Determination of the first natural frequency of vibration of a steel pole, under the effect of geometric nonlinearity, using optimization techniques / Determinação da primeira frequência natural de vibração de um pólo de aço, sob o efeito da não linearidade geométrica, utilizando técnicas de optimização

Authors

  • Marcelo Araujo da Silva Brazilian Journals Publicações de Periódicos, São José dos Pinhais, Paraná
  • Paulo Henrique dos Santos Matos

DOI:

https://doi.org/10.34117/bjdv7n10-140

Keywords:

Dynamic Analysis, Vibration, Geometrical Non-Linearity, Vibration Mode, Rayleigh method.

Abstract

This work aims to find a procedure to obtain an alternative formulation that represents the first mode of vibration of slender steel poles considering the effect of geometric non-linearity, using the Reyleigh-Ritz method, trigonometric formulations with optimization techniques and a finite element mathematical model. The application was on an existing polygonal steel pole. In order to consider the geometric non-linearity in the calculation of the natural frequencies of the respective structure, the concept of initial stiffness, geometric stiffness and effective stiffness, computed by the Rayleigh method for vibration problems in mechanical systems, was used. So, to optimize the computational time to obtain the modal response in dynamic analysis of the described structure, without neglecting the precision of the results of a rigorous analysis with sophisticated methodologies, alternative formulations to those described in NBR 6123 (1988) will bepresented in this work.

References

Associação brasileira de normas técnicas (2013), Errata 2: Forças devidas ao vento em edificações. Rio de Janeiro, NBR - 6123 (In Portuguese).

BRASIL, Reyolando Manoel Lopes Rebello da Fonseca; SILVA, Marcelo Araújo da. Introdução a dinâmica das estruturas: Para engenharia civil. 2ª ed. São Paulo, 2015 (In Portuguese).

WAHRHAFTIG, Alexandre De Macêdo. Estruturas esbeltas com efeito geométrico. 2ª ed. São Paulo 2017 (In Portuguese).

[THIMOSHENKO, Sthephen P.; GERE, James M. Theory of Elastick Stability. 17th. Co – Singapore, 1985.

BRASIL, Reyolando Manoel Lopes Rebello da Fonseca; SILVA, Marcelo Araujo da. Otimização de projetos de engenharia. 1ª ed. São Paulo, 2019 ( In Portuguese).

COUTINHO, Dereck Henrique; MAUPRIVEZ, Julien; CAYRES, Bruno Cesar. Dynamic analysis of railways using the finite element method. Brazilian Journal of Development, Curitiba, v.7, n.9, p.88094-88105 Sep. 2021

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Published

2021-10-13

How to Cite

da Silva, M. A., & Matos, P. H. dos S. (2021). Determination of the first natural frequency of vibration of a steel pole, under the effect of geometric nonlinearity, using optimization techniques / Determinação da primeira frequência natural de vibração de um pólo de aço, sob o efeito da não linearidade geométrica, utilizando técnicas de optimização. Brazilian Journal of Development, 7(10), 96882–96893. https://doi.org/10.34117/bjdv7n10-140

Issue

Section

Original Papers