MODAL ANALYSIS FOR FREE VIBRATION OF FOUR BEAM THEORIES

Anderson Soares da Costa Azevêdo¹; Simone dos Santos Hoefel¹

¹ Universidade Federal do Piauí

doi:10.20906/CPS/COB-2015-0991

Resumo

Beams are structural elements frequently used for support buildings, part of airplanes, ships, rotor blades and most engineering structures. In many projects it is assumed that these elements are subjected only to static loads, however dynamic loads induce vibrations, which changes the values of stresses and strains. Furthermore, these mechanical phenomenon cause noise, instabilities and may also develop resonance, which improves deflections and failure. Therefore study these structural behavior is fundamental in order to prevent the effects of vibration. The mechanical behavior of these structural elements may be described by differential equations, four widely used beam theories are Euler-Bernouli, Rayleigh, Shear and Timoshenko. This paper presents a comparison between these four beam theories for the free transverse vibration of uniform beam. Numerical examples are shown to beam models under classical boundary condition.

Palavras-chave: Euler-Bernoulli; Timoshenko; Free Vibration; Shear; Rayleigh