Journal of Applied Mechanics and Technical Physics

, Volume 58, Issue 6, pp 1108–1114 | Cite as

Effects of End Conditions of Cross-Ply Laminated Composite Beams on Their Dimensionless Natural Frequencies

  • A. F. A. Algarray
  • H. Jun
  • I.-E. M. Mahdi


The effects of the end conditions of cross-ply laminated composite beams on their dimensionless natural frequencies of free vibration is investigated. The problem is analyzed and solved by using the energy approach, which is formulated by a finite element model. Various end conditions of beams are used. Each beam has either movable ends or immovable ends. Numerical results are verified by comparisons with other relevant works. It is found that more constrained beams have higher values of natural frequencies of transverse vibration. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends because they are generated by longitudinal movements only.


laminated beam free vibration finite element method beam end conditions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Abramovich and A. Livshits, “Free Vibrations of Non-Symmetric Cross-Ply Laminated Composite Beams,” J. Sound Vibrat. 176 (5), 597–612 (1994).ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    S. Marur and T. Kant, “Free Vibration Analysis of Fiber Reinforced Composite Beams using Higher order Theories and Finite Element Modelling,” J. Sound Vibrat. 194 (3), 337–351 (1996).ADSCrossRefGoogle Scholar
  3. 3.
    J. Njuguna, H. Su, C. W. Cheung, and J. R. Banerjee, “The Influence of Ply Orientation on the Free Vibration of Composite Beams,” in Composite Systems—Macrocomposites, Microcomposites, Nanocomposites, Proc. of the Int. Conf., Sydney Australia, July 21–25, 2002.Google Scholar
  4. 4.
    M. Aydogdu, “Vibration Analysis of Cross-Ply Laminated Beams with General Boundary Conditions by Ritz Method,” Int. J. Mech. Sci. 47 (11), 1740–1755 (2005).CrossRefzbMATHGoogle Scholar
  5. 5.
    M. Aydogdu, “Free Vibration Analysis of Angle-Ply Laminated Beams with General Boundary Conditions,” J. Reinforced Plastics Composites 25 (15), 1571–1583 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    P. Vidal and O. Polit, “A Family of Sinus Finite Elements for the Analysis of Rectangular Laminated Beams,” Composite Structures 84 (1), 56–72 (2008).CrossRefGoogle Scholar
  7. 7.
    P. Vidal and O. Polit, “Vibration of Multilayered Beams Using Sinus Finite Elements with Transverse Normal Stress,” Composite Structures 92 (6), 1524–1534 (2010).CrossRefGoogle Scholar
  8. 8.
    P. Vidal and O. Polit, “A Sine Finite Element Using a Zig-Zag Function for the Analysis of Laminated Composite Beams,” Composites, B: Engineering 42 (6), 1671–1682 (2011).CrossRefGoogle Scholar
  9. 9.
    E. Carrera, G. Giunta, P. Nali, and M. Petrolo, “Refined Beam Elements with Arbitrary Cross-Section Geometries,” Comput. Structures 88 (5), 283–293 (2010).CrossRefGoogle Scholar
  10. 10.
    F. Biscani, G. Giunta, S. Belouettar, et al., “Variable Kinematic Beam Elements Coupled via Arlequin Method,” Composite Structures 93 (2), 697–708 (2011).CrossRefGoogle Scholar
  11. 11.
    G. Giunta, F. Biscani, S. Belouettar, et al., “Free Vibration Aanalysis of Composite Beams via Refined Theories,” Composites, B: Engineering 44 (1), 540–552 (2013).CrossRefGoogle Scholar
  12. 12.
    J. Li, Z. Wu, X. Kong, and W. Wu, “Comparison of Various Shear Deformation Theories for Free Vibration of Laminated Composite Beams with General Lay-Ups,” Composite Structures 108, 767–778 (2014).CrossRefGoogle Scholar
  13. 13.
    G. A. Hassan, M. A. Fahmy, and I. M. Goda, “The Effect of Fiber Orientation and Laminate Stacking Sequences on the Torsional Natural Frequencies of Laminated Composite Beams,” J. Mech. Design Vibrat. 1 (1), 20–26 (2013).Google Scholar
  14. 14.
    A. Pagani, E. Carrera, M. Boscolo, and J. R. Banerjee, “Refined Dynamic Stiffness Elements Applied to Free Vibration Analysis of Generally Laminated Composite Beams with Arbitrary Boundary Conditions,” Composite Structures 110, 305–316 (2014).CrossRefGoogle Scholar
  15. 15.
    K. Torabi, M. Shariati-Nia, and M. Heidari-Rarani, “Experimental and Theoretical Investigation on Transverse Vibration of Delaminated Cross-Ply Composite Beams,” Int. J. Mech. Sci. 115, 1–11 (2016).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mechanical Design and TheoryCollege of Mechanical and Electrical Engineering, NEFUHarbinChina
  2. 2.Department of Mechanical Engineering, Faculty of Engineering and TechnologyNile Valley UniversityAtbaraSudan

Personalised recommendations