Wave and vibration analysis of rotating periodic structures by wave-based methods

Danilo Beli, Priscilla Brandão Silva, Jean Mathieu Mencik, José Roberto de França Arruda

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

The vibration of flexible rotating structures has been extensively investigated by the rotordynamics community. The analysis is usually performed via the finite element method using normal mode superposition. However, some interesting features of these structures may be hidden using a modal approach. In this paper, a wave-based approach is used to study the dynamic behavior of flexible rotating structures. Using a wave description, it is straightforward to show that the gyroscopic effect inherent to flexible rotating structures breaks the time-reversal symmetry. This corresponds to an asymmetric wave propagation, i.e., a forward-going wave and its corresponding backward-going pair travel with different wave speeds. In this paper, we show that this feature of flexible rotating structures makes them a natural mechanical circulator. On the other hand, we show that in the case of inhomogeneous flexible rotating structures designed as spectral gap elastic materials, i.e., phononic crystals or locally resonant metamaterials, the rotational speed has a strong influence in the location and width of the band gaps. The mathematical formulation of these problems have been presented by the authors elsewhere. Here, the conceptual aspects of these investigations are discussed under the light of original numerical simulation results.

LanguageEnglish
Title of host publicationMechanisms and Machine Science
EditorsK. Cavalca, H. Weber
Place of PublicationCham
PublisherSpringer
Pages518-529
Number of pages12
ISBN (Electronic)978-3-319-99268-6
ISBN (Print)978-3-319-99267-9
DOIs
StatePublished - 2019

Publication series

NameMechanisms and Machine Science
Volume61
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992

Fingerprint

Periodic structures
Vibration analysis
Metamaterials
Wave propagation
Energy gap
Finite element method
Crystals
Computer simulation

Keywords

  • Asymmetric wave propagation
  • Metamaterial
  • Phononic crystal
  • Time-reversal symmetry
  • Wave finite element method

Cite this

Beli, D., Brandão Silva, P., Mencik, J. M., & de França Arruda, J. R. (2019). Wave and vibration analysis of rotating periodic structures by wave-based methods. In K. Cavalca, & H. Weber (Eds.), Mechanisms and Machine Science (pp. 518-529). (Mechanisms and Machine Science; Vol. 61). Cham: Springer. DOI: 10.1007/978-3-319-99268-6_36
Beli, Danilo ; Brandão Silva, Priscilla ; Mencik, Jean Mathieu ; de França Arruda, José Roberto. / Wave and vibration analysis of rotating periodic structures by wave-based methods. Mechanisms and Machine Science. editor / K. Cavalca ; H. Weber. Cham : Springer, 2019. pp. 518-529 (Mechanisms and Machine Science).
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Beli, D, Brandão Silva, P, Mencik, JM & de França Arruda, JR 2019, Wave and vibration analysis of rotating periodic structures by wave-based methods. in K Cavalca & H Weber (eds), Mechanisms and Machine Science. Mechanisms and Machine Science, vol. 61, Springer, Cham, pp. 518-529. DOI: 10.1007/978-3-319-99268-6_36

Wave and vibration analysis of rotating periodic structures by wave-based methods. / Beli, Danilo; Brandão Silva, Priscilla; Mencik, Jean Mathieu; de França Arruda, José Roberto.

Mechanisms and Machine Science. ed. / K. Cavalca; H. Weber. Cham : Springer, 2019. p. 518-529 (Mechanisms and Machine Science; Vol. 61).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Beli D, Brandão Silva P, Mencik JM, de França Arruda JR. Wave and vibration analysis of rotating periodic structures by wave-based methods. In Cavalca K, Weber H, editors, Mechanisms and Machine Science. Cham: Springer. 2019. p. 518-529. (Mechanisms and Machine Science). Available from, DOI: 10.1007/978-3-319-99268-6_36