A modified transfer matrix method for bending vibration of CFRP/Steel composite transmission shafting

  • Mo YangEmail author
  • Xian Zhou
  • Wen Zhang
  • Jianmin Ye
  • Yefa Hu


The bending vibration of transmission shafting directly influences dynamic performance of mechanical systems. The adoption of carbon fiber-reinforced plastics (CFRP) hollow shaft in the long-span transmission shafting can effectively reduce bending vibration. This paper aims to modify the transfer matrix method (TMM) for the CFRP/Steel composite transmission shafting system based on lamination theory and layer-wise beam theory. The dynamic kinetic equations of the steel and CFRP segments of the composite transmission shafting were modeled; then the bending vibration was solved by combining the boundary conditions of the CFRP/Steel composite transmission shafting. The experimental tests have been carried out in the CFRP/Steel composite transmission shafting to obtain the critical speed of rotation. Moreover, the results of modified TMM were compared with experimental tests, finite element method, and simply supported beam model. The comparison results show that the modified TMM proposed in this paper can effectively calculate the bending vibration characteristics of the CFRP/Steel composite transmission shafting system.


CFRP/Steel composite transmission shafting Modified transfer matrix method Bending critical rotating speed Vibration test 



This research was supported by the Ph.D. Research Fund of Hubei University of Arts and Science (No. 2059065).

Compliance with ethical standards

Conflict of interest

The authors declare that the funding did not lead to any conflict of interests regarding the publication of this manuscript. And there is no conflict of interest regarding the publication of this paper.

Data availability

The data used to support the findings of this study are included within the article.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringHubei University of Arts and ScienceXiangyangChina
  2. 2.School of Mechanical and Electronic EngineeringWuhan University of TechnologyWuhanChina

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