet.

Regional adjustments in grain production : a linear programming analysis /

"U.S. Dept. of Agriculture, in cooperation with Iowa Agriculture and Home Economics Experiment Station Center for agricultural and economic adjustment."

Regional adjustments in grain production : a linear programming analysis : mathematical models, proofs, methods of data collection and estimation, and supplementary tables /

Cover title.

Aggregate economic effects of alternative land retirement programs : a linear programming analysis /

Includes bibliographical references (p. 53-54).

Regional location of production of major field crops at alternative demand and price levels, 1975; a linear programing analysis,

Issued in cooperation with Iowa State University of Science and Technology, Agriculture and Home Economics Experiment Station, and the Center for Agricultural and Economic Development.

Interregional adjustments in crop and livestock production; a linear programming analysis,

Prepared in cooperation with the Center for Agricultural and Economic Development. Iowa Agriculture and Home Economics Experiment Station, Iowa State University.

Thermal stability analysis of organo-silicates, using solid phase microextraction techniques

An analysis of thermal degradation products evolved during the melt processing of organo-layered silicates (OLS) was carried out via the use of a solid phase microextraction (SPME) technique. Two commerical OLSs and one produced in-house were prepared for comparision. The solid phase microextraction technique proved to be a very effective technique for investigating the degradation of the OLS at a specific processing temperature. The results showed that most available OLSs will degrade under typical conditions required for the melt processing of many polymers, including thermoplastic polyurethanes. It is suggested that these degradation products may lead to changes in the structure and properties of the final polymer, particularly in thermoplastic polyurethanes, which seem significantly succeptable to the presence of these products. It is also suggested that many commercially available OLSs are produced in such a way that results in an excess of unbound organic modifier, giving rise to a greater quantity of degradation products. All OLSs where compared and characterised by TGA and GC-MS. (c) 2004 Elsevier B.V. All rights reserved.