Issue 49

D. Oshmarin et alii, Frattura ed Integrità Strutturale, 49 (2019) 800-813; DOI: 10.3221/IGF-ESIS.49.13 808 because although imaginary parts of these frequencies are close to each other, their magnitudes are very low in comparison with other possible options. Figure 4 : Projections of imaginary parts of complex eigenfrequencies coincidence lines in the R-L parameters space that have points of intersection. The number of eigenfrequence 1 4 5 12 15 I R =5.77 [kOhm], L =2.14 [H] 553.34 + i 1.36 753.82 + i 4.41 797.98 + i 3.75 1298.61 + i 4.12 1489.72 + i 4.06 II R =5.72 [kOhm], L =2.21 [H] 553.28 + i 1.38 753.70 + i 4.65 797.84 + i 3.95 1298.54 + i 3.73 1489.49 + i 3.68 III R =2.94 [kOhm], L =2.88 [H] 552.30 + i 1.01 747.78 + i 7.20 792.75 + i 5.17 1297.78 + i 0.96 1487.89 + i 0.95 IV R =13.99 [kOhm], L =2.42 [H] 554.65 + i 2.39 757.92 + i 4.10 801.76 + i 4.09 1295.43 + i 2.10 1485.87 + i 3.90 V R =5.75 [kOhm], L =2.20 [H] 553.30 + i 1.39 753.73 + i 4.64 797.86 + i 3.94 1298.53 + i 3.76 1489.49 + i 3.71 Table 3 : Parameters R and L of electric circuit at which imaginary parts are very close to each other for more than two frequencies and their corresponding complex eigenfrequencie. The last row of Tab. 3 (for the point V, see fig.4) gives the complex frequency values that correspond to the circuit parameters selected from the interval constrained by R and L values obtained for groups I and II (points I and II, see fig.4). The results presented in this row show considerably high and comparable values of imaginary parts for the frequencies from the groups mentioned above. This allows us to conclude that appreciable damping of vibrations may be possible at four frequencies (4th, 5th, 12th, 15th) with the aid of one single piezoelectric element shunted with one single series resonant RL circuit if the circuit element parameters are R =5.75 kOhm и L =2.20 H.