Control of a two-degree-of-freedom system with combined excitations

In this paper, the chaotic dynamics of parametrically, externally and tuned excited suspended cable is studied with negative cubic velocity feedback. The equations of motion of this system are exhibited by two-degree-of-freedom system including quadratic and cubic nonlinearities. Using the multiple scale perturbation technique, the response of the nonlinear system near the simultaneous primary, sub-harmonic, combined and internal resonance case of this system is extracted up to the second order approximation. The stability of the obtained numerical solution is investigated using frequency response equations. The effect of different parameters on the vibrating system behavior are investigated and reported. The simulation results are achieved using MATLAB (R2012a) programs.