Nonlinear Dynamics and Local Bifurcations in the Flexible Beam

The analysis of nonlinear dynamics and local bifurcations of a simply supported flexible beam subjected to harmonic axial excitation is presented. The equation of motion with quintic nonlinear term under the parametric excitation of the simply supported flexible beam is derived. The parametrically excited system is first transformed to the averaged equations using the method of multiple scales. The analysis of stability for the zero solution of the averaged equations is given. It is found that the zero solution is of a double zero eigenvalues and codimension-3 degenerate bifurcations can occur in the averaged equations. Numerical simulations are also given to find the bifurcation response curves.