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Free Vibration of Rotating Twisted Composite Stiffened Plate

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Advances in Materials, Mechanical and Industrial Engineering (INCOM 2018)

Part of the book series: Lecture Notes on Multidisciplinary Industrial Engineering ((LNMUINEN))

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Abstract

The paper presents a first-order shear deformation-based finite element model to investigate the free vibration response of the rotating twisted composite stiffened plate. An eight-noded isoparametric plate element having five degrees of freedom per node is combined with an isoparametric three-noded beam element of four degrees of freedom per node for modelling the plate and the stiffener element, respectively. The present formulation employs a constraint method to calculate the stiffness and mass matrices of the stiffener element attached to the plate element, wherein the degrees of freedom of the nodes of the stiffener element are transferred to the respective nodes of the plate element considering eccentricity to maintain the compatibility between plate and stiffener. The advantage of such method is that total number of degrees of freedom due to addition of the stiffener does not increase, thereby reducing the computational time. The governing equilibrium equation is derived from Lagrangian equation of motion. The Coriolis effect is not considered as the stiffened plate is allowed to rotate at moderate rotational speed only. Parametric studies have been conducted to investigate the effect of angle of fibre orientation, pretwist angle, stiffener depth-to-plate thickness ratio and rotational speeds on the fundamental frequency and mode shapes of the stiffened plate.

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Abbreviations

L :

Length of the plate (m)

b :

Width of the plate (m)

h :

Thickness of the plate (m)

b st :

Width of stiffener (m)

d st :

Depth of stiffener (m)

Ï• :

Pretwist angle of the plate (deg.)

ω n :

Fundamental natural frequency of the stiffened plate without rotation (rad/s)

\( \Omega^{\prime } \) :

Actual rotational speed (rad/s)

Ω:

Non-dimensional rotational speed \( \left( {\Omega =\Omega ^{{\prime }} /\omega_{\text{n}} } \right) \) (dimensionless)

References

  1. Leissa, A.W., Ewing, M.S.: Comparison of beam and shell theories for the vibrations of thin turbomachinery blades. J. Eng. Power 105(2), 383–392 (1983)

    Article  Google Scholar 

  2. Kielb, R.E., Leissa, A.W., Macbain, J.C.: Vibrations of twisted cantilever plates—a comparison of theoretical results. Int. J. Numer. Meth. Eng. 21(8), 1365–1380 (1985)

    Article  Google Scholar 

  3. Qatu, M.S., Leissa, A.W.: Vibration studies for laminated composite twisted cantilever plates. Int. J. Mech. Sci. 33(11), 927–940 (1991)

    Article  Google Scholar 

  4. Liew, K.M., Lim, C.W., Ong, L.S.: Vibration of pretwisted cantilever shallow conical shells. Int. J. Solids Struct. 31(18), 2463–2476 (1994)

    Article  Google Scholar 

  5. Kuang, J.H., Hsu, M.H.: The effect of fiber angle on the natural frequencies of orthotropic composite pre-twisted blades. Compos. Struct. 58(4), 457–468 (2002)

    Article  Google Scholar 

  6. Lee, J.J., Yeom, C.H., Lee, I.: Vibration analysis of twisted cantilevered conical composite shells. J. Sound Vib. 255(5), 965–982 (2002)

    Article  Google Scholar 

  7. Sreenivasamurthy, S., Ramamurti, V.: Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates. J. Strain Anal. Eng. Des. 16(2), 97–106 (1981)

    Article  Google Scholar 

  8. Ramamurti, V., Kielb, R.: Natural frequencies of twisted rotating plates. J. Sound Vib. 97(3), 429–449 (1984)

    Article  Google Scholar 

  9. Karmakar, A., Sinha, P.K.: Finite element free vibration analysis of rotating laminated composite pretwisted cantilever plates. J. Reinf. Plast. Compos. 16(16), 1461–1491 (1997)

    Article  Google Scholar 

  10. Rao, S.S., Gupta, R.S.: Finite element vibration analysis of rotating Timoshenko beams. J. Sound Vib. 242(1), 103–124 (2001)

    Article  Google Scholar 

  11. Hu, X.X., Sakiyama, T., Matsuda, H., Morita, C.: Fundamental vibration of rotating cantilever blades with pre-twist. J. Sound Vib. 271(1–2), 47–66 (2004)

    Article  Google Scholar 

  12. Kee, Y.J., Kim, J.H.: Vibration characteristics of initially twisted rotating shell type composite blades. Compos. Struct. 64(2), 151–159 (2004)

