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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It is also interesting to note that in case of applying of RL -circuit the character of distribution of level of damping along the spectrum qualitatively corresponds to the option when damping is achieved by application of viscoelastic material with complex dynamic moduli having the components which decrease along with increase in frequency. If we look at the magnitude of the shift of natural vibration frequencies in case when shunted piezoelectric elements are used, we see that it does not exceed 30% at the first vibration mode. The shift of values of natural vibration frequencies for all other modes does not exceed 10%. It is interesting to note that in the case of using the RL -circuit, the nature of the distribution of the degree of damping over the spectrum qualitatively corresponds to the option in which damping is carried out by using a viscoelastic material, the components of the complex modules of which decrease with increasing frequency. As for the magnitude of the shift of natural vibration frequencies observed when using shunted piezoelectric elements, in this case it does not exceed 30% in the first vibration mode. For the rest of the modes, the shift in the values of natural vibration frequencies does not exceed 10%. 4. Conclusions Now let us resume what we finally derived from the carried-out research. On the basis of the problem of natural vibrations for electro-viscoelastic bodies with passive electrical circuits it was shown that equipping an original structure with a viscoelastic layer and shunted piezoelectric element allows controlling damping properties of an electro-viscoelastic system. A comparative analysis of the effectiveness of application of two considered approaches to damping of vibrations at the specified modes performed on the basis of the cantilever plate allowed resuming that using piezoelectric elements shunted with resonant RL -circuits showed the highest efficiency among all the considered options. Application of piezoelectric elements shunted with RL -circuits apart of providing higher damping properties in comparison to other variants also showed the least influence on mass and size of the structure and much less distorted the original spectrum of natural vibration frequencies. However, the conventional approach related to using of viscoelastic materials has an important advantage which can be a decision-making factor in case of choosing mechanism of damping of structural vibrations for practical applications. Covering a structure with viscoelastic layer provides in more or less degree, realization of damping of vibrations at all vibration modes from the considered frequency range. In turn, an application of shunted piezoelectric elements requires accuracy in choosing vibration mode to be damped since this choice determines its location on a structure and also magnitude of values of parameters of electric circuit. The use of a piezoelectric element shunted by an external electrical circuit requires careful attention to which vibration mode is planned to be damped, since both its location on the structure and the value of the parameters of the external electrical circuit depend on this. The following conclusion can be drawn as a result of the comparative analysis of the presented approaches to damping of vibrations. If damping of individual vibration modes is required, then it is more efficient to use piezoelectric elements, to the electroded surfaces of which external electrical circuits are connected. If it is necessary to damp vibration modes that are realized in a certain frequency range, then the use of viscoelastic materials is preferable. In this case, it is necessary to take into account the properties of the viscoelastic material itself, in particular, the frequency dependence of its mechanical characteristics. Acknowledgements The reported study was funded by RFBR according to the research project No. 19-01-00158-a. References

Bachmann, F., Bergamini, A.E., Ermanni, P., 2012. Optimal piezoelectric positioning a strain-energy based finite element approach. Journal of Intelligent Material Systems and Structures, 23(14), 1575–1591.