Geometrically Nonlinear Free Vibrations of Laminated Composite Beams: An Effective Formulation
The purpose of the present paper is to show that the problem of geometrically non linear free vibration of symmetrically and asymmetrically laminated composite beams with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.
Paul P. Lin and Chunliang Zhang
K. El Bikri et al., "Geometrically Nonlinear Free Vibrations of Laminated Composite Beams: An Effective Formulation", Applied Mechanics and Materials, Vols. 105-107, pp. 1681-1684, 2012