# Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending
## 4 Results
As already pointed-out, the irregular (regular) shape of the loading curve of test 2 (3) is due to the discontinuous (continuous) character of the loading test. As regards to the acoustic emission, the cumulated AE energy graphs in Figure 8 show large jumps in correspondence to criticalities. In particular, Figure 8a (test 2) shows that AEs started near the peak load and afterward exhibited sharp increments near the global snap-backs and the final collapse. Figure 8b (test 3) shows first AEs near about the 90% of the peak load, followed by a large increment in correspondence to the peak load, just before the global snap-back, several increments in correspondence to local instabilities (say, local snap-backs), and a last sharp increment just before the final collapse. Since the pickups captured frequencies corresponding to all possible motions of the beam in space, namely longitudinal, torsional, vertical and lateral bending, and combination of them, a preliminary modal analysis was run to identify the frequencies of interest. A 2-D finite element beam model was therefore implemented in LUSAS software using plane stress elements [40]. Figure 9a shows the first three numerical frequencies of vertical vibration obtained for the unloaded pre-notched beam (i.e., in the stress-free condition) resting on four supports. Figure 7: Test 1: (**a**) collapsed specimen and (**b**) particular of the crack developed near the notch. Figure 9b shows the variation of the first three natural frequencies with the imposed vertical displacement for test 1. The curves show that the eigenfrequencies remained constant during the loading phase almost until the peak load was reached (the corresponding displacement is equal to 0.38 mm; see Figure 5). After, they started decreasing progressively. In particular, the reduction was equal to about 28%, 18%, and 8% for the first, the second, and the third frequency, respectively. This reductions in frequency can be correlated to a decrement of the element stiffness and, therefore, to the crack advancement [41]. As one might have expected, higher frequencies are less influenced than lower ones; thus, in monitoring the damage evolution, experimental frequency identification can be limited to a few lower frequencies. In Figure 10, a correlation between natural frequency variation and AEs is proposed. Figure 10a shows the first three experimental natural frequencies and the cumulated curve of AE energy vs. the vertical displacement. The diagrams clearly show that the natural frequencies decrease while the AE energy increases, i.e., as the damage advances. This also results clear from Figure 10b-d, where the first, second, and third natural frequencies of vertical vibration are plotted against the cumulated AE energy computed from the signals received by the AE sensors (S\({}_{\text{AE1}}\) = wideband sensor, S\({}_{\text{AE2}}\) = resonant sensor). In fact, the larger the amount of energy dissipated and emitted through material damage, the smaller the amount of elastic energy available to be converted into kinetic energy of vibration. The qualitative trends are similar for sensors S\({}_{\text{AE1}}\) and S\({}_{\text{AE2}}\); the only difference is in the quantity of energy registered by the two sensors. It is interesting to note that the natural frequencies decrease discontinuously with the cumulated AE energy (AEs are discontinuous, see Figure 10a). In particular,  
Figure 8: Load and cumulated AE energy vs. displacement diagrams for (**a**) test 2 and (**b**) test 3 (S\({}_{\text{AE1}}\) = wideband sensor). Figure 9: Test 1: (**a**) first three numerical (FEM) bending modes and related frequencies (unloaded beam, initial notch depth) and (**b**) experimental natural frequencies vs. displacement curves. we observe that a certain amount of AE energy must be emitted before initial/new decreases in the natural frequencies can be observed (Figure 10b-d); however, such amount of energy is not a constant.