Issue 49

D. Oshmarin et alii, Frattura ed Integrità Strutturale, 49 (2019) 800-813; DOI: 10.3221/IGF-ESIS.49.13 809 To illustrate that the possibility of damping properties of a structure with piezoelectric element increases while using a single resonant circuit, Fig. 5 shows the frequency response amplitudes of displacement vector component r U at point A when the system is excited by harmonic force r P applied at point B (Fig. 1b). The results shown were obtained for shunt circuit tuning for single-mode damping at 4th, 5th, 12th and 15th frequencies and for shunt circuit tuning according to the last row of Tab. 3 that provides damping properties increase for all four frequencies (4th, 5th, 12th, 15th). Figure 5 : Frequency response amplitudes for the displacement vector component r U at point A of the shell (Fig. 1b) at shunt circuit tuning for maximal damping 4th (blue line), 5th (red line), 12th (green line) and 15th (violet line) modes separately and at shunt circuit tuning for multimodal damping of all these (4th, 5th, 12th, 15th) modes (black line). D EFINITION OF SHUNT CIRCUIT PARAMETERS FOR DAMPING STRUCTURAL VIBRATIONS AT ALL THE FREQUENCIES IN THE SPECIFIED FREQUENCY RANGE he previous section demonstrated the possibility of damping vibrations for an electromechanical system at several separate frequencies within the specified frequency range using the same parameters as for shunt circuit elements. However, in technical applications it is conventionally necessary to ensure the damping of structural vibrations at all the frequencies within the specified frequency range. Within the framework of the problem under study, this can be achieved if the particular location of the piezoelectric element can be found at which electric potential takes eligible values for its reliant operation at all of the frequencies within the specified frequency range. The searching procedure of optimal location for piezoelectric element that provides possibility of multimodal vibration damping within specified frequency range was presented in [37]. Number of frequency Shell eigenfrequencies without electric circuit f [Hz] Shunt circuit optimal parameters for single-mode damping R [kOhm], L [H], Complex eigenfrequencies of the shell with tuned shunt circuit Re Im f f if   1 557.41 R =5434.43, L =6.57 554.26 + i 21.36 2 587.68 R =5204.20, L =6.32 586.81 + i 17.60 3 620.20 R =5954.96, L =5.69 636.32 + i 33.12 Table 4 : Natural vibration frequencies for the shell with piezoelectric element and no electric circuit and with electric circuit tuned to a single frequency. The object of the study remains the same: the shell presented in Fig. 1. The goal of the simulations is to provide damping of all the frequencies within the range 500–700 Hz while using the same technical devices: a single piezoelectric element and a single resonant series RL circuit. In this case, the piezoelectric element must be placed so that its centre of mass is offset from the clamped edges at 150 mm and is at a 30.2 о angle from the free-supported generatrix. Then in the frequency range 500–700 Hz, there will be three natural vibration frequencies at which the piezoelectric element generates sufficient electric potential. By analogy with previous calculations, Tab. 4 shows the natural vibration frequencies of the T