A simple formulation for large vibration amplitudes of laminated composite beams

Abstract

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. A simplified multimode approach, based on the explicit formulation developed previously for various nonlinear vibration problems, is derived, leading to a multimode explicit description, 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.