Geometrically non-linear forced vibrations of Euler–Bernoulli laminated composite beams

Abstract

The objective of this research is to study geometrically non-linear free vibrations and forced vibrations subjected to harmonic excitations of laminated composite beams. On the basis of Euler Bernoulli’s beam theory and Green-Lagrange’s hypothesis of geometric non-linearity, the theoretical model has been established. Taking into account the harmonic response, the transverse displacement function of the non-linear beam determined by applying Hamilton’s principle, the problem is reduced to a non-linear algebraic system solved by an approximate method. In order to verify this method, numerical examples for carbon/epoxy materials, under two boundary conditions, i.e. clamped-free and clamped- clamped, have been performed and the results are very consistent with those obtained in the literature. In addition, based on the approximate multimode method in the vicinity of the predominant mode, a nonlinear forced response was performed for a wide range of vibration amplitudes. It should also be noted that the effects on the non-linear forced dynamic response of the fiber orientation and number of layers, the excitation frequency and the level of the applied harmonic force have been studied and illustrated by various examples.