PSI - Issue 28

D.A. Oshmarin et al. / Procedia Structural Integrity 28 (2020) 1438–1448 Author name / Structural Integrity Procedia 00 (2019) 000–000

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made of viscoelastic material the dimensions of which coincide with the dimensions of the plate: vis l l  , vis b b  , vis h h  . The design scheme for this configuration is shown in Figure 1 Consider two options of viscoelastic materials. In the first case their physical and mechanical properties do not depend on frequency. This assumption can be valid within some limited frequency range. The following values of material constants having the form of complex dynamic moduli were chosen for this option of material: Re 671.15 G  MPa, Re 33.33 B  GPa, 0.2 g   , 0.2 b   . The value of specific density of the material is ρ =1200 kg/m 3 . The second option of viscoelastic material is characterized by frequency-dependent components of complex dynamic moduli. Graphical dependences on frequency Re Im Re Im , , , G G B B are shown in Figure 2. Two options of the frequency dependence were considered in order to have the analysis complete: components of complex dynamic moduli increase along with increase in frequency (fig.2a) and components of complex dynamic moduli decrease along with increase in frequency (fig.2b). These options of viscoelastic material are characterized by the value of specific density ρ =1200 kg/m 3

Fig. 1. Scheme of a plate completely covered with a viscoelastic layer. Configuration I.

The damping of structural vibrations in case of configuration II was provided by a mechanism of transformation of a part of mechanical energy into an electric one and its further dissipation as a heat and electromagnetic radiation. For this purpose, a piezoelectric element, electrodes of which connected to an electric circuit was used. Piezoelectric element had a rectangular shape and the following dimensions: 50 pz l  mm, 20 pz b  mm, 0.36 pz h  mm. The material of piezoelectric element is piezoceramics PZT-4 was polarized along the z-axis. Physical and mechanical properties of the piezoceramics were as follows: 10 2 11 22 13.9 10 C C N m    , 10 2 13 23 7.43 10 C C N m    , 10 2 12 7.78 10 C N m   , 10 2 33 11.5 10 C N m   , 10 2 44 55 2.56 10 C C N m    , 10 2 66 3.06 10 C N m   , 2 13 23 5.2 C m      , 2 33 15.2 C m   , 2 51 42 12.7 C m     , 9 11 22 6.45 10 э э F m     , 9 33 5.62 10 э F m    , 3 7500 kg m   . The piezoelectric element was considered perfectly bonded to the plate.