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Vibration, Eigenvalue problem, Inverse eigenvalue problem.


This paper summarize the authors previous effort on inverse eigenvalue problem and applies the theory to the model updating problem. Comments are made on how their procedure may be used to solve the damage detection problem.


Acta Mechanica Slovaca. Volume 15, Issue 3, Pages 38 – 45, ISSN 1335-2393


  Application of Inverse Vibration Problems to Model Updating


[1] Danek, O. (1982). Non conservative Dynamic Systems. Strojnícky Časopis, vol. 33, no. 6, pp. 667-680

[2] Starek, L., Inman, D.J. (2004). Design of Nonproportional Damped Systems via Symmetric Inverse Problem. Journal of Vibration and Acoustic, vol. 126, pp. 212-219
[3] Gohberg, I., et al. (1982). Matrix Polynomials. Academic Press
[4] Gladwell, G.M.L. (1986). Inverse Problem in Vibration. Martinus  Nijhoff Publishers, Boston, MA

[5] Lancaster, P., Maroulas, J. (1987). Inverse Eigenvalue Problems for Damped Vibrating Systems.Journal of Mathematical Analysis and Application, vol.123, no.1, pp. 238-261
[6] Lieven, N.A.J., Ewins, D.J. (1990). Expansion of Modal Data for Correlation. 8th IMAC, pp. 605-609
[7] Starek, L., Inman, D.J. (1991). On the Inverse Vibration Problem with Rigid Body Modes. ASME Journal of Applied Mechanics, vol.58, pp. 1101-1104
[8] Starek, L., Inman, D.J., Kress A. (1992). A Symmetric Inverse Vibration Problem. ASME Journal of Vibration and Acoustics, vol.114, pp. 564-568
[9] Starek L., Inman D.J. (1995). A Symmetric Inverse Vibration Problem with Over-damped modes. Journal of Sound and Vibration, vol. 181, no. 5, pp. 893-903

[10] Starek, L., Inman, D.J., Pilkey, D.J. (1995). A Symmetric Positive Definite Inverse Vibration Problem with Underdamped Modes. Proc. of Design Engineering Technical Conference, Boston, Messachusetts, DE, vol. 84-3, volume 3-Part C, ASME, pp. 1089-1094
[11] Starek, L., Inman, D.J. (1997). A Symmetric Inverse Vibration Problem for Non-proportional, Underdamped System. ASME Journal of Applied Mechanics, vol. 64, no. 3,

pp. 601-605

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