Advertisement

Mechanics of Composite Materials

, Volume 42, Issue 3, pp 231–242 | Cite as

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

  • K. S. Numayr
  • M. A. Haddad
  • A. F. Ayoub
Article

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.

Keywords

beams laminates composite materials free vibration natural frequency modal shape shear deformation rotary inertia 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Abramovich, “Shear deformation and rotary inertia effects of vibrating composite beams,” Compos. Struct., 20, 165–173 (1992).CrossRefGoogle Scholar
  2. 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).CrossRefGoogle Scholar
  3. 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).CrossRefGoogle Scholar
  4. 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).CrossRefGoogle Scholar
  5. 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).CrossRefGoogle Scholar
  6. 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).CrossRefGoogle Scholar
  7. 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).CrossRefGoogle Scholar
  8. 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).CrossRefGoogle Scholar
  9. 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).CrossRefGoogle Scholar
  10. 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. 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).CrossRefGoogle Scholar
  12. 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).CrossRefGoogle Scholar
  13. 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).CrossRefGoogle Scholar
  14. 14.
    J. M. Whitney, Structural Analysis of Laminated Anisotropic Plates, 1st Ed., Technical Publishing Company, Western Hemisphere (1987), pp. 263–295.Google Scholar
  15. 15.
    J. K. Suresh and C. Venkastensan, “Structural dynamic analysis of composite beams,” J. Sound Vibr., 143, No. 3, 503–519 (1990).CrossRefGoogle Scholar
  16. 16.
    M. Paz, Structural Dynamic Theory and Computations, Van Nostrand Reinhold Company, Inc., New York, USA (1980).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • K. S. Numayr
    • 1
  • M. A. Haddad
    • 1
  • A. F. Ayoub
    • 1
  1. 1.Civil Engineering Department JordanUniversity of Science and TechnologyIrbidJordan

Personalised recommendations