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On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator

On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator
On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator
There are many systems which consist of a nonlinear oscillator attached to a linear system, examples of which are nonlinear vibration absorbers, or nonlinear systems under test using shakers excited harmonically with a constant force. This paper presents a study of the dynamic behaviour of a specific two degree-of-freedom system representing such a system, in which the nonlinear system does not affect the vibration of the forced linear system. The nonlinearity of the attachment is derived from a geometric configuration consisting of a mass suspended on two springs which are adjusted to achieve a quasi-zero stiffness characteristic with pure cubic nonlinearity. The response of the system at the frequency of excitation is found analytically by applying the method of averaging. The effects of the system parameters on the frequency-amplitude response of the relative motion are examined. It is found that closed detached resonance curves lying outside or inside the continuous path of the main resonance curve can appear as a part of the overall amplitude-frequency response. Two typical situations for the creation of the detached resonance curve inside the main resonance curve, which are dependent on the damping in the nonlinear oscillator, are discussed
0022-460X
1823-1835
Gatti, Gianluca
8a9fe0e2-c408-4188-bf10-e93bf247205c
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Gatti, Gianluca
8a9fe0e2-c408-4188-bf10-e93bf247205c
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13

Gatti, Gianluca, Kovacic, Ivana and Brennan, Michael J. (2010) On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator. Journal of Sound and Vibration, 329 (10), 1823-1835. (doi:10.1016/j.jsv.2009.11.019).

Record type: Article

Abstract

There are many systems which consist of a nonlinear oscillator attached to a linear system, examples of which are nonlinear vibration absorbers, or nonlinear systems under test using shakers excited harmonically with a constant force. This paper presents a study of the dynamic behaviour of a specific two degree-of-freedom system representing such a system, in which the nonlinear system does not affect the vibration of the forced linear system. The nonlinearity of the attachment is derived from a geometric configuration consisting of a mass suspended on two springs which are adjusted to achieve a quasi-zero stiffness characteristic with pure cubic nonlinearity. The response of the system at the frequency of excitation is found analytically by applying the method of averaging. The effects of the system parameters on the frequency-amplitude response of the relative motion are examined. It is found that closed detached resonance curves lying outside or inside the continuous path of the main resonance curve can appear as a part of the overall amplitude-frequency response. Two typical situations for the creation of the detached resonance curve inside the main resonance curve, which are dependent on the damping in the nonlinear oscillator, are discussed

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Published date: 10 May 2010

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Local EPrints ID: 79137
URI: http://eprints.soton.ac.uk/id/eprint/79137
ISSN: 0022-460X
PURE UUID: c92ee292-addb-48f5-8f21-34791ee084fd

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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 00:28

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Contributors

Author: Gianluca Gatti
Author: Ivana Kovacic
Author: Michael J. Brennan

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