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Zero and root loci of disturbed spring-mass systems

Zero and root loci of disturbed spring-mass systems
Zero and root loci of disturbed spring-mass systems
Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.
particle chain, complex poles, exclusion regions, atomic lattices, bubble vibration, mode veering
1364-5021
1-28
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c

Lecomte, Christophe (2014) Zero and root loci of disturbed spring-mass systems. Proceedings of the Royal Society A, 470 (2164), 1-28. (doi:10.1098/rspa.2013.0751).

Record type: Article

Abstract

Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.

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Published date: 12 February 2014
Keywords: particle chain, complex poles, exclusion regions, atomic lattices, bubble vibration, mode veering
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 361927
URI: http://eprints.soton.ac.uk/id/eprint/361927
ISSN: 1364-5021
PURE UUID: 3d0f5941-22b1-455d-bc04-75b7b016ec63

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Date deposited: 07 Feb 2014 10:17
Last modified: 28 Aug 2019 18:50

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