Issue 46

I. Shardakov et alii, Frattura ed Integrità Strutturale, 46 (2018) 383-390; DOI: 10.3221/IGF-ESIS.46.35 386  The main geometric characteristics of the model structure: column space is 2 m; height of the floor is 1.5 m; cross section of the column is 200 × 200 mm; cross-section of the cross beam is 200 × 250 mm; thickness of the slab is 150 mm; diameter of the reinforcement of columns and lower chords of cross beams is 12 mm, diameter of the other reinforcement is 8 mm.  Physical characteristics of concrete:   0.102 ;  17.2 G GPa;     7 3.46 10 ;   2507 kg/ m 3 .  Physical characteristics of steel:   0.3 ;  76.9 G GPa;   0 ;   7800 kg/ m 3 .  Characteristic dimension of the finite element mesh: 0.1 m.  Integration time step: 10 –5 s. V ERIFICATION OF THE MATHEMATICAL MODEL BASED ON EXPERIMENTAL RESULTS o verify the mathematical model, we performed a series of experiments, in which the dynamic deformation response of the structure to a locally applied external impulse force was analyzed. We used three loading schemes, of which two involved impact loading of the column and the registration of the deformation response to this impact at different points of the columns (Fig.3, a, b) and the third (Fig. 3, c) provided impact load of the lower edge of the floor slab and the registration of the response at its upper edge. Locations of the sensors recording the response of the structure to the externally applied impact loads are indicated by the red dots in the figures. These sensors recorded the vector component of acceleration directed along the normal to the surface, at which the sensors were located. Fig. 3 presents the fragments of the general model structure shown in Figs. 1 and 2c. These are the fragments in which the deformation response to the impact action was analyzed. The sizes of the selected fragments of the structure were chosen in such a way that at the points of recording the deformation responses there are no waves reflected from the boundaries of the fragment within the time interval under consideration. The external impulse force was generated by a striker with a mass of 460 g. The value of acceleration W ( t ), resulting from the impact of the striker on the surface of the structure, was recorded by an accelerometer ZetLab BC111 fixed to the striker. The range of recorded frequencies of this accelerometer is 0.5-15000 Hz. The deformation response of the structure to the impulse force was registered by the ZetLab BC110 accelerometers, fixed at various points of the structure (the range of recorded frequencies is 0.5–10000 Hz). Transformation of the collected sensor data to a digital form was performed synchronously using the ADC ZET 017-U8 with a frequency of 50 kHz. (a) (b) (c) Figure 3: Schemes of loading and registration of response. As an example, Fig. 4 shows the experimentally measured shape of the force impulse and the corresponding Fourier image (load diagram is given in Fig. 3a). As follows from these data, the impulse duration is 0.28 ms, and the main part of impulse energy is localized in the frequency range of 0-5 kHz. It should be noted that the experimentally recorded value of the force impulse was used in the mathematical model (1) - (5) to specify the boundary condition (4). Then, the results of numerical simulation were compared with experimental data obtained from accelerometers recording the deformation responses to impact. When making a comparison, the calculated and experimental data were subjected to frequency filtering, ensuring the removal of the signal at frequencies above 6 kHz. Fig. 5 shows a series of vibrograms and the corresponding Fourier images for three loading schemes (a, b, c) presented in Fig. 3. The experimental data are indicated by blue lines and the simulation data - by red lines. A comparison of the results obtained demonstrates good agreement between the model and the experiment in the frequency range from 0 to 6kHz. T