An approach to determination of shunt circuits parameters for damping vibrations

Figures & data

Figure 1. Elements of an external electrical circuit: (a) – resistance (), (b) – capacitance (), (c) inductance ().

Figure 2. Calculation schemes of structures with a piezoelectric element: (a) plate; (b) shell.

Figure 3. Surfaces of the real part of the first complex eigenfrequency (blue) and the frequency of the electrical circuit oscillations (red) for the plate (a) and shell (c) and the projections of their coincidence lines for the plate (b) and shell (d).

Figure 4. Surfaces of dependence of the imaginary parts of the first complex eigenfrequency of the structure (colored) and the integrated complex frequency of oscillatory circuit (gray) on the and parameters of the external circuit for the plate (a) and the shell (b).

Figure 5. Surfaces of dependence of the imaginary part of the first complex eigenfrequency of the structure on the and parameters of the external circuit for the plate (a) and the shell (b).

Table 1. The results of definition of optimal parameters of shunt circuit and for two vibration modes of the plate and the shell on the basis of formulas (20) and condition (17).

			Calculations by formulas (20)			Calculations by condition (17)
Mode	,	,
number		nF
Plate
1	13.58	11.27		13.85 1.33	0.098		13.80 1.42	0.104
	13.86			13.71 1.53	0.113		13.77 1.44	0.106
2	72.15	11.71		71.55 1.66	0.023		72.42 2.60	0.036
	72.33			73.78 3.40	0.047		72.15 2.60	0.036
Shell
1	554.25	11.31		564.42 18.78	0.034		556.84 26.01	0.047
	557.41			541.30 38.08	0.069		556.72 32.50	0.059
4	755.77	11.33		771.95 9.88	0.013		767.09 29.83	0.039
	759.57			721.16 45.06	0.017		767.50 35.17	0.046