Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response. 2nd Report. Hysteretic Damped Absorber.

Abstract

For a large number of engineering problem, we may encounter hysteretic damped systems. Internal damping in the viscoelastic materials and structural damping at a joint, support, bearing, or other assembly are considered to be the hysteretic damping. The principal difference between the viscous damping and the hysteretic damping is that for the viscous damping the energy dissipated per cycle depends linearly on the frequency of vibration, whereas for the hysteretic damping it is independent of the frequency. In this paper, we derive the exact algebraic solutions for design of a hysteretic damped dynamic vibration absorber attached to undamped or damped primary systems for various performance indexes. The absorber is designed on the basis of the H∞ optimization, that is, minimization of the maximum amplitude response of the primary systems to periodic excitation. The solutions obtained here are compared with the approximate ones based on the classical method familiarly called the fixed-points theory.