• Contents V46
• Online Suppl
• CTAC 2004
• Part 1
• Part 2
• Part 3
• Part 4
• Author index
• Journal home
• RSS News
• Information
• for Readers
• for Authors
• for Referees
• Other e-journals
• Aust Math Soc
• 
  

ANZIAM J. 46(E) pp.C658--C671, 2005.

Problem of close eigenvalues in the vibration testing of structures

V. Gershkovich

N. Haritos

(Received 25 October 2004, revised 8 June 2005)

Abstract

We outline our vibration based testing approach towards reconstruction of structural properties and damage detection of large structures. Our emphasis is on developing algorithms for the detection of close or coinciding eigenvalues and their calculation --- a commonly encountered situation that has not been adequately addressed in the modal analysis literature nor in commercial software.

Download to your computer

• Click here for the PDF article (215 kbytes) We suggest printing 2up.
• Click here for its BiBTeX record

Authors

V. Gershkovich

N. Haritos

Dept. of Civil & Environmental Engineering, University of Melbourne, Australia. mailto:nharitos@unimelb.edu.au

Published July 25, 2005. ISSN 1446-8735

References

1. Arnold V. Modes and quasi-modes, Functional Analysis and Applications, 6(2):12--20, 1972.
2. Chalko T., Gershkovich V., and Haritos N. Optimal Design of Modal Experiment for Bridge Structures, Proc. XIII Intern. Modal Analysis Conf., (IMAC-XIII), Nashville, p.571--577, 1995.
3. Chalko T., Gershkovich V., and Haritos N. Direct Simulation Modal Approximation Technique, Proc. XIV Intern. Modal Analysis Conf., (IMAC-XIV), Dearborn, p.1130--1136, 1996.
4. Chalko T., Gershkovich V., and Haritos N. Modal Parameter Estimation with Uniform Tolerances, Proc. Intern. Modal Analysis Conf., (IMAC-XV), Tokyo, Japan, p.689--695, 1997.
5. Chalko T., Gershkovich V., and Haritos N. Modal Analysis and Spectral Geometry, Proc. CTAC97, World Scientific, 1:115--122, 1998.
6. Doebling S. W., Farrar S. R., Prime M. B., and Shevitz D. W., Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review, Los Alamos Nat.Lab. Report, LA-13070-MS, 1996. URL
7. Donelly H., Fefferman C. Nodal sets of eigenfunctions on Riemannian manifolds, Inv. Math., 93:161--183, 1988.
8. Ewins D. J. Modal Testing --- Theory and Practice, John Wiley, New York, 1985.
9. Kato T. Perturbation theory for linear operators, Springer-Verlag, 1966.
10. Lazutkin V. KAM Theory and Semiclassical Approximations to Eigenfunctions, Springer-Verlag, 1993.
11. Nadirashvili N. Some topics in spectral geometry, Sem. de theorie spectrale et geometrie, Chambery-Grenoble, 9--12, 1990--91.
12. Safarov Y., Vassiliev D. The asymptotic Distribution of Eigenvalues of Partial Differential Operators, Trans. of Math. Monogr., Amer. Math. Soc., 1997.
13. Sohn H., Farrar S. R., Hemez F. N., Shunk D., Stinemates D. W., Nader B. R., A review of structural health monitoring literature 1996--2001, Los Alamos Nat. Lab. Report, LA-13976-MS, 2003. URL