Nonlinear dynamics of a cantilever beam carrying an attached mass with 1:3:9 internal resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1: 3: 9 internal resonances for principal and combination parametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set of first order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system. Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.