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Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness
Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness
Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper.
vibration isolation, nonlinear stiffness, duffing equation, nonlinear transmissibility, hsdls
0020-7403
22-29
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Lopes, V.
c2ba0cd8-31e9-4f89-b042-02cca1c58233
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Lopes, V.
c2ba0cd8-31e9-4f89-b042-02cca1c58233

Carrella, A., Brennan, M.J., Waters, T.P. and Lopes, V. (2012) Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55 (1), 22-29. (doi:10.1016/j.ijmecsci.2011.11.012).

Record type: Article

Abstract

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper.

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More information

Published date: February 2012
Keywords: vibration isolation, nonlinear stiffness, duffing equation, nonlinear transmissibility, hsdls
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 350111
URI: https://eprints.soton.ac.uk/id/eprint/350111
ISSN: 0020-7403
PURE UUID: ad2d48f0-13bb-43b1-8c93-66e0a0426830

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Date deposited: 18 Mar 2013 16:04
Last modified: 18 Jul 2017 04:37

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