PSI - Issue 32

D.A. Oshmarin et al. / Procedia Structural Integrity 32 (2021) 158–165 Oshmarin D.A., Iurlova N.A., Sevodina N.V., Iurlov M.A. / StructuralIntegrity Procedia 00 (2021) 000 – 000

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(although the efficiency of damping depends on the certain mode). Butfromtheotherhandapplicationofpiezoelectric elements shunted with external electric circuits is as a rule aimed to damping vibrations at one single mode which an external circuit is tuned on. ConsideraresistiveR-circuit (madeofonlyoneresistive element) as an external circuit that shunts piezoelectric element and provides damping of vibrations at the specified modes. Thepreviouslymadeinvestigationsdemonstratedthatthehighest damping effect from application of a viscoelastic material is achieved at bending modes of vibrations (Mead, 1999; Nashif et.al., 1985; Stanway et al., 2003). Taking intoaccountthefactthat the use of shunted piezoelectric elements allows achieving the best damping only at one single mode all further investigations were carried out at the example of the first two modes of vibrations. The piezoelectric element is located at the surface of the plate as so as to provide the best damping of vibrations at the first or the second bending mode of vibrations. Despite the fact that we are interested in damping of vibrations only at one specified mode we also watch the changes in damping coefficient for the other mode. Since the viscoelastic layer completely covers the surface of the plate the locations of the piezoelectric element providing the best damping at the specified mode coincide with ones determined for the elastic plate without a viscoelastic layer. Thefurther calculations were done for all four schemes represented at figure 2. Thus, we expect that the presence of a piezoelectric element shunted with a corresponding electric circuit will increase the level of damping provided by a viscoelastic layer for the mode under consideration.Theobjective of the current study is in checking out of this assumption and also in evaluating the increase in the level of damping. Andherethequestionis whether a resulting value of damping coefficient is a sum of contribution of each mechanism of energy dissipation or not. Itisalsointerestingtoknowwhetherthiseffect expands to other vibration modes. Consider the influence of shunting the piezoelectric element with a resistive circuit made only of a resistor. Inthiscaseelectricimpedance (complex resistance)oftheexternal circuit is Z=R . Table 1. Values of damping characteristics of two vibration modes under consideration for optimal configurations of the electro-viscoelastic system with a resistive circuit

Presence of an element Piezo Visco R-circuit

-2

R , kΩ

Scheme

ω Re

ω Im

ξ·10

-

+ + +

- - -

1.254

11.223 0.141

+ + + +

0 (s/c)

15.265 0.193 1.724

A1

∞ (o/c) 15.434 0.201 1.788

-

+ +

950 900

13.530 0.131 1.168

+

2.525

15.363 0.284

-

+ + +

- - -

1.258

70.263 0.886

+ + + +

0 (s/c)

85.310 1.076 1.529

A2

∞ (o/c) 86.142 1.112 1.580

-

+ +

200 130

76.200 0.679 0.965

+

2.513

85.706 1.516

-

+ + +

- - -

1.254

-

11.223 0.141

+ + + +

0 (s/c)

13.403 0.142 1.266

B1

∞ (o/c) 13.683 0.145 1.290

-

+ +

950

13.530 0.131 1.168

+

2.519

1100

13.549 0.283

-

+

-

1.258

B2

-

70.263 0.886