PSI - Issue 44

Elena Michelini et al. / Procedia Structural Integrity 44 (2023) 1530–1537 Elena Michelini et al / Structural Integrity Procedia 00 (2022) 000 – 000

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iterative procedure stops when a better agreement between numerical and AVT results is achieved. Table 3. Modal properties obtained from the initial FE analysis. Mode f num,0 [Hz] M x num,0 [%] M y num,0 [%] f AVG [Hz]   f 0  [%] 1 3.81 0.76 60.83 3.38 12.71 2 3.90 68.56 0.54 3.55 9.85 3 4.49 0.85 3.49 4.08 9.99 4 4.97 1.27 0.00 4.44 11.93 5 5.54 0.52 1.65 5.24 5.81

1 st mode

2 nd mode

3 rd mode

4 th mode

5 th mode

Fig. 6. Numerical mode shapes from the initial FE model.

The best agreement was obtained by considering different values of the elastic modulus in X and Y directions, through a progressive reduction of the stiffness in the X direction until obtaining an inversion of the first two translational modes. The results summarized in Table 4 and Fig. 7 were obtained by applying a reduction of 12.5% (so having E X = 1979 MPa and E Y = 2262 MPa, which are both within the range suggested by the Italian Code for the considered masonry). A better agreement on frequencies was further obtained by applying to both E X and E Y a calibration coefficient calculated as the square of the ratio of the first mode periods respectively derived from the numerical model and from the AVT, equal to C = 0.83. These latter results are summarized in the last two columns of Table 4 (f num,2 ). Table 4. Modal properties obtained from the calibrated FE analysis. Mode f num,1 [Hz] M x num,1 [%] M y num,1 [%] f AVG [Hz]   f 1  [%] f num,2   f 2  [%] 1 3.71 66.77 2.96 3.38 9.73 3.38 0.04 2 3.75 3.08 56.88 3.55 5.72 3.42 3.57 3 4.37 0.85 4.33 4.08 7.07 3.98 2.38 4 4.81 1.14 0.00 4.44 8.27 4.38 1.27 5 5.39 0.47 1.98 5.24 2.94 4.92 6.10

Fig. 7. Numerical mode shapes from the calibrated FE model.