Vibration Reduction of Two Degree of Freedom Nonlinear System Subject to Parametric Excitation via Negative Feedback Velocity

Negative velocity controller (NVC) is used to reduce the vibration of a two degree of freedom nonlinear system subjected to parametric excitation forces. The vibrating motion of the system described by two coupled differential equation, the worst resonance case of the system near the sub-harmonic resonance (ω ≃ 2ω2 ). The method of multiple scales perturbation technique (MSPT) is applied to obtain the periodic response equation near the selected resonance case. Study the controls on the worst resonance case numerically. The stability of the obtained numerical solution is investigated using both phase plane methods and frequency response equations. Effects of different parameters on the system behavior are studied numerically.