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


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.

Original languageEnglish
Title of host publicationMechanisms and Machine Science
EditorsK. Cavalca, H. Weber
Place of PublicationCham
Number of pages12
ISBN (Electronic)978-3-319-99268-6
ISBN (Print)978-3-319-99267-9
Publication statusPublished - 2019

Publication series

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


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


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