Identification of damage in beam and plate structures using parameter‐dependent frequency changes

Abstract

Damage of a structure affects its stiffness properties and induces a shift in the free frequency spectrum. In the paper, an additional parameter is introduced, such as concentrated elastic or rigid support and mass. The evolution of natural frequencies is analyzed for varying parameter values with respect to damage location. This frequency variation is used in assessing the location and magnitude of damage by introducing the damage indices or by solving the identification problem requiring the minimization of the parameter dependent distance functional. The first part of the paper is concerned with the sensitivity analysis of damage indices with respect to support or mass location. The second part deals with the identification problem for which the specific examples are treated.

Structural damage identification using frequency and modal changes

“…where DI i can be called the 'damage index' associated with i-th natural frequency [2]. The variation of λ i specified by (8), in view of (5), can be now expressed as follows:…”

“…Let us note that there was no constraint set on the stiffness variation, and then the model predicts some element stiffness moduli higher than EI. The analysis presented here was based on the work of Dems and Mróz [2] which has been concerned with the damage identification method using parameter dependent evolution of natural frequencies.…”

“…The eigenmodes of undamaged structure are assumed as known and their variation for damaged structure is assessed analytically or neglected, cf. Dems and Mróz [2]. However, when the mode shape changes are measured, then the identification procedure is augmented by using modal assurance criteria, mode curvature or an energy distribution in consecutive structural elements, and variation of position of mode lines.…”

“…A general sensitivity study of natural frequencies and modes with respect to cracks and holes was presented, for instance, by Gudmundson [5], Garstecki and Thermann [6] as well as Dems and Mróz [7] for geometrically non-linear vibration and stability problems. The damage identification using some additional control parameters in order to increase the sensitivity of structural response with increasing damage and to maximize the assumed distance norm between the measured and structural model response was also presented in [2].…”

Crack identification in plates using 1-D discrete wavelet transform

“…acoustic emission (Rogers, 2005), X-rays (Shinoba et al, 2004), eddy current (Gros, 1995), ultrasonography (Zhang et al, 2004), magnetic field (Lee et al, 2004) or soft computing methods such as artificial neural networks (Waszczyszyn and Ziemiań-ski, 2001) and evolutionary algorithms (Burczyński et al, 2004). The traditional approach, based on the analysis of natural frequencies (Dems and Mróz, 2001) and modal shapes of structure vibrations (Ostachowicz and Kaczmarczyk, 2001), is still used and further developed. However, the global static or dynamic structural response is rather insensitive to localized damage.…”