Abstract
In this paper four semi-active dynamic vibration absorbers (DVAs) are analytically studied, where the time delay induced by measurement and execution in control procedure is included in the system. The first-order approximate analytical solutions of the four semi-active DVAs are established by the averaging method, based on the illustrated phase difference of the motion parameters. The comparisons between the analytical and the numerical solutions are carried out, which verify the correctness and satisfactory precision of the approximate analytical solutions. Then the effects of the time delay on the dynamical responses are analyzed, and it is found that the stability conditions for the steady-state responses of the primary systems are all periodic functions of time delay, with the same period as the excitation one. At last the effects of time delay on control performance are discussed.
Highlights
Dynamic vibration absorber (DVA), called as tuned vibration absorber (TVA), is a subsystem attached to the primary system and designed to cancel or mitigate the unexpectedly transmitted force or motion to the primary system [1,2]
Nishihara and Asami divided the design purposes for DVA parameters into three kinds, named as H2 optimization to minimize the maximum amplitude of the primary system, H∞ optimization to minimize the total energy of the primary system in overall frequency, and stability maximization to attenuate the transient response of the primary system as soon as possible [5]
Jalili and Olgac [28] extended the above results to an active DVA using partial state feedback with controlled time delay, and discussed the parameters range for stable motion and the sensitivity analysis
Summary
Dynamic vibration absorber (DVA), called as tuned vibration absorber (TVA), is a subsystem attached to the primary system and designed to cancel or mitigate the unexpectedly transmitted force or motion to the primary system [1,2]. Jalili and Olgac [28] extended the above results to an active DVA using partial state feedback with controlled time delay, and discussed the parameters range for stable motion and the sensitivity analysis. From these references about the effects of time delay on vibration control, one could find that inappropriate time delay could affect the stability of the controlled system and may enlarge the response of the primary system, which will deteriorate the control performance of DVA.
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