Issue 48

J. Prawin et alii, Frattura ed Integrità Strutturale, 48 (2019) 513-522; DOI: 10.3221/IGF-ESIS.48.49 519 where the first damage index 1 i ( DI ) indicates the ratio of the sum of the power spectrum amplitudes of ‘n’ superharmonics to power spectrum amplitude of linear excitation harmonic (i.e FFT amplitude (A) at excitation frequency  X ). The second damage index indicates the extension of the first approach to the curvature based index and N represents the total number of degrees of freedom. 1 2 3 4 5 6 7 8 9 10 11 0 2 4 6 8 10 proposed damage index ( without noise) proposed damage index (with 10% noise) DI 1 (without noise) DI 1 (with 10% noise) DI 2 (without noise) DI 2 (with 10% noise) Damage Index Sensor Nodes 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 proposed damage index ( without noise) proposed damage index (with 10% noise) DI 1 (without noise) DI 1 (with 10% noise) DI 2 (without noise) DI 2 (with 10% noise) Damage Index Sensor Nodes (a) (b) Figure 7 : Various damage indices (a) 20% crack depth (b) 7% crack depth For this investigation on the proposed damage index with previous works, the closing crack is simulated in simply supported beam in element no.4 with crack depth equal to 20% and 7% of overall depth of the beam. The results of the damage index estimated using Eqn. (1) and Eqn. (3) is furnished in Fig. 7 (a) for the beam having crack equal to 20% of total depth. Similarly the results of the damage index corresponding to the case of simply supported beam with crack depth equal to 7% of overall depth of the beam is shown in Fig. 7 (b). Before computing the damage index, the computed acceleration time history responses are polluted with 10% noise. It can be observed from Fig. 7 (a) that the peak value of all the damage indices is at the exact location of the breathing crack. However it can be observed from Fig. 7 (b), the two damage indices corresponding to the previous approaches fail to detect smaller cracks due to consideration of only a few superharmonics and difficulty in distinguishing noise and true nonlinear harmonic. For example, the damage index 1 DI shows multiple peaks which creates confusion and difficult to conclude the exact location of the breathing crack. While the damage index 2 DI shows a peak at the wrong location. Therefore, the earlier approaches [6-8] fail to detect subtle cracks; however, the proposed method identifies the minor damages very precisely by reliably extracting all the possible higher order harmonics. E XPERIMENTAL VALIDATION part from the above numerical investigations, experimental studies have been carried out by considering a cantilever beam with single and multiple breathing cracks (i.e. two test specimens), to test and verify the proposed closing crack localization algorithm. The experimental set up followed in the present work is popularly used by Prime et.al . [11] and Douka et.al ., [12] earlier for validation of their crack diagnosis algorithms. The single crack test beam shown in Fig. 8, is constructed by bonding two aluminium alloy beams (i.e. four pieces) together. The faces of the top plates in contact induce breathing behaviour. The instrumentation set up is same for both the specimens and shown in Fig. 8. The length of the beam is 1m for both the test specimens. The cross-section dimension of both the specimens is same and found to be 0.0254 x 0.0127m. The ratio of the thickness of the top and bottom plates decides the crack depth. The top and bottom plate thicknesses corresponding to single crack test specimen (case-1) are 1.5875 mm and 11.1125mm respectively. This results in a crack depth of 12.5% of the overall depth of the beam and the crack is simulated at 0.4m (i.e. located between sensor 3 and 4) from the fixed end. Similarly, the top and bottom plate thicknesses corresponding to two crack specimen (case-2) are 3.175mm and 9.525mm which results in 25% crack depth of the total depth of the beam. In the case of two crack experimental specimen shown in Fig. 9, the first crack at 0.2m is located between sensor 2 and 3 (closer to sensor 2), while the second crack at 0.7m from the fixed end is located between sensor 5 and 6 (closer to sensor 6). The two crack A