Image sequences and wavelets for vibration analysis: Part 2: Extraction of modal dampings and modeshapes

Abstract

The paper presents the extraction procedure for modal damping and modeshapes from image sequences obtained through the use of optical measurements. The modal dampings are extracted from the image sequence used to identify a cantilever's natural frequencies through the use of the continuous wavelet transform. The identification of the first five vibration modeshapes of the cantilever is attempted. The differences between the theoretical and experimental modeshapes are tracked back to the experimental set-up and a procedure that compensates for this effect is introduced and proved to be successful. The modal assurance criterion (MAC) is computed for the five modes, indicating high correlation for the first four modes, while the fifth was not possible to identify, due to insufficient spatial resolution.

The wavelet transform plays a central role, since it is involved in every stage of the analysis: image edge detection, modeshape extraction, natural frequencies identification and modal damping extraction from multi-degree-of-freedom (MDOF) decays. This paper discusses the issues that need to be tackled with optical measurements, such as temporal and spatial resolution of the image sequence acquisition.

Keywords

optical measurements edge detection continuous wavelet modal damping extraction modeshapes from image sequences

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References

Dynamic Testing Agency Modal testing primer. In Primer on Best Practice in Dynamic Testing, 1993 (Chameleon Press, London).

Patsias

Staszewski

W. J.

Tomlinson

G. R.

Image sequences and wavelets for vibration analysis. Part 1: Edge detection and extraction of natural frequencies. Proc. Instn Mech. Engrs, Part C, Journal of Mechanical Engineering Science, 2002, 216 (C9), 885–900.

Dugundji

Envelopes and pre-envelopes of real wave-forms. IRE Trans. Inf. Theory, March 1958, IT-4, 53–57.

Staszewski

W. J.

Identification of damping in MDOF systems using time-scale decomposition. J. Sound Vibr., 1997, 203 (2), 283–305.

Chui

C. K.

An Introduction to Wavelets— Wavelet Analysis and Its Applications, 1992, Vol. 1 (Academic Press, New York).

Staszewski

W. J.

The application of time-variant analysis to gearbox fault detection. PhD thesis, Department of Engineering, University of Manchester, February 1994.

Rioul

Vetterli

Wavelets and signal processing. IEEE SP Mag., October 1991, 14–38.

Randall

R. B.

Frequency Analysis, 3rd edition, 1987 (Brüel and Kjær).

Patsias

Extraction of dynamic characteristics from vibrating structures using image sequences. PhD thesis, University of Sheffield, November 2000.

10.

Feldman

Non-linear free vibration identification via the Hilbert transform. J. Sound Vibr., 1997, 208 (30), 475–489.

11.

Plunkett

Measurement of damping. In Structural Damping (Ed. Ruzicka

J. E.

), papers presented at the Colloquium on Structural Damping, ASME Annual Meeting, Atlantic City, New Jersey, December 1959, Sec. 5, pp. 117–131 (Pergamon Press).

12.

Chapra

S. C.

Canale

R. P.

Numerical Methods for Engineers— With Programming and Software Applications, 1998 (WCB/McGraw-Hill, Singapore).

13.

Matlab Function Reference, Vol. 1; Reference, Version 5, June 1999 (Mathworks Inc., Natick, Massachusetts).

14.

Ewins

D. J.

Modal Testing: Theory, Practice and Application, 2nd edition, September 2000 (Research Studies Press).

15.

Äström

Heyden

Stochastic modelling and analysis of image acquisition and sub-pixel edge detection. Downloaded from Internet site http://citeseer.nj.nec.com/2563.html , September 2001.