A Homogenisation Procedure for the Steady State Periodic Forced Response of Laminated Composite Beams at Large Vibration Amplitudes

Abstract

The purpose of the present paper is to show that the problem of geometrically non linear steady state periodic forced response 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 equilibrium 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, to determine the effect of the excitation frequency and level of the applied harmonic force on its dynamic response at large vibration amplitudes, which are found to be in a good agreement with the published results.