Issue 52

J. Akbari et alii, Frattura ed Integrità Strutturale, 52 (2020) 269-280; DOI: 10.3221/IGF-ESIS.52.21 273 Length (m) b (mm) h(mm) 3 ρ (kg/m ) E (GPa) 5.0 100 50 7850 210 Table 1: Mechanical and geometrical specifications of the studied beams. For finite element modeling, the beam length is evenly divided into 100 elements. Thus, the length of each element is 50mm. The modal information of the beams has been extracted from a finite - element modeling of each beam. In order to simulate the damaged finite element model, the height of the damaged element is reduced to 0.95h e.g. d h =0.95h for 5% damage. The modal curvature of the beam ( Φ  ) is calculated using the central finite difference method as Eqn.(11). 2 Φ (L- Δ L)-2 Φ (L)+ Φ (L+ Δ L) Φ = ( Δ L)  (11) where, , Φ   are the mode shapes and the curvature of mode shapes, respectively. As well, L refers to the length of the beam. Here, for studying of the damage detection in the noisy conditions, the signal to noise ratio (SNR) is defined. This ratio is introduced as the ratio of the power of the input signal without any pollution, to the power of the white noise signal. This ratio is a criterion for comparing the desirability of a signal to the noise and is defined as Eqn.(12) signal db 10 noise p SNR =10log ( ) p (12) where, signal noise P , P are the power of the signal and the power of noise, respectively. The higher values of SNR for a signal indicates the lower contamination of the signal. In this paper, SNR is set to 75, 65 and 55 dB for providing the noisy data. Scenario no. Support condition No. of damaged elements Damage Intensity (%) Order of mode shape in s ignal energy Order of mode shape in wavelet 1 Pined-Pined 20,30,80 5,5,5 1 4 2 Pined-Pined 48,51,54 5,5,5 1 3 3 Pined-Pined 5,95 5,5 3 1 4 Pined-Pined 1,99 5,5 6 1 5 Pined-Pined 20,50,80 10,10,10 1 3 6 Pined-Pined 20,50,80 5,10,15 1 3 7 Clamped-Clamped 10,20,90 5,5,5 5 3 8 Clamped-Clamped 20,23,26 5,5,5 3 3 9 Clamped-Clamped 30,45,80 5,10,15 3 3 Table 2: The proposed scenarios of damage detection on beams without noisy conditions. Results without noisy data In this section, damage detection for multiple- damage detection for pined-pined and clamped-clamped boundary conditions has been presented. For this purpose, several scenarios with and without noisy conditions have been designated. Firstly, the modal data for intact and damaged beams are extracted, and then the discrete wavelet is imposed on the mode shapes using MATLAB functions [18]. Secondly, using Eqn.(4) the coefficients of discrete wavelets are obtained, and employing Eqn.(10), the energy of the signal is obtained. In Tab. 2, the designed scenarios for damage detection without noise on the beams have been presented.