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On the jump-up and jump-down frequencies of the Duffing oscillator

On the jump-up and jump-down frequencies of the Duffing oscillator
On the jump-up and jump-down frequencies of the Duffing oscillator
In this paper, simple approximate non-dimensional expressions, and the corresponding displacement amplitudes for the jump-up and jump-down frequencies of a softening and hardening lightly damped Duffing oscillator with linear viscous damping are presented. Although some of these expressions can be found in the literature, this paper presents a full set of expressions determined using the harmonic balance approach. These analytical expressions are validated for a range of parameters by comparing the predictions with calculations from direct numerical integration of the equation of motion. They are also compared with similar expressions derived using a perturbation method. It is shown that the jump-down frequency is dependent on the degree of nonlinearity and the damping in the system, whereas the jump-up frequency is dependent primarily upon the nonlinearity, and is only weakly dependent upon the damping. An expression is also given for the threshold of the excitation force and the nonlinearity that needs to be exceeded for a jump to occur. It is shown that this is only dependent upon the damping in the system.
0022-460X
1250-1261
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Kovacic, I.
0cc9489a-2da3-418d-8908-6a902809ef3b
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Kovacic, I.
0cc9489a-2da3-418d-8908-6a902809ef3b
Carrella, A.
1a1904a5-80c2-435a-b3d4-2e26d87ece61
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f

Brennan, M.J., Kovacic, I., Carrella, A. and Waters, T.P. (2008) On the jump-up and jump-down frequencies of the Duffing oscillator. Journal of Sound and Vibration, 318 (4-5), 1250-1261. (doi:10.1016/j.jsv.2008.04.032).

Record type: Article

Abstract

In this paper, simple approximate non-dimensional expressions, and the corresponding displacement amplitudes for the jump-up and jump-down frequencies of a softening and hardening lightly damped Duffing oscillator with linear viscous damping are presented. Although some of these expressions can be found in the literature, this paper presents a full set of expressions determined using the harmonic balance approach. These analytical expressions are validated for a range of parameters by comparing the predictions with calculations from direct numerical integration of the equation of motion. They are also compared with similar expressions derived using a perturbation method. It is shown that the jump-down frequency is dependent on the degree of nonlinearity and the damping in the system, whereas the jump-up frequency is dependent primarily upon the nonlinearity, and is only weakly dependent upon the damping. An expression is also given for the threshold of the excitation force and the nonlinearity that needs to be exceeded for a jump to occur. It is shown that this is only dependent upon the damping in the system.

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More information

Published date: 23 December 2008
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 65213
URI: https://eprints.soton.ac.uk/id/eprint/65213
ISSN: 0022-460X
PURE UUID: 0286a476-30e1-46d6-9c3a-5972628ab941

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Date deposited: 05 Feb 2009
Last modified: 13 Mar 2019 20:19

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