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, etc. In the present work, a 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 more than one change in the beam cross-section. In the present study, the natural frequencies and the mode shapes of beams with two step changes in cross-sections are investigated. Combinations of the classical clamped, pinned, sliding and free type end supports are considered. The first three natural frequencies of the studied beams are evaluated for some types of end supports. The proposed method can be extended to beams with any number of changes in cross-section.
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