    Article  Google Scholar 

  13. Joseph, S.V., Mohanty, S.C.: Free vibration of a rotating sandwich plate with viscoelastic core and functionally graded material constraining layer. Int. J. Struct. Stab. Dyn. 17(10), 1750114 (2017)

    Article  MathSciNet  Google Scholar 

  14. Chandrashekhara, K., Kolli, M.: Free vibration of eccentrically stiffened laminated plates. J. Reinf. Plast. Compos. 16(10), 884–902 (1997)

    Article  Google Scholar 

  15. Prusty, B.G., Satsangi, S.K.: Finite element transient dynamic analysis of laminated stiffened shells. J. Sound Vib. 248(2), 215–233 (2001)

    Article  Google Scholar 

  16. Nayak, A.N., Bandyopadhyay, J.N.: Free vibration analysis of laminated stiffened shells. J. Eng. Mech. 131(1), 100–105 (2005)

    Article  Google Scholar 

  17. Sahoo, S., Chakravorty, D.: Stiffened composite hypar shell roofs under free vibration: Behaviour and optimization aids. J. Sound Vib. 295(1), 362–377 (2006)

    Article  Google Scholar 

  18. Sadek, E.A., Tawfik, S.A.: A finite element model for the analysis of stiffened laminated plates. Comput. Struct. 75(4), 369–383 (2000)

    Article  Google Scholar 

  19. Qing, G., Qiu, J., Liu, Y.: Free vibration analysis of stiffened laminated plates. Int. J. Solids Struct. 43(6), 1357–1371 (2006)

    Article  Google Scholar 

  20. Yuan, W.X., Dawe, D.J.: Free vibration and stability analysis of stiffened sandwich plates. Compos. Struct. 63(1), 123–137 (2004)

    Article  Google Scholar 

  21. Guo, M., Harik, I.E., Ren, W.X.: Free vibration analysis of stiffened laminated plates using layered finite element method. Struct. Eng. Mech. 14(3), 245–262 (2002)

    Article  Google Scholar 

  22. Li, D., Qing, G., Liu, Y.: A layerwise/solid-element method for the composite stiffened laminated cylindrical shell structures. Compos. Struct. 98, 215–227 (2013)

    Article  Google Scholar 

  23. Bhar, A., Phoenix, S.S., Satsangi, S.K.: Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: A comparative perspective. Compos. Struct. 92(2), 312–321 (2010)

    Article  Google Scholar 

  24. Zhao, W., Kapania, R.K.: Vibrational analysis of unitized curvilinearly stiffened composite panels subjected to in-plane loads. In: 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 1500 (2016)

    Google Scholar 

  25. Castro, S.G., Donadon, M.V.: Assembly of semi-analytical models to address linear buckling and vibration of stiffened composite panels with debonding defect. Compos. Struct. 160, 232–247 (2017)

    Article  Google Scholar 

  26. Rout, M., Bandyopadhyay, T., Karmakar, A.: Free vibration analysis of pretwisted delaminated composite stiffened shallow shells: a finite element approach. J. Reinf. Plast. Compos. 36(8), 619–636 (2017)

    Article  Google Scholar 

  27. Rout, M., Hota, S.S., Karmakar, A.: Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, doi: 0954406216686389 (2017)

    Google Scholar 

  28. Damnjanović, E., Marjanović, M., Nefovska-Danilović, M.: Free vibration analysis of stiffened and cracked laminated composite plate assemblies using shear-deformable dynamic stiffness elements. Compos. Struct. 180, 723–740 (2017)

    Article  Google Scholar 

  29. Cook, R.D.: Concepts and Applications of Finite Element Analysis. Wiley, Hoboken (2007)

    Google Scholar 

  30. Bathe, K.J.: Finite Element Procedures in Engineering Analysis. PHI, New Delhi (1990)

    Google Scholar 

  31. Das, H.S., Chakravorty, D.: Bending analysis of stiffened composite conoidal shell roofs through finite element application. J. Compos. Mater. 45, 525–542 (2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, India

    Mrutyunjay Rout & Amit Karmakar

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  1. Mrutyunjay Rout
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  2. Amit Karmakar
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Correspondence to Mrutyunjay Rout .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal, India

    Prasanta Sahoo

  2. Department of Mechanical Engineering, University of Aveiro , Aveiro, Portugal

    J. Paulo Davim

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Rout, M., Karmakar, A. (2019). Free Vibration of Rotating Twisted Composite Stiffened Plate. In: Sahoo, P., Davim, J. (eds) Advances in Materials, Mechanical and Industrial Engineering. INCOM 2018. Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-96968-8_17

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  • DOI: https://doi.org/10.1007/978-3-319-96968-8_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96967-1

  • Online ISBN: 978-3-319-96968-8

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