Optimization of Response of a Dynamic Vibration Absorber Forming Part of the Main System by the Fixed-point Theory

Abstract

In the classic form of the Dynamic Vibration Absorber (DVA), a damped DVA is attached to an undamped primary mass, and the main tuning objective is to minimize the dynamic response of the primary mass. Recently proposed structural systems with the selfcontrol ability such as controlled mega-substructure and core tubes with suspension systems use part of the main structure as a dynamic vibration absorber. Because the DVA in the self-control structural systems is a part of the main structure, the control objective of these kinds of systems is dual not only to limit the motion of the primary system but also to reduce the vibration of the DVA. In the present study, the simplified classic model of the DVA with the primary mass under the harmonic excitation is studied and the fixed-point theory is used to derive the optimum parameters of the DVA to minimize the maximum displacement and acceleration responses of the DVA. The effects of different design parameters such as the mass and stiffness ratios of the DVA on the response of the system are investigated. It is shown that the coordinates of one of the fixed points in both displacement and acceleration responses of the DVA are independent of the natural frequency and damping ratios. This point plays an important role in the optimization procedure. For a specific range of the mass ratios of the DVA, the maximum response of the DVA is larger than that of the primary mass; therefore, optimization based on the response of the DVA yields a better result for the self-control structural system.