A Comparison between Active and Passive Vibration Control of Non-Linear Simple Pendulum. Part I: Transversally Tuned Absorber and Negative Gφn Feedback

Vibrations and dynamic chaos should be controlled in structures and machines. The most famous method of vibration control is using absorbers or tuned dampers or neutralizers. The main aim is to improve the system behavior at different resonance conditions. Two main strategies are used. They are passive and active control methods. In this paper, a tuned absorber, in the transversally direction, is added to an externally excited pendulum, which is simulated by a second order non-linear differential equation having both quadratic and cubic non-linearties, subjected to harmonic excitation. The absorber is usually designed to control one frequency at primary resonance where system damage is probable. The quenching efficiency of the system is studied. Active control is applied to the system via negative velocity feedback or its square or cubic value. The multiple time scale perturbation technique is applied throughout. An approximate solution is derived up to the second order approximation. The stability of the system is investigated applying both frequency response equations and phase plane methods. The effects of the absorber on system behavior are studied numerically. Optimum working conditions of the system are extracted when applying both passive and active control methods.