Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Projeto, Desenvolvimento e implementação de um Robô Voador de Inspiração Biológica

Este trabalho consiste no projeto, desenvolvimento e implementação de uma máquina voadora de inspiração biológica. Para a sua construção, é elaborado um estudo do voo nos seres biológicos de forma a obter alguma informação para o seu dimensionamento e é elaborada uma análise de projetos que utilizem as mesmas características de voo. Com os dados recolhidos neste estudo, é elaborado o projeto da máquina. Numa última fase, com recurso a materiais leves, é implementada uma máquina capaz de exercer as forças envolvidas no voo, força de propulsão e força de sustentação, e são elaborados estudos a fim de perceber quais os pontos fortes e os pontos fracos da mesma.