This paper investigates the transient response of a dynamical system modelling an automatic dynamic balancing mechanism for eccentric rotors. By using recently developed computational techniques, pseudospectra of the linearisation of the system about an equilibrium are computed. This approach allows one to quantify which eigenvalues are most sensitive to perturbation. It is shown how the sensitivity of the eigenvalues directly influences the transient response. Furthermore, the e ect which a variation of the damping coe cients has on the pseudospectra structure is considered. A transient growth due to the non-normality of the linearised system is shown to lead to an exponential decay or to a collapse back to the stable equilibrium; these e ects are identified with the changes in the sensitivities of the eigenvalues under variation of the damping parameters. This provides a new insight into the full nonlinear system, in which qualitatively similar transient responses are shown to occur.
Sponsorship: This work was funded by the EPSRC grant GR/535684/01. The authors wish to thank T. Wagenknecht, J. Agarwal, P. Lancaster and P. Psarrakos for providing the code allowing computation of structured pseudospectra.
Professor Friswell gratefully acknowledges the support of the Royal Society through a Royal Society-Wolfson Research Merit Award.
- non-normality, basin of attraction, pseudospectra, transient growth