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

Free vibration characteristics of an isolation system with a spring relaxed damper
Free vibration characteristics of an isolation system with a spring relaxed damper
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.
International Institute of Acoustics and Vibration
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Waters, T.P.
6850ea36-2df6-41b6-9693-c8a7fa834bea
Brennan, M.J.
7f39b4f4-810d-49d5-be90-1656c7b8069a
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Waters, T.P.
6850ea36-2df6-41b6-9693-c8a7fa834bea
Brennan, M.J.
7f39b4f4-810d-49d5-be90-1656c7b8069a

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 .

Record type: Conference or Workshop Item (Paper)

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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More information

Published date: 2005
Additional Information: Paper 684
Venue - Dates: 12th International Congress on Sound and Vibration (ICSV12), Lisbon, Portugal, 2005-07-11 - 2005-07-14

Identifiers

Local EPrints ID: 28507
URI: http://eprints.soton.ac.uk/id/eprint/28507
PURE UUID: 492223f1-3b35-4a09-a8bb-9939eb7ebec5

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Date deposited: 28 Apr 2006
Last modified: 06 Mar 2024 17:41

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Contributors

Author: A. Carrella
Author: T.P. Waters
Author: M.J. Brennan

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