Archive of Applied Mechanics

, Volume 79, Issue 12, pp 1083–1098 | Cite as

Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method

  • Li Jun
  • Li Xiaobin
  • Hua Hongxing


The dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. The exact dynamic stiffness matrix is found directly from the analytical solutions of the basic governing differential equations of motion. The Poisson effect, shear deformation, rotary inertia, in-plane deformation are considered in the analysis. Application of the derived dynamic stiffness matrix to several particular laminated beams is discussed. The influences of Poisson effect, material anisotropy, slenderness and end condition on the natural frequencies of the beams are investigated. The numerical results are compared with the existing solutions in literature whenever possible to demonstrate and validate the present method.


Generally laminated beams Third-order shear deformation theory Free vibration Dynamic stiffness matrix Poisson effect 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Vibration, Shock and Noise InstituteShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.School of Transportation, Wuhan University of TechnologyWuhanPeople’s Republic of China

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