The Effect of Fiber Orientation and Laminate Stacking Sequences on the Torsional Natural Frequencies of Laminated Composite Beams

Galal. A. Hassan¹, Mohammed. A. Fahmy^2, and Ibrahim. M. Goda²

¹Mechanical Design and Production Department Faculty of Engineering, Cairo University, Giza Egypt

²Industrial and Manufacturing Engineering Department Faculty of Engineering, Fayoum University, Fayoum Egypt

Cite this paper:
Galal. A. Hassan, Mohammed. A. Fahmy and Ibrahim. M. Goda. The Effect of Fiber Orientation and Laminate Stacking Sequences on the Torsional Natural Frequencies of Laminated Composite Beams. Journal of Mechanical Design and Vibration. 2013; 1(1):20-26. doi: 10.12691/jmdv-1-1-4

Abstract

The composite materials are well known by their excellent combination of high structural stiffness and low weight. The main feature of these anisotropic materials is their ability to be tailored for specific applications by optimizing design parameters such as stacking sequence, ply orientation and performance targets. Finding free torsional vibrations characteristics of laminated composite beams is one of the bases for designing and modeling of industrial products. With these requirements, this work considers the free torsional vibrations for laminated composite beams of doubly symmetrical cross sections. The torsional vibrations of the laminated beams are analyzed analytically based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes due to fiber orientation of the laminated beams are neglected. Also, the torsional vibrations of the laminated beams analyzed by shear deformation theory in which the shear deformation effects are considered. Numerical analysis has been carried out using finite element method (FEM). The finite element software package ANSYS 10.0 is used to perform the numerical analyses using an eight-node layered shell element to describe the torsional vibration of the laminated beams. The rotary inertia and shear deformation effects of the element are taken. The influence of fiber directions and stacking sequences of laminates on torsional natural frequencies were investigated. Also, the effects of boundary conditions are demonstrated. Numerical results, obtained by the ANSYS 10.0, classical lamination theory, and shear deformation theory are presented to highlight the effects of fibers orientation and layers stacking sequence on torsional frequencies of the beams. The results obtained by ANSYS are compared against the classical lamination theory, as well as shear deformation theory.

Keywords:
composite materials laminated composite beams torsional vibrations shear deformation finite element analysis

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Abramovich A, Livshits A., (1994), “Free vibration of non-symmetric cross-ply laminated composite beams”, Journal of Sound and Vibration, Vol. 38, pp. 597-612.
[2]	Banerjee, J.R., (1998), “Free vibration of axially loaded composite timoshenko beams using the dynamic stiffness matrix method”, Computers and Structures, Vol. 69, pp. 197-208.
[3]	Calım FF, (2008), “Free and forced vibrations of non-uniform composite beams”, Composite Structures.
[4]	Chandrashekhara K., Bangera K.M., (1992), “Free vibration of composite beams using a refined shear flexible beam element”, Computer and Structures, Vol. 43, pp. 719-727.
[5]	Danial Gay, Hoa SV., Tsai SW., (2003), Composite materials design and applications, Boca Raton, London New York, Washington.
[6]	Eisenberger M, Abramovich H, Shulepov O., (1995), “Dynamic stiffness analysis of laminated beams using a first-order shear deformation theory”, Composite Structure, Vol. 31, pp. 265-271.
[7]	Eisenbeger M. (1997) “Torsional vibrations of open and variable cross section bars”, Thin-Walled Structures, Vol. 28, pp. 269-278.
[8]	Evangelos J., Sapountzakis, (2005), “Torsional vibrations of composite bars by BEM”, Composite Structures, Vol. 70, pp. 229-239.
[9]	Gorman DJ., (1975), “Free vibration analysis of beams and shafts”, New York.
[10]	Jun L, Hongxing H, Rongying S., (2008), “Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams”, Composite Structures, Vol. 84, pp. 87-98.
[11]	Kameswara Rao C., Mirza S., (1989), “Torsional vibrations and buckling of thin-walled beams on elastic foundation”, Thin-Walled Structures, Vol. 7, PP. 73-82.
[12]	Kameswara RC., (1988), “Torsional frequencies and mode shapes of generally constrained shafts and piping” Journal of Sound and Vibration, Vol. 125, pp. 115-121.
[13]	Kapuria S, Alam N., (2006), “Efficient layerwise finite element model for dynamic analysis of laminated piezoelectric beams”, Computer Methods in Applied Mechanics and engineering, Vol. 195, pp. 2742-2760.
[14]	Khdeir A.A., Reddy J.N., (1994), “Free vibration of cross-ply laminated beams with arbitrary boundary conditions”, International Journal of Engineering Science, Vol. 32, pp. 1971-1980.
[15]	Kollar LP., (2001), “Flexural-torsional vibration of open section composite beam with shear deformation”, International Journal of Solids and Structures, Vol. 38, pp. 7543-7558.
[16]	Krishnaswamy S., Chandrashekhara K., Wu W.Z.B., (1992), “Analytical solutions to vibration of generally layered composite beams”. Journal of Sound and Vibration, Vol. 159, pp. 85-99.
[17]	La'szlo' P., George S., (2003), Mechanics of composite structures, Cambridge University, New York, United States of America.
[18]	Lee J., Kim S.E., (2002), “Flexural-torsional coupled vibration of thin-walled”, Composite Structures, Vol. 80, pp. 133-144.
[19]	Matsunaga H., (2001), “Vibration and buckling of multilayered composite beams according to higher order deformation theories”, Journal of Sound and Vibration, Vol. 246, pp. 47-62.
[20]	Qiao Pizhong, Zou Guiping., (2002), “Free vibration analysis of fiber-reinforced plastic composite cantilever I-beams”, Mechanics of Advanced Materials and Structure, Vol. 9, pp. 359-373.
[21]	Qiao P., Zou G., Song G., (2002) “Analytical and experimental study of vibration behavior of FRP composite I-beams”, 15th ASCE Engineering Mechanics Conference, New York.
[22]	Shadmehri F., Haddadpour H., Kouchakzadeh, M.A., (2007), “Flexural-torsional behavior of thin-walled composite beams with closed cross-section composite beams with channel sections”, Thin-Walled Structures, Vol. 45, pp. 699-705.
[23]	Song SJ, Waas A., (1997), “Effects of shear deformation on buckling and free vibration of laminated composite beams”, Composite Structures, Vol. 37, pp.3 3-43.
[24]	Teh KK, Huang CC., (1979), “The vibration of generally orthotropic beams-A finite element approach”, Journal of Sound and Vibration, Vol. 62, pp. 195-206.
[25]	Vinson JR, Sierakowski RL., (2004), the behaviour of structures composed of composite materials, New York, Boston, Dordrecht, and Moscow.
[26]	Yildirim V., (2000), “Effect of the longitudinal to transverse moduli ratio on the in-plane natural frequencies of symmetric cross-ply laminated beams by the stiffness method” Composite Structures, Vol. 50, pp. 319-26.
[27]	Yõldõrõm V, Kõral E., (2000), “Investigation of the rotary inertia and shear deformation effects on the out-of-plane bending and torsional natural frequencies of laminated beams”, Composite Structures,Vol. 49, pp. 313-320.