Free vibration of axially loaded composite beams with general boundary conditions using hyperbolic shear deformation theory

The natural frequencies, mode shapes and buckling loads of the laminated composite beams subject to concentrated axial forces are investigated on the basis of hyperbolic shear deformation theory. In the analysis the effects of axial force, Poisson effect, shear deformation, rotary inertia and coupling between axial and transverse deformations are taken into account. The spectral finite element method is adopted with particular reference to the Wittrick–Williams algorithm when investigating the free vibration of axially loaded composite beams. The exact spectral element matrix is established by directly solving the governing differential equations of the laminated beams in free vibration. Two illustrative examples are worked out to show the influences of axial force and boundary condition on the free vibration and buckling behaviors of the laminated composite beams. Comparison with the available solutions in the literature demonstrates the accuracy and reliability of the proposed formulation.