Analysis of modal frequencies of beams by a numerical and analytical approach

Resumo

While static loads are more predictable and commonly applied in a project, dynamic ones are more
complex due to its irregularity and its dependency on time. But the importance of knowing how the structures are
affected and behave when dynamic loads are applied is essential to a building. Into the dynamic analysis, the
natural frequency is one of the modal parameters vastly used to describe the comportment and the problems that
the dynamic loads cause, such as resonance that induces to higher deflections. Thus, this paper will perform modal
analysis of a steel beam, undamaged and damaged, through two different calculus approaches: analytical and
numerical. The analytical approach data used in the modal analysis was calculated based on three generical
equations; for the numerical study, ABAQUS software based in the finite element method was used. The numerical
model was created in 1D, 2D, and 3D for the undamaged beam to compare the results with the parametric ones,
and in 2D for the damaged beam. The natural frequencies obtained by all method was satisfactory, and this
outcome might be useful for more complex research as composite structures composed by a steel beam and a
concrete slab.