Zero and root loci of disturbed spring-mass systems

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


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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.

Item Type: Book Section
Additional Information: Paper No.161 (Format - USB Pen Drive)
ISBNs: 0854329102 (paperback)
9780854329106 (paperback)
Keywords: disturbed spring mass system, analytical transfer function, zero and root locus, chebyshev polynomials, exclusion ellipse
Subjects: Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions : University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Dynamics
Faculty of Engineering and the Environment > Institute of Sound and Vibration Research > Dynamics Research Group
Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute
ePrint ID: 160735
Accepted Date and Publication Date:
July 2010Published
Date Deposited: 20 Jul 2010 13:18
Last Modified: 31 Mar 2016 13:28

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