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Archive of Applied Mechanics

, Volume 88, Issue 4, pp 481–502 | Cite as

Vibration characteristics of rotating orthotropic cantilever plates using analytical approaches: a comprehensive parametric study

  • Hamidreza Rostami
  • Ahmad Rahbar Ranji
  • Firooz Bakhtiari-Nejad
Original
  • 194 Downloads

Abstract

This manuscript is concerned with the free vibration analysis of rotating orthotropic cantilever plates attached with an arbitrary stagger angle to a hub. The general governing equations which include both the centrifugal inertia forces and Coriolis effects are derived using Hamilton’s principle. The results are obtained using extended Kantorovich method and extended Galerkin method which are compared with each other, and available data in the literature and in good agreements are observed. A very detailed study of the influence of varying stiffness ratio, rotation speed, stagger angle, hub radius ratio and aspect ratio on the dynamic characteristics is conducted. These investigations provide complementary results, which leads to improvement in design and appropriate optimization of the material and geometry in this class of problems. The observation of the results shows that the crossing/veering phenomenon is influenced by the stiffness ratio, stagger angle and hub radius ratio. It is found that the centrifugal stiffening rate in the spanwise bending modes is constant, while in the torsion mode is changeable. The plate with the lower stiffness ratio has the higher centrifugal stiffening rate.

