Zero and root loci of disturbed spring-mass systems

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.


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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: Conference or Workshop Item (Paper)
Additional Information: Paper No.161 (Format - USB Pen Drive)
ISBNs: 9780854329106 (print)
0854329102 (print)
Keywords: disturbed spring mass system, analytical transfer function, zero and root locus, chebyshev polynomials, exclusion ellipse
Organisations: Statistical Sciences Research Institute, Dynamics Group
ePrint ID: 160735
Date :
Date Event
July 2010Published
Date Deposited: 20 Jul 2010 13:18
Last Modified: 18 Apr 2017 03:49
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