Total decoupling of general quadratic pencils, Part II: Structure preserving isospectral flows

Journal of Sound and Vibration

Volumn 309, Issue 1-2, 2008, Pages 112-128

  Chu, Moody T ^a   Del Buono, Nicoletta ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DEGREES OF FREEDOM (MECHANICS); LINEARIZATION; MATHEMATICAL TRANSFORMATIONS;

DIAGONAL MATRICES; DIAGONAL REDUCTION; ISOSPECTRAL TRANSFORMATIONS; QUADRATIC PENCILS;

MATRIX ALGEBRA;

EID: 35448978753     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.05.052     Document Type: Article

References (18)

1. Tisseur F., and Meerbergen K. The quadratic eigenvalue problem. SIAM Review 43 (2001) 235-286
2. I. Gohberg, P. Lancaster, L. Rodman, Computer science and applied mathematics, Matrix Polynomials, Academic Press, New York, 1982.
3. Lancaster P. Lambda-Matrices and Vibrating System (1996), Pergamon Press, Oxford
4. Holz U.B., Golub G.H., and Law K.H. A subspace approximation method for the quadratic eigenvalue problem. SIAM Journal on Matrix Analysis and Applications 26 (2005) 498-521
5. M.T. Chu, N. Del Buono, Total decoupling of a general quadratic pencil, part I: theory, Journal of Sound and Vibration, 2007, accepted for publication.
6. Garvey S.D., Friswell M.I., and Prells U. Co-ordinate transformations for second order systems, I: general transformations. Journal of Sound and Vibration 258 (2002) 885-909
7. Garvey S.D., Friswell M.I., and Prells U. Co-ordinate transformations for second order systems, II: elementary structure-preserving transformations. Journal of Sound and Vibration 258 (2002) 911-930
8. Garvey S.D., Prells U., Friswell M., and Chen Z. General isospectral flows for linear dynamic systems. Linear Algebra and Its Applications 385 (2004) 335-368
9. Horn R.A., and Johnson C.R. Matrix Analysis (1991), Cambridge University Press, New York
10. Uhlig F. A canonical form for a pair of real symmetric matrices that generate a nonsingular pencil. Linear Algebra and Its Applications 14 (1976) 189-209
11. Gohberg I., Lancaster P., and Rodman L. Spectral analysis of selfadjoint matrix polynomials. Annals of Mathematics 112 (1980) 33-71
12. Bloch A.M., and Iserles A. On an isospectral Lie-Poisson system and its Lie algebra. Foundations of Computational Mathematics 6 (2006) 121-144
13. Steeb W.H., and Louw J.A. Nahm's equation, singular point analysis, and integrability. Journal of Mathematical Physics 27 (1986) 2458-2460
14. Van Eetvelt P. Private Communication (2004), University of Nottingham
15. Geometric Integration Interest Group, Foundations of Computational Mathematics〈 http://www.focm.net/gi/〉.
16. Iserles A., Munthe-Kaas H.Z., Nørsett S.P., and Zanna A. Lie-group methods. Acta Numerica 9 (2000) 215-365
17. Equations of motion for MDOF systems, An Online Eduction by eFunda, California 〈 http://www.efunda.com/formulae/vibrations/mdof_eom.cfm〉.
18. Shampine L.F., and Reichelt M.W. MATLAB ODE suite. SIAM Journal on Scientific Computing 18 (1997) 1-22