Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

Complex networks and data mining: toward a new perspective for the understanding of complex systems

Complex systems, i.e. systems composed of a large set of elements interacting in a non-linear way, are constantly found all around us. In the last decades, different approaches have been proposed toward their understanding, one of the most interesting being the Complex Network perspective. This legacy of the 18th century mathematical concepts proposed by Leonhard Euler is still current, and more and more relevant in real-world problems. In recent years, it has been demonstrated that network-based representations can yield relevant knowledge about complex systems. In spite of that, several problems have been detected, mainly related to the degree of subjectivity involved in the creation and evaluation of such network structures. In this Thesis, we propose addressing these problems by means of different data mining techniques, thus obtaining a novel hybrid approximation intermingling complex networks and data mining. Results indicate that such techniques can be effectively used to i) enable the creation of novel network representations, ii) reduce the dimensionality of analyzed systems by pre-selecting the most important elements, iii) describe complex networks, and iv) assist in the analysis of different network topologies. The soundness of such approach is validated through different validation cases drawn from actual biomedical problems, e.g. the diagnosis of cancer from tissue analysis, or the study of the dynamics of the brain under different neurological disorders.

De Cabo Verde para Lisboa: Cartas e remessas científicas da expedição naturalista de João da Silva Feijó (1783-1796). Vol. I - Documentação do Arquivo Histórico Ultramarino

Transcrição dos documentos relativos à expedição naturalista de João da Silva Feijó a Cabo Verde (1783-96), existentes no Arquivo Histórico Ultramarino e respetivo enquadramento histórico

De Cabo Verde para Lisboa: Cartas e Remessas Científicas da Expedição de João da Silva Feijó (1783-1796). Vol. II – Documentação da Biblioteca Nacional de Portugal e do Arquivo Histórico do Museu Nacional de História Natural e da Ciência da Universidade de Lisboa

Revisão botânica das tabelas de plantas, em Fevereiro de 2015, por Maria Cristina Duarte

Euler angles, Bryant angles and Euler parameters

This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work. In addition, for all the types of coordinates considered in this chapter, a characterization of the transformation matrix is fully described.

Analytical and numerical investigation of the ultra-relativistic Euler equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

As fórmulas de Euler em projeção estereográfica e seu significado físico no levantamento de indicatrizes óticas

As fórmulas de Euler são deduzidas a partir de triângulos esféricos obtidos da representação estereográfica das rotações φ, θ, ψ. Um exemplo de aplicação a uma secção arbitrária de gipsita é incluído.

Travels in the Confederation, 1783-1784. From the German. Translated and edited by Alfred J. Morrison.

2

Travels in the Confederation, 1783-1784. From the German. Translated and edited by Alfred J. Morrison.

1