Nonlinear normal modes of nonuniform exible beams

Autores

  • Gustavo Wagner
  • Roberta Lima
  • Rubens Sampaio

DOI:

https://doi.org/10.5540/03.2022.009.01.0279

Palavras-chave:

Nonuniform exible beams, Nonlinear normal modes, Co-rotational nite element, Harmonic Balance Method

Resumo

Flexible beams contain geometric nonlinearities emanated from the large displacements and large rotations of the cross sections. When the geometry of the beam is nonuniform, the equation of motion becomes complicated to derive, but can be eficiently approximated using the co-rotational nite element method. This paper proposes a procedure to compute nonlinear normal modes (NNM) of nonuniform exible beams. The Rosenberg's definition of NNM is applied. The periodic solutions are computed using the Harmonic Balance Method (HBM) and the continuation of the modes properties with respect to the energy level is performed using the arc-length method. Examples of clamped-clamped beams with dierent cross sections variations are presented, illustrating the respective impacts in the NNMs.

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Biografia do Autor

Gustavo Wagner

Departamento de engenharia mecânica, PUC-Rio, Rio de Janeiro, RJ

Roberta Lima

Departamento de engenharia mecânica, PUC-Rio, Rio de Janeiro, RJ

Rubens Sampaio

Departamento de engenharia mecânica, PUC-Rio, Rio de Janeiro, RJ

Referências

J.C.R. Albino et al. Co-rotational 3D beam element for nonlinear dynamic analysis of risers manufactured with functionally graded materials (FGMs). In: Engineering Structures 173 7 Figure 5: NNM motion of Beam 2 at low and high energies. Fourier coe cients of the motion at middle and one quarter of the beam. (2018), pp. 283299. issn: 0141-0296. doi: https://doi.org/10.1016/j.engstruct.2018. 05.092.

B. Cochelin. Numerical computation of nonlinear normal modes using HBM and ANM. In: Modal Analysis of Nonlinear Mechanical Systems. Ed. by G. Kerschen. Vienna: Springer Vienna, 2014, pp. 251292. isbn: 978-3-7091-1791-0. doi: https://doi.org/10. 1007/978-3-7091-1791-0_6.

K.M. Hsiao and J.Y. Jang. Dynamic analysis of planar exible mechanisms by co-rotational formulation. In: Computer Methods in Applied Mechanics and Engineering 87.1 (1991), pp. 114. issn: 0045-7825. doi: https://doi.org/10.1016/0045-7825(91)90143-T.

M. Iura and S.N. Atluri. Dynamic analysis of planar exible beams with nite rotations by using inertial and rotating frames. In: Computers & Structures 55.3 (1995), pp. 453462. issn: 0045-7949. doi: https://doi.org/10.1016/0045-7949(95)98871-M.

G. Kerschen et al. Nonlinear normal modes, Part I: A useful framework for the structural dynamicist. In: Mechanical Systems and Signal Processing 23.1 (2009), pp. 170194. issn: 0888-3270. doi: https://doi.org/10.1016/j.ymssp.2008.04.002.

M. Krack and J. Gross. Harmonic Balance for Nonlinear Vibration Problems. Mathematical Engineering. Cham, Switzerland: Springer International Publishing, 2019. isbn: 978- 3-030-14023-6. doi: https://doi.org/10.1007/978-3-030-14023-6.

R.U. Seydel. Practical Bifurcation and Stability Analysis. Interdisciplinary Applied Mathematics. New York, USA: Springer New York, 2009. isbn: 978-1-4419-1739-3. doi: https: //doi.org/10.1007/978-1-4419-1740-9.

G. Wagner. An excursion in the dynamics of exible beams: from modal analysis to nonlinear modes. PhD Thesis. Mechanical Engineering Department, Pontical Catholic University of Rio de Janeiro, 2022.

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Publicado

2022-12-08

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