Random Vibration and the Single Degree-of-Freedom Vibratory System: A Symbolic Quantification of Isolation and Packaging Performance

Abstract

With twenty years of research, active and semi-active systems have been shown to have certain performance advantages over passive suspensions in certain operating regimes. Chalasani and Redfield and Karnopp have shown that, depending on the performance index and weightings, active control improves performance from little to moderately. There are situations where passive control is quite satisfactory and the complexities and cost of more active means may not be warranted. To further the understanding of the tradeoffs involved and the performance potentials of active suspensions, this paper symbolically quantifies the isolation and stroke performance for a one degree-of-freedom vibratory system subject to a stochastic disturbance input acting through the suspension. The system of this paper models that of tracked vehicles and a class of isolation systems quite well. It also gives insight into low and high frequency performance for two degree-of-freedom systems such as a typical suspension model for automobiles, aircraft, and rail vehicles. Because of the nature of the single degree-of-freedom model, issues of handling cannot be readily addressed in this work. The 1 DOF model does not adequately predict dynamic tire forces. The main contributions of this work are the closed form symbolic solutions developed for optimal suspension responsemore » and the demonstration of the marked similarity between the frequency and mean square response of the 1 degree-of-freedom model of this paper and the more involved 2 degree-of-freedom model incorporating a so-called unsprung mass.''« less