Geometrically Nonlinear Free Vibrations of Laminated Composite Beams: An Effective Formulation

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. 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.

Geometrically Nonlinear Free Vibration of Composite Materials: Clamped-Clamped Functionally Graded Beam with an Edge Crack Using Homogenisation Method

“…A homogenisation procedure already proposed in [6][7][8][9] for the case of rectangular plates and beams, is used to reduce the problem studied to that isotropic homogeneous cracked beams, in order to show the effect of the crack and the volume fraction on structural dynamic characteristics such as natural frequencies.…”