Dinâmica de máquinas rotativas: um instrumento de aprendizagem no ensino médio
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Data
2019-05-22
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Universidade Federal de Goiás
Resumo
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.
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Modelagem matemática, Dinâmica de máquinas rotativas, Ensino médio, Mathematical modeling, Rotordynamics, High School
Citação
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.