Dinâmica de máquinas rotativas: um instrumento de aprendizagem no ensino médio

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Universidade Federal de Goiás


In this work, a modeling approach in Mathematics Education is made. Modeling has not yet arrived significantly the schools, probably because many educators have difficulty justifying the use of mathematics taught, or because they have little time for class preparation. In addition to precarious training, there are few materials the Basic Education (High School). This dissertation intends to produce a material that can minimize this need. Therefore, an approach is made on the History of Rotary Machines, taking as a principle the origin of the wheel, from the age of the stone, where it appears the Wheel of Potter's of 3500 BC. Its use in war machines is shown in all the old Roman Empire and arrives until the construction of first Turbine of Aelopile Reaction of Hero. With the advancement of the science of the time, we have the construction of Water Wheels, probably the first tools implemented by mankind to crush seeds, and reports great scientists such as Euler and Bernoulli and Joseph Lagrange, who made great contributions during the scientific revolution, and thus culminates in the invention of First Parson Turbine. The History of the Rotating Machine, facilitates the understanding of its functionalities. There was a theoretical basis of the Ordinary Differential Equations, in which homogeneous linear equations with coefficients are used constants, where its solution is based on functions and equations widely known in High School (Equations of the Second Degree, Polynomial Functions, Trigonometric Functions, and Exponential Functions). Based on Hooke's Law and in the Second Newton Law, it is shown the simplest of vibratory systems and types of movements. In rotor dynamics, the rotor was defined, its elements and the type of movement using the Jeffcott Model, very useful for establishing concepts and definitions. It also seeks to understand the physical meaning of the solutions with their graphical analysis.



Modelagem matemática, Dinâmica de máquinas rotativas, Ensino médio, Mathematical modeling, Rotordynamics, High School


SILVA, S. J. Dinâmica de máquinas rotativas: um instrumento de aprendizagem no ensino médio. 2019. 66 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Catalão, 2019.