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

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vibrations; stat u is a value of component z u of displacement vector at the free end of the plate under static loading   0,0,1 F  N, applied to its free end.

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b

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Fig. 2. Relations between values of mechanical response and loading factors for (a) clamp movement, (b) force, (c) potential difference, (d) current

The results shown in Fig.2 correspond to the linear formulation of the problem and are well-known. However, the impact of two loading factors on the system simultaneously opens up the possibility of controlling the mechanical response of the system. In particular, by changing the angle of phase shift α between the operating loads. Since harmonic vibrations of the structure are considered, the greatest effect of the second loading factor is achieved in two cases: 0   (loads act in phase) and 180   (loads act in opposite phase). In the first case, it is assumed to observe an increase in the level of mechanical response, and in the second – a decrease. Due to the linearity of the mathematical formulation used, we expect that the resulting value of the mechanical response will be the sum of the values of the mechanical response from the action of each of the loading factors. Based on this assumption, we believe that the minimum oscillation amplitude will be observed in the case when the value of the control electrical signal cont U or cont I will provide the value of the amplitude     cont cont targ u U u I u   , which is realized under the action of a mechanical load. Thus, to determine the optimal characteristics of the control electrical signal, it is sufficient to know how the amplitude of the forced vibrations u depends on the magnitude of the electrical loading. Having dependencies   cont u U and   cont u I regardless its form (analytical, graphical, tabular, etc.), it is possible to obtain inverse dependencies, i.e. the dependences of the optimal values of the control signal on the magnitude of the mechanical response   cont U u and   cont I u . Using the inverse dependencies   cont U u and   cont I u , it is possible to determine the value of the optimal parameters of the control electrical signal to obtain targ u . Based on the results obtained earlier (Fig.2) the relations between the magnitude of the potential difference and the current and the magnitude of the mechanical response of the plate were determined. The plots of these relations for the three vibration modes under consideration are presented in logarithmic coordinates in Fig.3. The blue color