Free vibration characteristics of an isolation system with a spring relaxed damper

Carrella, A., Waters, T.P. and Brennan, M.J. (2005) Free vibration characteristics of an isolation system with a spring relaxed damper. In Proceedings of the Twelfth International Congress on Sound and Vibration. International Institute of Acoustics and Vibration. 8 pp .

Abstract

Vibration isolators are frequently represented by the classical Voigt model of a spring and viscous damper in parallel. In cases where this model is appropriate, isolation at high frequencies is compromised by transmission of forces through the damper. This drawback can be mitigated against to some extent by including a ‘relaxation’ spring in series with the damper. The forced response of this ‘Zener’ model is discussed in the literature. This paper is concerned with the free vibration characteristics of the Zener model. Analytical expressions are given for the roots of the characteristic equation and the root loci are presented. As the damping coefficient increases, the effective damping in the system is seen to rise, peak and then tend to zero as the damping coefficient tends to infinity. It is further shown that when the relaxation spring stiffness is less than precisely eight times the primary spring stiffness then critical damping cannot be achieved. Conversely, when this ratio of stiffnesses is greater than eight then two critical damping values exist and the damping ratio can no longer be defined in the conventional way. Alternative ways of quantifying damping for such a model are discussed.

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