PSI - Issue 50

D.A. Oshmarin et al. / Procedia Structural Integrity 50 (2023) 212–219 Oshmarin D.A., Iurlova N.A., Sevodina N.V. / Structural Integrity Procedia 00 (2019) 000 – 000

219

8

5 var1 1.531 10 u   

According to the obtained results, maximal values of mechanical response are equal to

and

6 for the schemes represented at fig.4a and fig 4b correspondingly. Based on the relations represented in table 2 optimal values of potential difference and current amperage were calculated as 1 var1 1.895 10 opt U    V; 7 var1 1.007 10 opt I    A; 2 var 2 3.046 10 opt U    V; 8 var 2 1.618 10 opt I    A for the corresponding values of the mechanical response. Next for these values of electric loading we obtained FRPs for cases when two loading factors (force and electric load) act simultaneous. In order to demonstrate optimality of the calculated values opt U and opt I two additional series of calculations were performed. For these calculations the following (non optimal) values of voltage and amperage were chosen 1 1 var1 1 10 no U    V; 1 7 var1 0.5 10 no I    A; 1 2 var 2 2 10 no U    V; 1 8 var 2 1 10 no I    A; 2 1 var1 3 10 no U    V; 2 7 var1 1.5 10 no I    A; 2 2 var 2 4 10 no U    V; 2 8 var 2 2 10 no I    A. All options of combination of loading factors represented in table 2. Figure 5 shows the FRPS for all variants of combinations of loading factors presented in Table 3. The black dashed line in Figure 5 indicates the frequency response for the I variant of combinations of load values, the blue solid line for the II variant, the red dashed line for the III variant, the green dashed line for the IV variant. The results shown in Fig.5 confirm the fact that the values of the optimal parameters obtained on the basis of the ratios given in Table 2 are indeed optimal, since they provide the minimum amplitude of forced steady-state vibrations among all the considered combinations of loading factors. Thus, the proposed method really makes it possible to determine the optimal values of the parameters of the control electrical impact, at which the minimum amplitude of the forced steady-state vibrations of the system is achieved. 5. Conclusions In current research, on the basis of solving the problem of forced steady-state vibrations of piecewise homogeneous electro-viscoelastic bodies, the influence of the magnitude of the applied mechanical or electrical impact, as well as their combination on the mechanical response of a structure, was investigated. Numerical results obtained for the example of a cantilever plate with a piezoelectric element attached to its surface, shown that the magnitude of its mechanical response can be controlled quite effectively only with the combined action of mechanical and electrical loads. It is established that the resulting mechanical response of the structure in case of simultaneous action of two loading factors is an algebraic sum of mechanical responses to the action of each of the factors separately. An approach has been proposed for determining the parameters of the control electrical impact, which allows achieving a minimum level of mechanical response of a plate under forced steady-state vibrations in case of excitation by a mechanical load. The results obtained in the framework of this study can be the basis for the development of algorithms for solving problems of controlling the dynamic behavior of electro-viscoelastic structures. Acknowledgements The reported study was funded by RFBR and Perm region accordin g to the project № 19 -41-590007-r_a. References Iurlova N.A., Oshmarin D.A., Sevodina N.V., Iurlov M.A., 2019. Algorithm for solving problems related to the natural vibrations of electro viscoelastic structures with shunt circuits using ANSYS data. International Journal of Smart and Nano Materials, 10 (2), 156-176 Kligman, E.P., Matveenko, V.P., 1997. Natural Vibration Problem of Viscoelastic Solids as Applied to Optimization of Dissipative properties of Constructions. International Journal of Vibration and Control, 3(1), 87-102. Tani J., Takagi T., Qiu J., 1998. Intelligent Material Systems: Application of Functional Materials. Applied Mechanics Reviews, 51(8), 505-521 Ayres J.W., Lalande F., Rogers C.A., Chaudhry Z., 1996. Qualitative health monitoring of a steel bridge joint via piezoelectric actuator/sensor patches. SPIE Nondestructive Evaluation Techniques for Aging Infrastructure & Manufacturing, AZ 8р. Fuller C.R., Elliot S.J., Nelson P.A., 1997. Active Control of Vibration, Academic Press, London Preumont A., 2011. Vibration Control of Active Structures: An Introduction (3rd ed.), Springer-Verlag, Berlin. var 2 2.466 10 u   