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Investigation of free vibrations of composite beams by using the finite-difference method

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Abstract

The free-vibration behavior of symmetrically laminated fiber-reinforced composite beams with different boundary conditions is examined. The effects of shear deformation and rotary inertia, separately and/or in combination, on the free-vibration properties of the beams are investigated. The finite-difference method is used to solve the partial differential equations describing the free-vibration motion in each case. The effect of shear deformation on the natural frequencies is considerable, especially for higher frequencies, whereas the influence of rotary inertia is less significant. The study includes comparisons with results available in the literature. In addition, the impact of such factors as the span/depth ratio, fiber orientation, stacking sequence, and material type on free vibrations of the composite beams is investigated.

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References

  1. H. Abramovich, “Shear deformation and rotary inertia effects of vibrating composite beams,” Compos. Struct., 20, 165–173 (1992).

    Article  Google Scholar 

  2. H. Abramovich, M. Eisenberger, and O. Shulepov, “Dynamic stiffness matrix for symmetrically laminated beams using a first order shear deformation theory,” Compos. Struct., 31, No. 4, 265–271 (1995).

    Article  Google Scholar 

  3. K. K. Teh and C. C. Huang “The vibrations of generally orthotropic beams, a finite element approach, ” J. Sound Vibr., 62, No. 2, 195–206 (1979).

    Article  Google Scholar 

  4. K. Chandrashekhara and K. M. Bangera, “Free vibration of composite beams using a refined shear flexible element,” Comput. Struct., 43, No. 4, 719–727 (1992).

    Article  Google Scholar 

  5. Ch. Lee, D. Liu, and X. Lu, “Static and vibration analysis of laminated composite beams with an interlaminar shear stress continuity theory,” Int. J. Numer. Meth. Struct. Eng., 33, 409–424 (1992).

    Article  Google Scholar 

  6. H. D. Hodges, R. A. Atigan, V. Fulton, M. Rehfield, and W. Lawurence, “Free vibration analysis of composite beams,” J. Amer. Helicopt. Soc., 36, No. 3, 36–47 (1991).

    Article  Google Scholar 

  7. K. D. Maiti and P. K. Sinha, “Bending and free vibration analysis of shear deformable laminated composite beams by finite element method,” Compos. Struct., 29, No. 4, 421–431 (1994).

    Article  Google Scholar 

  8. G. Shi and K. Y. Lam, “Finite-element vibration analysis of composite beams based on a higher-order beam theory,” J. Sound Vibr., 219, No. 4, 707–721 (1999).

    Article  Google Scholar 

  9. A. A. Khdeir and J. N. Reddy, “Free vibration of cross-ply laminated beams with arbitrary boundary conditions,” Int. J. Eng. Sci., 31, No. 12, 1971–1980 (1994).

    Article  Google Scholar 

  10. Y. Teboub and P. Hajela, “Free vibration of generally layered composite beams using symbolic computations,” in: Collection of Technical Papers-Proceedings of the AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Vol. 1, AIAAM, New York, NY, USA (1994), pp. 182–192.

    Google Scholar 

  11. S. Krishnaswamy, K. Chandrahekhara, and W. Z. B. Wu, “Analytical solution to vibration of generally layered composite beams,” J. Sound Vibr., 159, No. 1, 85–99 (1992).

    Article  Google Scholar 

  12. K. Chandrashekhara, K. Krishnamurthy, and S. Roy, “Free vibration of composite beams including rotary inertia and shear deformation,” Compos. Struct., 14, No. 4, 269–279 (1990).

    Article  Google Scholar 

  13. K. Chandrashekhara and K. M. Bangera, “Free vibration of composite beams using a refined flexible element,” Comput. Struct., 43, No. 4, 719–727 (1992).

    Article  Google Scholar 

  14. J. M. Whitney, Structural Analysis of Laminated Anisotropic Plates, 1st Ed., Technical Publishing Company, Western Hemisphere (1987), pp. 263–295.

    Google Scholar 

  15. J. K. Suresh and C. Venkastensan, “Structural dynamic analysis of composite beams,” J. Sound Vibr., 143, No. 3, 503–519 (1990).

    Article  Google Scholar 

  16. M. Paz, Structural Dynamic Theory and Computations, Van Nostrand Reinhold Company, Inc., New York, USA (1980).

    Google Scholar 

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Authors and Affiliations

  1. Civil Engineering Department Jordan, University of Science and Technology, P.O. Box 3030, Irbid, Jordan

    K. S. Numayr, M. A. Haddad & A. F. Ayoub

Authors
  1. K. S. Numayr
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  2. M. A. Haddad
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  3. A. F. Ayoub
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Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 331–346, May–June, 2006.

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Numayr, K.S., Haddad, M.A. & Ayoub, A.F. Investigation of free vibrations of composite beams by using the finite-difference method. Mech Compos Mater 42, 231–242 (2006). https://doi.org/10.1007/s11029-006-0033-4

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  • DOI: https://doi.org/10.1007/s11029-006-0033-4

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