Nonlinear dynamics and bifurcations of an axially moving beam

The present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linens subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied.