NON-LINEAR OSCILLATIONS OF A SIMPLY-SUPPORTED THIN-WALLED COMPOSITE BEAM

MACHADO SEBASTIÁN PABLO; CORTÍNEZ VÍCTOR HUGO

Brasília, DF, Brasil

Congreso; 19th International Congress of Mechanical Engineering; 2007

ABCM

A geometrically non-linear theory is used to study the dynamic behavior of a thin-walled composite beam. The model is based on a small strain and large rotation and displacements theory, which is formulated through the adoption of a higher-order displacement field and takes into account shear flexibility (bending and warping shear). In the analysis of a weakly nonlinear continuous system, the Ritz’s method is employed to express the problem in terms ofgeneralized coordinates. Then, perturbation method of multiple scales is applied to the reduced system in order to obtain the equations of amplitude and modulation. In this paper, the non-linear 3D oscillations of a simply-supported beam are examined, considering a cross-section having one symmetry axis. Composite is assumed to be made of symmetric balanced laminates and especially orthotropic laminates. The model, which contains both quadratic and cubic non-linearities, is assumed to be in internal resonance condition. Steady-state solution and their stability are investigated by means of the eigenvalues of the Jacobian matrix. The software XPP-AUTO is used to trace the branches of the equilibrium solutions. The equilibrium solution is governed by the modal coupling and experience a complex behavior composed by saddle-noddle, hopf and double period bifurcations.