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Dynamic characterizations of O- and X-carbon nanotube-reinforced rings

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Abstract

Ring structures have been widely used in engineering devices and systems. When oscillations occur, the oscillation effects can be reduced by applying designable carbon nanotube (CNT)-reinforced materials to the ring. The dynamic characterizations and microscopic behaviors of CNT-reinforced rings of three distribution types of CNT, namely, X-distribution (X) type, uniform distribution (UD) type and O-distribution (O) type, are given. The influence of doped CNTs on the mechanical properties of the matrix ring is analyzed by comparing different CNT distributions on the membrane stiffness, bending stiffness and frequency. The microscopic membrane force-induced component and bending moment-induced component are studied to reflect the transverse and circumferential actions. The effects of different CNTs distributions on the transverse and circumferential action are evaluated. Analytical results demonstrate that the CNTs can improve the mechanical properties of the ring. The X type greatly affects the bending behavior, while the O type mainly affects the membrane behavior. Thus, for transverse oscillations dominated by the bending moment-induced component, the X type CNTs can greatly reduce the transverse oscillations influences.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 12272175, 12102182 and 11872206) and the State Key Laboratory of Mechanics and Control for Aerospace Structures (Grant No. MCMS-E-0521G01).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control for Aerospace Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Hongjie Li, Yan Deng & Hornsen Tzou

  2. Interdisciplinary Research Institute of Aeronautics and Astronautics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Hongjie Li, Yan Deng & Hornsen Tzou

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  1. Hongjie Li
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  2. Yan Deng
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Correspondence to Yan Deng or Hornsen Tzou.

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Appendix

Appendix

Tables 4 and 5 show the membrane stiffness, bending stiffness and frequency of the CNT-reinforced rings and PP ring. Table 6 gives the frequency increase rate of the CNT-reinforced rings, relative to the PP ring. Table 7 shows the frequency of the CNT-reinforced rings under different volume fractions. Finally, the frequency increase rate at volume fractions ranging from 0.11 to 0.14 and from 0.14 to 0.17 is listed in Table 8. Note: \(f_{1}\) is the transverse component frequency and \(f_{2}\) is the circumferential component frequency of ring.

Table 4 Membrane stiffness and bending stiffness
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Table 5 Frequency of ring
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Table 6 Frequency increase rate of the CNT-reinforced rings
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Table 7 Frequency of CNT-reinforced rings under different volume fractions
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Table 8 Frequency increase rate at volume fractions ranging from 0.11 to 0.14 and from 0.14 to 0.17. Again, \(f_{1}\) is the transverse component frequency and \(f_{2}\) is the circumferential component frequency of ring’s \(k = 2\) mode
Full size table

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Li, H., Deng, Y. & Tzou, H. Dynamic characterizations of O- and X-carbon nanotube-reinforced rings. Acta Mech 235, 779–795 (2024). https://doi.org/10.1007/s00707-023-03778-x

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  • DOI: https://doi.org/10.1007/s00707-023-03778-x

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