Perturbed solution of free non-linear vibrations of composite beams

The aim of this study is to characterize the free non-linear vibration behavior of composite beams by using polynomial finite element method with shape functions based on Legendre polynomials or sinusoidal functions. The beams are subjected to different boundary conditions. Non-linear frequencies and modes shapes are obtained using asymptotic linearization method applied on the fundamental vibrating mode. The different composite beams are subjected to different layer dispositions. The nature of the interface between layers is of no object in this study. Navier–Bernoulli hypothesis on the transverse sections is adopted. The study concerns the influence of geometrical non-linearities of the free dynamical behavior. The analysis is performed thus by considering the influence of the vibration amplitude on the modal frequencies of the structure. The solutions are obtained by numerical simulation and by semi-analytical method using asymptotic linearization applied in the real temporal modal space. The numerical values are compared to the different ones obtained in literature.