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. / Structural Integrity Procedia 00 (2021) 000 – 000

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The properties of a viscoelastic material are set via real parts of complex dynamic moduli and corresponding tangents of mechanical losses: Re 750 G  MPa, 4 Re 3.725 10 B   MPa, 0.2 g   , 0 b   . Sincethefactthatweconsiderdampingofvibrationsat separate modes (single-mode damping) all calculations were performed in the vicinity of each natural vibration frequency. Regardingthisin current research we use the assumption that the values of complex dynamic moduli are constant within the whole frequency range under consideration. Specificdensityoftheviscoelastic material is 1200   kg/m 3 . Dimensions of the plate were chosen as: length 210 l  mm, width 26 b  .mm. Thecurrentresearchconsidersthecaseinwhichviscoelasticelement completely covers the surface of the plate, i.e., dimensions of a viscoelastic layer are equal to: 210 vis l l   mm, 26 vis b b   mm. Thicknesses of the plate h and the viscoelastic layer vis h are equal to 0.6 vis h h   mm. Arectangularpiezoelectricelementhavingthedimensions pz l = 50 mm, pz b = 20 mm, pz h = 0.36 mm is attached to the surface of the plate. ThepiezoelectricelementismadeofPZT-4 piezoceramics and polarized along Z-axis (fig.1). Physicalandmechanicalpropertiesofpiezoelectricelement were set as follows: 10 11 22 13.9 10 Pa C C    , 10 13 23 7.43 10 Pa C C    , 10 12 7.78 10 Pa C   , 10 33 11.5 10 Pa C   , 10 44 55 2.56 10 Pa C C    , 10 66 3.06 10 Pa C   , 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   . First, we establish how the connection of a resistive electric circuit (R-circuit) to the piezoelectric element affects the dissipative properties of the electro-viscoelastic structure under study. Considertwooptionsofmutualarrangementof viscoelastic and piezoelectric elements in relation to each other: option 1 – elements are located at opposite sides of the plate, option 2 – piezoelectric element located over the viscoelastic element. Here we also consider two options of location of piezoelectric element in relation to the plate: option A – nearby the clamped edge, option B – in the middle of the plate. Theschematicsofalloptionsare represented at figure 2. The elastic plate is colored in blue, the viscoelastic layer is colored in yellow and the piezoelectric element is colored red. Accordingtotheschematicsatfig.2 the following designations of possible combination of location of piezoelectric element in relation to the plate and to the viscoelastic layer were introduced: A1, B1, A2, B2. Thehighestvalues of dissipative properties of the structure can be reached by a complete coverage of the plate surface with the layer of maximal thickness conditioned by structural restrictions. Inotherwords,inthiscase, we obtain a two-layered plate with layers that are equal in thickness. Hereoneofthe layers made of an elastic material, and the second one made of a viscoelastic material.

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Fig.2. Computational schemes of the structure with the viscoelastic element and the piezoelectric element shunted with electric circuit having the total impedance Z: (a) Location of the piezoelectric element A Option 1 (A1); (b) Location of the piezoelectric element B Option 1 (B1); (c) Location of the piezoelectric element A Option 2 (A2); (d) Location of the piezoelectric element B Option 2 (B2) If shunted piezoelectric elements are used for damping of structural vibrations its location in structure is the matter of utmost importance. Herewiththebestlocationofpiezoelectricelementfor damping of vibrations at i -th mode as a rule is not as good for damping of vibrations at other modes. From the one hand covering a structure with a viscoelastic layer is claimed to damp vibrations at all modes within the frequency range under consideration