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Numerical and Experimental Modal Analysis of a Cantilever Beam Axially Loaded by a Tendon Which Is Attached in a Single Spanwise Location

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Abstract

It has been recently proposed to incorporate a tendon in a rotorcraft blade to introduce a means of controlling its dynamics properties. This has been shown as an effective resonance avoidance mechanism that should allow rotorcraft to operate with shape adaptive blades or with variable rotor speed, thereby increasing their performance and efficiency. In the previous studies, the tendon was attached to the blade’s tip, passed freely through its whole body and was fixed at the root of the blade. The tendon was therefore free to vibrate unrestrictedly inside the blade. This, despite delivering the required changes to dynamics, may not be the most optimal and viable design. In this paper, a modification of this concept is investigated. Unlike in the previous studies, the tendon does not pass freely through the blade, but it is connected to it in a single spanwise location using a mechanical attachment. This coupled blade-tendon system is studied both numerically and experimentally. The blade is modelled as the Euler-Bernoulli beam, the tendon as a taut string, and the attachment point as a concentrated mass. The boundary and connectivity conditions are used to ensure the required coupling between the beam and the tendon. Free vibration analysis is conducted using a boundary value problem solver and a bench-top experiment is used for validation of the numerical results. The variation of modal properties with the applied tendon tension and the location of the attachment point is investigated. It is found that many features observed in the previous studies, such as the frequency shift and frequency loci veering, are still exhibited by the modified system, but they are manifested under different loading conditions. In this way, the attachment points may influence the ability to control the beam’s dynamic properties. The implications of these phenomena for the application of an active tendon in rotorcraft are discussed.

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References

  1. Rauleder, J., van der Wall, B.G., Abdelmoula, A., Komp, D., Kumar, S., Ondra, V., Titurus, B., Woods, B.K.S.: Aerodynamic performance of morphing blades and rotor systems. In: AHS International 74th Annual Forum & Technology Display, Phoenix, Arizona (2018)

    Google Scholar 

  2. Dibble, R.P., Titurus, B.: Helicopter rotor blade modal tuning using internal preloads. In: International Conference on Noise and Vibration Engineering (ISMA2016) (2016)

    Google Scholar 

  3. Ondra, V., Dibble, R.P., Titurus, B.: Towards an application of an active tendon in rotorcraft: a numerical and experimental study of coupled bending-torsion vibration of a beam-tendon system. In: International Conference on Noise and Vibration Engineering (ISMA2018) (2018)

    Google Scholar 

  4. Ondra, V., Titurus, B.: Theoretical and experimental modal analysis for a beam-tendon system. Mech. Syst. Signal Process. (2019, under review)

    Google Scholar 

  5. Ondra, V., Titurus, B.: Free vibration analysis of rotating pre-twisted beams subjected to tendon-induced axial loading. J. Sound Vib. (2019, under review)

    Google Scholar 

  6. Ondra, V., Dibble, R.P., Titurus, B.: The use of an active tendon concept in rotorcraft with variable-speed rotors. In: AIAA Science and Technology Forum and Exposition (AIAA SciTech 2019) (2019)

    Google Scholar 

  7. Rao, S.S.: Vibration of Continuous Systems. Wiley, New York (2007)

    Google Scholar 

  8. Rosen, A.: Structural and dynamic behaviour of pretwisted rods and beams. Appl. Mech. Rev. 44(12), 483–515 (1991)

    Article  Google Scholar 

  9. Hodges, D.H.: Nonlinear Composite Beam Theory. American Institute of Aeronautics and Astronautics, Reston (2006)

    Google Scholar 

  10. Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics. Wiley, New York (2008)

    MATH  Google Scholar 

  11. Cheng, G., Zu, J.W.: Dynamic analysis of an optical fiber coupler in telecommunications. J. Sound Vib. 268(1), 15–31 (2003)

    Article  Google Scholar 

  12. Cao, D.X., Zhang, W.: Global bifurcations and chaotic dynamics for a string-beam coupled system. Chaos Solitons Fractals 37(3), 858–875 (2008)

    Article  MathSciNet  Google Scholar 

  13. Kierzenka, J., Shampine, L.F.: A BVP solver based on residual control and the Matlab PSE. ACM Trans. Math. Softw. 27(3), 299–316 (2001)

    Article  MathSciNet  Google Scholar 

  14. Ewins, D.J.: Modal Testing: Theory, Practice and Application. Research Studies Press Ltd, Philadelphia (2000)

    Google Scholar 

  15. Bazant, Z.P., Cedolin, L.: Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. World Scientific, Singapore (2010)

    Google Scholar 

  16. Virgin, L.N.: Vibration of Axially-Loaded Structures. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  17. Timoshenko, S., Gere, J.M.: Theory of Elastic Stability. Engineering Societies Monographs. Dover Publications, New York (1961)

    Google Scholar 

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Acknowledgements

The authors would like to acknowledge the financial support of the European Community’s Horizon 2020 Program provided through the project “Shape Adaptive Blades for Rotorcraft Efficiency (SABRE)”, Grant Agreement 723491.

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Correspondence to Vaclav Ondra .

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Ondra, V., Titurus, B. (2020). Numerical and Experimental Modal Analysis of a Cantilever Beam Axially Loaded by a Tendon Which Is Attached in a Single Spanwise Location. In: Mains, M.L., Dilworth, B.J. (eds) Topics in Modal Analysis & Testing, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12684-1_10

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  • DOI: https://doi.org/10.1007/978-3-030-12684-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12683-4

  • Online ISBN: 978-3-030-12684-1

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