Modelagem matemática de sistemas vibratórios com aplicação de autovalores

Abstract

The present work aims to contribute to the teaching and learning process of disciplines such as Linear Algebra and Differential Equations, suggesting a study methodology based on mathematical modeling of mechanical systems and application of eigenvalues of problem, as well as encourage high school students to explore mathematics, a revealing and essential science, showing that content such as complex numbers, determinants, trigonometry, etc., some of these mistakenly questioned about its practical utility, can be used for the benefit of people, for example, providing more security and stability to buildings , essential in modern times. Initially, the contents will be displayed formally required for the understanding of vibrating systems with two degrees of freedom to apply them subsequently in the determination of natural frequencies of vibration of a two storey building. Also, a demo will be made of how to calculate the eigenvalues through of computational tools, the softwares MATLAB and R. Using the softwares, the determination of natural frequencies becomes even more practical and thus shows that the application of the problem is quite simple and has obvious practical use.