Authors : Janaina Cunha Vaz Albuquerque and Jose Juliano de Lima
Abstract: Stepped beams with elastic end supports have been extensively investigated due to their importance in structural engineering fields, including active structures, structural elements with integrated piezoelectric materials, shaft-disc system components, turbomachinery blades and many other structural configurations. In the present research, a mathematical modeling is proposed to determine the natural frequencies of a stepped beams without the need to research with a large number of discretization elements and different kinds of meshes within the domain. The mathematical modeling is proposed for stepped beams with elastic end supports. The analysis is based on the classical Euler-Bernoulli beam theory. In comparison with the published literature on the transverse vibration of single cross section change beams, there are relatively few works covering beam vibration when there is >1 change in the beam cross section. In the present study, the natural frequencies and the mode shapes of beams with variable geometry or material discontinuities are investigated. The mode shapes of a beam with multiple step changes in cross section are discussed theoretically and experimentally. Numerical results obtained by Euler-Bernoulli beam theory are compared with experimental results.
Janaina Cunha Vaz Albuquerque and Jose Juliano de Lima, 2013. Dynamic Characteristics of Euler-Bernoulli Beams with Multiple Step Changes in Cross Section or Multiple Geometric. Journal of Engineering and Applied Sciences, 8: 248-254.