Approximate Expression for Design of Optimal Dynamic Absorbers Attached to Damped Linear Systems (2nd Report, Optimization Process Based on the Fixed-Points Theory)

Abstract

This paper proposes an expression for design of optimal dynamic absorbers attached to damped linear systems. The classical expressions were derived from the assumption that the primary system has no damping. There are two optimization criteria in the design of the dynamic absorber: the fixed-points theory and the minimum variance criterion. In the fixed-points theory, the dynamic absorber is optimally tuned and damped with respect to the primary system so that the two resonant amplitudes of the main mass are equal. On the other hand, in the latter criterion the area under the power spectrum density curve of the main mass is adjusted to take the minimum value. The new expression proposed in this paper is based on the fixed-points theory. However, there are no fixed points in the resonance curves of the damped linear systems, so the analytic procedure becomes impossible. Therefore a perturbation method is used to obtain the expression, and the accuracy of the solution is discussed. © 1995, The Japan Society of Mechanical Engineers. All rights reserved.