Dynamics of a non-uniform Euler-Bernoulli beam: sensitivity study in the parameter space - Ribeiro, Lilian M.; Soares, Gilson V.; Almeida, Alexandre C. L.; Oliveira, Adélcio C. (Journal of Applied Nonlinear Dynamics, 2026)
The dynamics and spectrum of vibrations of non-uniform Euler-Bernoulli beam were investigated. The beam cross section varies linearly in direction of its length. Spacial and temporal solutions were investigated, spacial by Differential transform Method and temporal by four order Runge Kutta. A comparison between temporal numerical solutions and generalized Landau analytical approximations was conducted. There is a significant region, in parameter spaces, that the generalized Landau solution works well, and that there is a region, in parameter space, where the system behaves as it was periodic for practical reasons, thus we name it as almost stable attractor. It was shown that the solutions are strongly sensible to parameters that are related to geometrical and physical proprieties of the beam, it means that a small deviation on parameters can change the dynamics from convergent to divergent, and between those regimes, there is a region on parameter space that the model imitates a periodic system.