PSI - Issue 54

J.V. Araújo dos Santos et al. / Procedia Structural Integrity 54 (2024) 575–584 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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in Equation (3.1) can be collected to obtain a directional independent parameter, such as ‖ ( ) ‖ 2 ( , ) = [ ( 2 ) ( , ) + ( 2 ) ( , ) + ( 2 ) ( , )] 1/2 where ‖ ( ) ‖ 2 ( , ) is the Euclidean norm of the strain vector ( ) . The procedure to evaluate the modal strains and their norm in order to identify the damage in a plate from a noisy full data set of modal displacements ( (n ) ) ( , ) consists of seven steps, involving smoothing, differentiation, and computation of the three modal strains and their norm: 1. Smooth the noisy full data set ( (n ) ) ( , ) with a moving window defined by setting ( 0 − , 0 − )= ( (n ) ) ( , ) in Eq. (2.16) to obtain the smoothed full data set ( (s ) ) ( , ) ; 2. Differentiate the full data set ( (s ) ) ( , ) with moving windows defined by setting ( 0 − , 0 − )= ( (s ) ) ( , ) (Δ ) 2 ⁄ , =2 ; ( 0 − , 0 − )= ( (s ) ) ( , ) (Δ ) 2 ⁄ =2 ; and ( 0 − , 0 − )= ( (s ) ) ( , )⁄(Δ Δ ), =1 , =1 ; in Equations (2.17), (2.18), and (2.19) to obtain the full data sets 2 ( (d ) ) ( , ) 2 ⁄ , 2 ( (d ) ) ( , ) 2 ⁄ , and 2 ( (d ) ) ( , ) ⁄ , respectively; 3. Smooth the full data sets 2 ( (d ) ) ( , ) 2 ⁄ , 2 ( (d ) ) ( , ) 2 ⁄ , and 2 ( (d ) ) ( , ) ⁄ with moving windows defined by setting ( 0 − , 0 − )= 2 ( (d ) ) ( , ) 2 ⁄ , ( 0 − , 0 − )= 2 ( (d ) ) ( , ) 2 ⁄ , and ( 0 − , 0 − )= 2 ( (d ) ) ( , ) ⁄ , respectively, in Eq. (2.16) to obtain the smoothed full data sets 2 ( (s ) ) ( , ) 2 ⁄ , 2 ( (s ) ) ( , ) 2 ⁄ , and 2 ( (s ) ) ( , ) ⁄ ; 4. Compute ( ) ( , ) , ( ) ( , ) , ( ) ( , ) according to Eq. (3.1); 5. Smooth the full data sets ( ) ( , ) , ( ) ( , ) , ( ) ( , ) by setting ( 0 − , 0 − )= ( ) ( , ) , ( 0 − , 0 − )= ( ) ( , ) , ( 0 − , 0 − )= ( ) ( , ) , respectively, in Eq. (2.16) ) to obtain the smoothed full data sets (s)( ) ( , ) , (s)( ) ( , ) , (s)( ) ( , ) ; 6. Compute ‖ ( ) ‖ 2 ( , ) according to Eq. (3.2); 7. Smooth the full data set ‖ ( ) ‖ 2 ( , ) by setting ( 0 − , 0 − )=‖ ( ) ‖ 2 ( , ) in Eq. (2.16) to obtain the smoothed full data set ‖ ( ) ‖ 2 (s) ( , ) . 4. Results 4.1. Damage Scenarios and Cases A plate of aluminum with a Young’s modulus of 67 GPa, Poisson ratio of 0.3 and mass density 2700 kg/m 3 is analyzed in this study. The plate has an in-plane area of 300 x 300 mm 2 and a thickness of 3 mm. The simulations of damage consisted in reducing the plate thickness to create slots with different geometries in several locations. The set of three damage scenarios studied is described in Figure 4.1. Scenario 1 and 2 refers to single damage, being the former a very localized damage (square slot) and the latter a rather extensive damage in one direction (rectangular

(3.2)