Instability Analysis of Laminated Composite Beams Subjected to Parametric Axial Load
The integral form of equations of motion of composite
beams subjected to varying time loads are discretized using a
developed finite element model. The model consists of a straight five
node twenty-two degrees of freedom beam element. The stability
analysis of the beams is studied by solving the matrix form
characteristic equations of the system. The principle of virtual work
and the first order shear deformation theory are employed to analyze
the beams with large deformation and small strains. The regions of
dynamic instability of the beam are determined by solving the
obtained Mathieu form of differential equations. The effects of nonconservative
loads, shear stiffness, and damping parameters on
stability and response of the beams are examined. Several numerical
calculations are presented to compare the results with data reported
by other researchers.
[1] Bolotin V.V., The Dynamic Stability of Elastic Systems, Holden-
Day, San Francisco, 1964.
[2] R. K. Kapania and S. Raciti, "Nonlinear vibrations of
unsymmetrically laminated beams," AIAA J. 27(2), pp. 201-210,
1988.
[3] F. Yuan and R. E. Miller, "A higher order finite element for
laminated beams," Comp. Struct. 14, pp. 125-150, 1990.
[4] B. S. Manjunatha and T. Kant, "New theories for
symmetric/unsymmetric composite and sandwich beams with C0
finite elements", Comp. Struct. 23, pp. 61-73, 1993.
[5] Bassiouni, A. S., R. M. Gad-Elrab, and T. H. Elmahdy (1999).
"Dynamic Analysis for Laminated Composite Beams". Composite
Structures 44 (2-3), pp. 81-87.
[6] Loja M. A. R., Barbosa J. I. and Soares C. M. M., "Static and
dynamic behaviour of laminated composite beams", International
Journal of Structural Stability and Dynamics, (2001), pp. 545-560.
[7] Ramtekkar G. S., and Desai Y. M. "Natural vibrations of laminated
composite beams by using mixed finite element modeling", Journal
of Sound and Vibration, 2002, pp. 635-651.
[8] Subramanian P. "Dynamic analysis of laminated composite beams
using higher order theories and finite elements", Composite
Structures, 2006, pp.342-353.
[9] Adams RD, Bacon DGC. "Effect of fiber orientation and laminate
geometry on the dynamic properties of CFRP", J. of Compos. Mater.
1973, pp.402-408.
[10] Ni, R.G., Adams, R.D., "The damping and dynamic moduli of
symmetric laminated composite beams, theoretical and experimental
results", Journal of Composite Materials, 1984. 18(2), pp.104-121.
[11] D. L. Logan, Finite Element Method, Brooks/Cole, CA, USA, 2002.
[12] Maiti K. D. and Sinha P. K., "Bending and free vibration analysis of
shear deformable laminated composite beams by finite element
method," Comp. Struct. 29, pp. 421-431, 1994.
[13] L. Librescue, S. Thangitham, "Parametric instability of laminated
composite shear-deformable flat panels subjected to in-plane edge
loads", Int. J. Nonlinear Mechanics, pp.263-273, 1990.
[1] Bolotin V.V., The Dynamic Stability of Elastic Systems, Holden-
Day, San Francisco, 1964.
[2] R. K. Kapania and S. Raciti, "Nonlinear vibrations of
unsymmetrically laminated beams," AIAA J. 27(2), pp. 201-210,
1988.
[3] F. Yuan and R. E. Miller, "A higher order finite element for
laminated beams," Comp. Struct. 14, pp. 125-150, 1990.
[4] B. S. Manjunatha and T. Kant, "New theories for
symmetric/unsymmetric composite and sandwich beams with C0
finite elements", Comp. Struct. 23, pp. 61-73, 1993.
[5] Bassiouni, A. S., R. M. Gad-Elrab, and T. H. Elmahdy (1999).
"Dynamic Analysis for Laminated Composite Beams". Composite
Structures 44 (2-3), pp. 81-87.
[6] Loja M. A. R., Barbosa J. I. and Soares C. M. M., "Static and
dynamic behaviour of laminated composite beams", International
Journal of Structural Stability and Dynamics, (2001), pp. 545-560.
[7] Ramtekkar G. S., and Desai Y. M. "Natural vibrations of laminated
composite beams by using mixed finite element modeling", Journal
of Sound and Vibration, 2002, pp. 635-651.
[8] Subramanian P. "Dynamic analysis of laminated composite beams
using higher order theories and finite elements", Composite
Structures, 2006, pp.342-353.
[9] Adams RD, Bacon DGC. "Effect of fiber orientation and laminate
geometry on the dynamic properties of CFRP", J. of Compos. Mater.
1973, pp.402-408.
[10] Ni, R.G., Adams, R.D., "The damping and dynamic moduli of
symmetric laminated composite beams, theoretical and experimental
results", Journal of Composite Materials, 1984. 18(2), pp.104-121.
[11] D. L. Logan, Finite Element Method, Brooks/Cole, CA, USA, 2002.
[12] Maiti K. D. and Sinha P. K., "Bending and free vibration analysis of
shear deformable laminated composite beams by finite element
method," Comp. Struct. 29, pp. 421-431, 1994.
[13] L. Librescue, S. Thangitham, "Parametric instability of laminated
composite shear-deformable flat panels subjected to in-plane edge
loads", Int. J. Nonlinear Mechanics, pp.263-273, 1990.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52296", author = "Alireza Fereidooni and Kamran Behdinan and Zouheir Fawaz", title = "Instability Analysis of Laminated Composite Beams Subjected to Parametric Axial Load", abstract = "The integral form of equations of motion of composite
beams subjected to varying time loads are discretized using a
developed finite element model. The model consists of a straight five
node twenty-two degrees of freedom beam element. The stability
analysis of the beams is studied by solving the matrix form
characteristic equations of the system. The principle of virtual work
and the first order shear deformation theory are employed to analyze
the beams with large deformation and small strains. The regions of
dynamic instability of the beam are determined by solving the
obtained Mathieu form of differential equations. The effects of nonconservative
loads, shear stiffness, and damping parameters on
stability and response of the beams are examined. Several numerical
calculations are presented to compare the results with data reported
by other researchers.", keywords = "Finite element beam model, Composite Beams,stability analysis", volume = "2", number = "2", pages = "166-11", }