Eigenderivative Analysis of Asymmetric Non-Conservative Systems

S Adhikari (Cambridge University) & MI Friswell (University of Wales Swansea)

International Journal for Numerical Methods in Engineering, Vol. 51, No. 6, June 2001, pp. 709-733

Abstract

In general, the damping matrix of a dynamic system or structure is such that it can not be simultaneously diagonalized with the mass and stiffness matrices by any linear transformation. For this reason the eigenvalues and eigenvectors and consequently their derivatives become complex. Expressions for the first and second order derivatives of the eigenvalues and eigenvectors of these linear, non-conservative systems are given. Traditional restrictions of symmetry and positive definiteness have not been imposed on the mass, damping and stiffness matrices. The results are derived in terms of the eigenvalues and left and right eigenvectors of the second-order system so that the undesirable use of the first-order representation of equations of motion can be avoided. The usefulness of the derived expressions is demonstrated by considering a non-proportionally damped two degree-of-freedom symmetric system, and a damped rigid rotor on flexible supports.

Paper Availability

This material has been published in the International Journal for Numerical Methods in Engineering, Vol. 51, No. 6, June 2001, pp. 709-733. Unfortunately the copyright agreement with Wiley InterScience does not allow for the PDF file of the paper to be available on this website. However the paper is available from the Wiley website - see the link below.


Link to paper using doi:10.1002/nme.186



Comments on this paper by MS Jankovic

Comments on Eigenderivative analysis of asymmetric non-conservative systems by S. Adhikari and M. I. Friswell (International Journal for Numerical Methods in Engineering 2001; 51:709-733) by MS Jankovic. International Journal for Numerical Methods in Engineering, 56(2), 325-328, 2003.


Link to comments using doi:10.1002/nme.643

International Journal for Numerical Methods in Engineering on Wiley InterScience


Authors' Response

Authors' reply to 'Comments on Eigenderivative analysis of asymmetric non-conservative systems'' by S. Adhikari and M. I. Friswell, International Journal for Numerical Methods in Engineering, 56(2), 329-330, 2003.


Link to reply using doi:10.1002/nme.685