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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
We discuss analytical properties of a (possibly damped) disturbed chain of identical springs and masses. We particularly focus on a rank-one disturbance, such as a spring or damper, at or between the first and last masses. The displacements of the disturbed and undisturbed systems due to forcing at any mass are expressed in terms of Chebyshev polynomials. We present several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain. In particular, we show that there exists an elliptical region in the frequency-disturbance magnitude plane from which zeros are excluded.
disturbed spring mass system, analytical transfer function, zero and root locus, chebyshev polynomials, exclusion ellipse
0854329102
14pp
University of Southampton
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
Brennan, M.J.
Kovacic, Ivana
Lopes Jr, V.
Murphy, K.
Petersson, B.
Rizzi, S.
Yang, T.
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
Brennan, M.J.
Kovacic, Ivana
Lopes Jr, V.
Murphy, K.
Petersson, B.
Rizzi, S.
Yang, T.

Lecomte, Christophe (2010) Zero and root loci of disturbed spring-mass systems. Brennan, M.J., Kovacic, Ivana, Lopes Jr, V., Murphy, K., Petersson, B., Rizzi, S. and Yang, T. (eds.) In Recent Advances Structural Dynamics: Proceedings of the X International Conference. University of Southampton. 14pp .

Record type: Conference or Workshop Item (Paper)

Abstract

We discuss analytical properties of a (possibly damped) disturbed chain of identical springs and masses. We particularly focus on a rank-one disturbance, such as a spring or damper, at or between the first and last masses. The displacements of the disturbed and undisturbed systems due to forcing at any mass are expressed in terms of Chebyshev polynomials. We present several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain. In particular, we show that there exists an elliptical region in the frequency-disturbance magnitude plane from which zeros are excluded.

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More information

Published date: July 2010
Additional Information: Paper No.161 (Format - USB Pen Drive)
Keywords: disturbed spring mass system, analytical transfer function, zero and root locus, chebyshev polynomials, exclusion ellipse
Organisations: Statistical Sciences Research Institute, Dynamics Group

Identifiers

Local EPrints ID: 160735
URI: http://eprints.soton.ac.uk/id/eprint/160735
ISBN: 0854329102
PURE UUID: 28c52bf9-ff6b-43d4-ada7-d01adb5feb14

Catalogue record

Date deposited: 20 Jul 2010 13:18
Last modified: 18 Jun 2020 16:32

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