Keywords

Vibration analysis Rotating blades Analytical methods Orthotropic plates 

References

  1. 1.
    Southwell, R., Gough, B.: The free transverse vibration of airscrew blades. Br. ARC Rep. Memo. 766, 358–369 (1921)Google Scholar
  2. 2.
    Schilhansl, M.: Bending frequency of a rotating cantilever beam. J. Appl. Mech. Trans. Am. Soc. Mech. Eng. 25, 28–30 (1958)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Hodges, D.H., Rutkowski, M.J.: Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA. J. 19, 1459–1466 (1981)CrossRefzbMATHGoogle Scholar
  4. 4.
    Borri, M., Mantegazza, P.: Some contributions on structural and dynamic modeling of helicopter rotor blades. Aerotec. Missili. Spaz. 64(9), 143–154 (1985)zbMATHGoogle Scholar
  5. 5.
    Yokoyama, T.: Free vibration characteristics of rotating Timoshenko beam. Int. J. Mech. Sci. 30, 743–755 (1988)CrossRefzbMATHGoogle Scholar
  6. 6.
    Vyas, N.S., Rao, J.S.: Equations of motion of a blade rotating with variable angular velocity. J. Sound Vib. 156(2), 327–336 (1992)CrossRefzbMATHGoogle Scholar
  7. 7.
    Naguleswaran, J.S.: Lateral vibration of a centrifugally tensioned uniform Euler–Bernoulli beam. J. Sound Vib. 176, 613–624 (1994)CrossRefzbMATHGoogle Scholar
  8. 8.
    Da Silva, M.R.M.C.: A comprehensive analysis of the dynamics of a helicopter rotor blade. Int. J. Solids Struct. 35, 619–635 (1998)CrossRefzbMATHGoogle Scholar
  9. 9.
    Yoo, H.H., Shin, S.H.: Vibration analysis of rotating cantilever beams. J. Sound Vib. 212, 807–828 (1998)CrossRefGoogle Scholar
  10. 10.
    Rao, S.S., Gupta, R.S.: Finite element analysis of rotating Timoshenko beams. J. Sound Vib. 242(1), 103–124 (2001)CrossRefzbMATHGoogle Scholar
  11. 11.
    Chung, J., Yoo, H.H.: Dynamic analysis of a rotating cantilever beam by using the finite element method. J. Sound Vib. 249(1), 147–164 (2002)CrossRefGoogle Scholar
  12. 12.
    Marugabandhu, P., Griffin, J.H.: A reduced-order model for evaluating the effect of rotational speed on the natural frequencies and mode shapes of blades. Trans. ASME J. Eng. Gas Turbines Power 125, 772–776 (2003)CrossRefGoogle Scholar
  13. 13.
    Banerjee, J.R., Su, H.: Dynamic stiffness formulation and free vibration analysis of a spinning composite beam. Comput. Struct. 84, 1208–1214 (2006)CrossRefGoogle Scholar
  14. 14.
    Lee, S.Y., Sheu, J.J.: Free vibration of an extensible rotating inclined Timoshenko beam. J. Sound Vib. 304, 606–624 (2007)CrossRefzbMATHGoogle Scholar
  15. 15.
    Piovan, M.T., Sampaio, R.: A study on the dynamics of rotating beams with functionally graded properties. J. Sound Vib. 327, 134–143 (2009)CrossRefGoogle Scholar
  16. 16.
    Li, L., Zhang, D.G., Zhu, W.D.: Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect. J. Sound Vib. 333, 1526–1541 (2014)CrossRefGoogle Scholar
  17. 17.
    Genta, G., Feng, C., Tonoli, A.: Dynamics behavior of rotating bladed discs: a finite element formulation for the study of second and higher order harmonics. J. Sound Vib. 329, 5289–5306 (2010)CrossRefGoogle Scholar
  18. 18.
    Chiu, Y.-J., Chen, D.-Z.: The coupled vibration in a rotating multi-disk rotor system. Int. J. Mech. Sci. 53, 1–10 (2011)CrossRefGoogle Scholar
  19. 19.
    Dohnal, F., Knopf, E., Nordmann, R.: Efficient modelling of rotor-blade interaction using substructuring. In: Proceedings of the 9th IFToMM ICORD. Mechanism and Machine Science vol. 21, pp. 143–153 (2015)Google Scholar
  20. 20.
    Dokainish, M.A., Rawtani, R.: Vibration analysis of rotating cantilever plates. Int. J. Numer. Methods Eng. 3(2), 233–248 (1971)CrossRefzbMATHGoogle Scholar
  21. 21.
    Ramamurti, V., Kielb, R.: Natural frequencies of twisted rotating plates. J. Sound Vib. 97, 429–449 (1984)CrossRefGoogle Scholar
  22. 22.
    Wang, J.T.S., Shaw, D., Mahrenholtz, O.: Vibration of rotating rectangular plates. J. Sound Vib. 112(3), 455–468 (1987)CrossRefGoogle Scholar
  23. 23.
    Rao, J.S., Gupta, K.: Free vibrations of rotating small aspect ratio pretwisted blades. Mech. Mach. Theory 22(2), 159–167 (1987)CrossRefGoogle Scholar
  24. 24.
    Yoo, H.H., Kim, S.K.: Free vibration analysis of rotating cantilever plates. AIAA J. 40(11), 2188–2196 (2002)CrossRefGoogle Scholar
  25. 25.
    Yoo, H.H., Kim, S.K.: Flapwise bending vibration of rotating plates. Int. J. Numer. Methods Eng. 55, 785–802 (2002)CrossRefzbMATHGoogle Scholar
  26. 26.
    Yoo, H.H., Kim, S., Inman, D.: Modal analysis of rotating composite cantilever plates. J. Sound Vib. 258, 233–246 (2002)CrossRefGoogle Scholar
  27. 27.
    Yoo, H.H., Pierre, C.: Modal characteristic of a rotating rectangular cantilever plate. J. Sound Vib. 259(1), 81–96 (2003)CrossRefGoogle Scholar
  28. 28.
    Lim, H.S., Yoo, H.H.: Modal analysis of cantilever plates undergoing accelerated in-plane motion. J. Sound Vib. 297, 880–894 (2006)CrossRefGoogle Scholar
  29. 29.
    Hashemi, S.H., Farhadi, S., Carra, S.: Free vibration analysis of rotating thick plates. J. Sound Vib. 323, 366–384 (2009)CrossRefGoogle Scholar
  30. 30.
    Sinha, S.K., Turner, K.E.: Natural frequencies of a pre-twisted blade in a centrifugal force field. J. Sound Vib. 330(11), 2655–2681 (2011)CrossRefGoogle Scholar
  31. 31.
    Sun, J., Kari, L., Arteaga, I.L.: A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton’s principle. J. Sound Vib. 332, 1355–1371 (2013)CrossRefGoogle Scholar
  32. 32.
    Sun, J., Arteaga, I.L., Kari, L.: Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory. Compos. Struct. 99, 276–287 (2013)CrossRefGoogle Scholar
  33. 33.
    Li, L., Zhang, D.G.: Free vibration analysis of rotating functionally graded rectangular plates. Compos. Struct. 136, 493–504 (2016)CrossRefGoogle Scholar
  34. 34.
    Sinha, S.K., Zylka, R.P.: Vibration analysis of composite airfoil blade using orthotropic thin shell bending theory. Int. J. Mech. Sci. 121, 90–105 (2017)CrossRefGoogle Scholar
  35. 35.
    Rostami, H., Rahbar, A.R., Bakhtiari-Nejad, F.: Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates. Int. J. Mech. Sci. 115–116, 438–456 (2016)CrossRefGoogle Scholar
  36. 36.
    Kim, H.S., Cho, M., Kim, G.I.: Free-edge strength analysis in composite laminates by the extended Kantorovich method. Compos. Struct. 49, 229–235 (2000)CrossRefGoogle Scholar
  37. 37.
    Ungbhakorn, V., Singhatanadgid, P.: Buckling analysis of symmetrically laminated composite plates by the extended Kantorovich method. Compos. Struct. 73, 120–128 (2006)CrossRefGoogle Scholar
  38. 38.
    Ranji, A.Rahbar, Rostami, H.: A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions. J. Mech. Sci. Technol. 24, 357–364 (2010)CrossRefGoogle Scholar
  39. 39.
    Ranji, A.R., Rostami, H.: A semi-analytical technique for bending analysis of cylindrical panels with general loading and boundary conditions. J. Mech. Sci. Technol. 26(6), 1711–1718 (2012)CrossRefGoogle Scholar
  40. 40.
    Meirovitch, L.: Principles and Techniques of Vibrations. McGraw Hill, New York (1997)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Hamidreza Rostami
    • 1
  • Ahmad Rahbar Ranji
    • 1
  • Firooz Bakhtiari-Nejad
    • 2
  1. 1.Department of Ocean EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran

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