Issue 49

D. Oshmarin et alii, Frattura ed Integrità Strutturale, 49 (2019) 800-813; DOI: 10.3221/IGF-ESIS.49.13 806 Figure 2 : Relationship surfaces of imaginary parts of complex eigenfrequiencies Im  depending on variation of shunt circuit parameters R and L for the five frequencies under study. It is important to note that although plots of relationship surfaces of damping indices for different complex eigenfrequencies have points and lines of coincidence, numerical results show some difference. This can be explained by the tolerance of setting the optimal parameters of shunting circuit. The more significant digits of R and L values is taken into account the more close to each other the values of imaginary parts are. 1 st frequency 4 th frequency 5 th frequency 12 th frequency 15 th frequency R =4.41 [kOhm], L =3.57 [H] 551.77 + i 1.98 755.40 + i 23.76 791.50 + i 23.58 1296.47 + i 0.71 1486.35 + i 0.76 R =2.45 [kOhm], L =1.19 [H] 553.67 + i 0.45 754.17 + i 1.11 798.66 + i 0.93 1281.48 + i 25.43 1507.57 + i 25.76 Table 2 : Values of complex natural vibration frequencies in the case of parameters of the external circuit that provide maximal and close to each other values of imaginary parts. Tab. 2 shows the R and L values at which pairs of 4th and 5th frequencies and 12th and 15th frequencies have maximal and almost coincident values of imaginary parts. It also shows the corresponding complex natural vibration frequencies for the five modes under study. The frequencies having maximal imaginary parts, that are very close to each other in magnitude, are highlighted in bold. A comparison of the imaginary parts presented in Tabs. 1 and 2 allows us to make a conclusion about the possibility of damping two frequencies using one single piezoelectric element shunted with one single series resonant RL circuit with its parameters selected in the appropriate way. At the same time, the damping indices Im  for 4th/5th and 12th/15th frequencies are lower than those at shunt circuit tuning for single-mode damping, which provides the maximal the decay rate of vibrations for one single mode (see Tab.