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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamics of a non-uniform Euler-Bernoulli beam: sensitivity study in the parameter space

Journal of Applied Nonlinear Dynamics 7(2) (2018) 205--221 | DOI:10.5890/JAND.2018.06.009

Lilian M. Ribeiro; Gilson V. Soares; Alexandre C. L. Almeida; Adélcio C. Oliveira

Departamento de Física eMatemática, Universidade Federal de São João Del Rei C.P. 131,Ouro Branco, MG, 36420-000, Brazil

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Abstract

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.

Acknowledgments

The authors acknowledge FAPEMIG for financial support. ACO and ACLA acknowledge the support of the Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) through grant No.APQ-01366-16.

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