Abstract
In part I [1] we dealt with a tuned absorber, which can move in the transversally direction, where it is added to an externally excited pendulum. 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 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 obtained applying passive and active control methods. Both control methods are demonstrated numerically. In this paper, a tuned absorber, in the longitudinal direction, is added to an externally excited pendulum. Active control is applied to the system via negative acceleration feedback or via negative angular displacement or its square or cubic value. An approximate solution is derived up to the second order approximation for the system with absorber. 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.
Highlights
Vibrations and dynamic chaos are undesired phenomenon in structures
Eissa [3] has shown that a non-linear absorber can be used to control the vibration of a non-linear system
He has shown that the non-linear absorber widens its range of applications, and its damping coefficient should be kept minimum for better performance [4]
Summary
Vibrations and dynamic chaos are undesired phenomenon in structures They cause disturbance, discomfort, damage and destruction of the system or the structure. Eissa and El-Ganaini [6,7] studied the control of both vibration and dynamic chaos of both internal combustion engines and mechanical structures having quadratic and cubic nonlinearties, subjected to harmonic excitation using single and multi-absorbers. The optimal vibration absorber is utilized for controlling higher mode [14] Another approach of active damping of mechanical structures is the hybrid system, which is a combination of semi-active and active treatments, in which the advantages of individual schemes are combined, while eliminating their shortcomings [15]. Optimum working conditions of the system are obtained applying both passive and active control methods.
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