Nonlinear Dynamics of a Travelling Beam Subjected to Multi-frequency Parametric Excitation

摘要

This paper deals with two frequency parametric excitation in presence of internal resonance. The cubic nonlinearity is inserted into the equation of motion by considering the midline stretching of the beam. The perturbation method of multiple scales is applied directly to the governing nonlinear fourth order integro-partial differential equation of motion. This leads to a set of first order differential equations known as the reduced equations or normalized reduced equations, which are utilized to determine the additional instability zones, appeared in the trivial state stability plot, the bifurcation and stability of fixed-points, periodic, quasi-periodic, mixed mode and chaotic responses. The transition of system behaviour from stable periodic to unstable chaotic occurs through intermittency route.