Abstract
A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Reddy J.N.: Mechanics of laminated composite plates and shells: theory and analysis. CRC, Boca Raton (2004)
Soldatos K., Elishakoff I.: A transverse shear and normal deformable orthotropic beam theory. J.Sound Vib. 155(3), 528–533 (1992)
Chandrashekhara K., Bangera K.: Free vibration of composite beams using a refined shear flexible beam element. Comput. Struct. 43(4), 719–727 (1992)
Marur S.R., Kant T.: vibration analysis of fiber reinforced composite beams using higher order theories and finite element modelling. J. Sound Vib. 194(3), 337–351 (1996)
Kant T., Marur S.R., Rao G.S.: Analytical solution to the dynamic analysis of laminated beams using higher order refined theory. Compos. Struct. 40(1), 1–9 (1997)
Marur S.R., Kant T.: A higher order finite element model for the vibration analysis of laminated beams. J. Vib. Acoust. 120(3), 822–824 (1998)
Marur S.R., Kant T.: On the angle ply higher order beam vibrations. Comput. Mech. 40, 25–33 (2007)
Shi G., Lam K.Y.: Finite element vibration analysis of composite beams based on higher-order beam theory. J. Sound Vib. 219(4), 707–721 (1999)
Murthy M.V.V.S., Mahapatra D.R., Badarinarayana K., Gopalakrishnan S.: A refined higher order finite element for asymmetric composite beams. Compos. Struct. 67(1), 27–35 (2005)
Subramanian P.: Analysis of laminated composite beams using higher order theories and finite elements. Compos. Struct. 73(3), 342–353 (2006)
Jun L., Xiaobin L., Hong xing H.: Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method. Arch. Appl. Mech. 79, 1083–1098 (2009)
Jun L., Hong xing H.: Dynamic stiffness analysis of laminated composite beams using trigonometric shear deformation theory. Compos. Struct. 89(3), 433–442 (2009)
Jun L., Hongxing H.: Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory. Meccanica 46, 1299–1317 (2011)
Vidal P., Polit O.: A family of sinus finite elements for the analysis of rectangular laminated beams. Compos. Struct. 84(1), 56–72 (2008)
Vidal P., Polit O.: Vibration of multilayered beams using sinus finite elements with transverse normal stress. Compos. Struct. 92(6), 1524–1534 (2010)
Khdeir A.A., Reddy J.N.: Free vibration of cross-ply laminated beams with arbitrary boundary conditions. Int. J. Eng. Sci. 32(12), 1971–1980 (1994)
Khdeir A.A., Reddy J.N.: Buckling of cross-ply laminated beams with arbitrary boundary conditions. Compos. Struct. 37(1), 1–3 (1997)
Song S.J., Waas A.M.: Effects of shear deformation on buckling and free vibration of laminated composite beams. Compos. Struct. 37(1), 33–43 (1997)
Karama M., Harb B.A., Mistou S., Caperaa S.: Bending , buckling and free vibration of laminated composite with a transverse shear stress continuity model. Compos. B Eng. 29(3), 223–234 (1998)
Karama M., Afaq K.S., Mistou S.: Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Int. J. Solids Struct. 40(6), 1525–1546 (2003)
Matsunaga H.: Vibration and buckling of multilayered composite beams according to higher order deformation theories. J. Sound Vib. 246(1), 47–62 (2001)
Aydogdu M.: Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Int. J. Mech. Sci. 47(11), 1740–1755 (2005)
Aydogdu M.: Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Compos. Sci. Tech. 66(10), 1248–1255 (2006)
Aydogdu M.: Free vibration analysis of angle-ply laminated beams with general boundary conditions. J. Reinforced Plastics Compos. 25(15), 1571–1583 (2006)
Zhen W., Wanji C.: An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams. Compos. Struct. 8(4), 337–349 (2008)
Vo T.P., Thai H.T.: Static behaviour of composite beams using various refined shear deformation theories. Compos. Struct. 94(8), 2513–2522 (2012)
Touratier M.: An efficient standard plate theory. Int. J. Eng. Sci. 29(8), 901–916 (1991)
Jones R.M.: Mechanics of Composite Materials. Taylor & Francis, London (1999)
Chen W.Q., Lv C.F., Bian Z.G.: Free vibration analysis of generally laminated beams via state-space-based differential quadrature. Compos. Struct. 63(3–4), 417–425 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vo, T.P., Thai, HT. & Inam, F. Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory. Arch Appl Mech 83, 605–622 (2013). https://doi.org/10.1007/s00419-012-0707-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-012-0707-4