Keywords: vibration, damages, natural frequency, finite element method, superposition principle.

Damage influences the dynamic behaviour of structures [1,2,3,4], changing their geometry, and consequently their mechanical and dynamic characteristics such as natural frequencies, mode shapes, damping ratio and stiffness. These features, used in damage detection, are identified from measured response time-histories (most often accelerations or strains) or spectra of these time-histories [5,6].

This paper presents the case of symmetric supported beams as well as asymmetrically supported beams. The undamaged beams are considered with constant cross-section and stiffness.

First were used analytical methods, subsequently a finite element analysis was performed for similar beams, both methods revealing very close results for all analysed support types, confirmed also by experimental measurements, for which modular equipment was used with a single accelerometer.

The second step was to define the frequency changes of the first ten weak-axis bending vibration modes for different types of cracks. Each damage has a unique signature or pattern in the natural frequency shift spectrum for asymmetrically supported beams. For symmetrically supported beams, arising from symmetry conditions, there are always two locations providing one pattern.

Afterwards, for similar beams previously studied, a series of two cracks were realized, followed by dynamic behaviour analysis. Thus, the effect of multiple cracks on frequency changes was defined. Finally, the effect of multiple cracks on several beams was compared with the sum of the effect of individual similar cracks.

The investigations lead to the conclusion that the superposition principle is valid, so the frequency changes of a beam with multiple cracks have a similar effect with the sum of frequency changes produced by each individual crack. Statistical methods were developed to extract the parameters of individual cracks from the data obtained by measurements of multiple damaged beams.

1

P. Cawley, R.D. Adams, "The location of defects in structures from measurements of natural frequencies", Journal of Strain Analysis, 14(2), 49-57, 1979. doi:10.1243/03093247V142049

2

S.W. Doebling, C.R. Farrar, M.B. Prime,D.W. Shevitz, "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review", Report No. LA 13070-MS, Los Alamos National Laboratory, Los Alamos, NM, 1996.

3

O.S. Salawu, "Detection of structural damage through changes in frequency: a review", Engineering Structures, 19(9), 18-723, 1997. doi:10.1016/S0141-0296(96)00149-6

4

S.W. Doebling, C.R. Farrar, M.B. Prime, "A summary review of vibration based damage identification methods", Shock Vibration Digest, 30(2), 91-105, 1998. doi:10.1177/058310249803000201

5

A. Morassi, F. Vestroni, "Dynamic Methods for Damage Detection in Structures", CISM Courses and Lectures, 499, Springer, Wien New York, 2008. doi:10.1007/978-3-211-78777-9

6

M.I. Friswell, "Damage identification using inverse methods", Phil. Trans. R. Soc. A, 365, 393-410, 2007. doi:10.1098/rsta.2006.1930

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