Using negative velocity feedback controller to reduce the vibration of a suspended cable

The system of suspended cable with mixed excitation forces is controlled in this paper by using negative linear velocity feedback controller. The equations of motion of this system contain quadratic and cubic nonlinearities. The multiple scale perturbation technique is applied to determine the response of the nonlinear system near the simultaneous sub-harmonic and combined resonance case of this system. The stability of the obtained numerical solution is investigated using frequency response equations. The effect of different parameters on the vibrating system are investigated and reported.