In this paper, an approach is proposed that allows for the selecting of the parameters of the shunt circuit that provide multimodal damping of vibrations for the corresponding piezoelectric element location. This technique is based on a solution to the natural vibration problem for an electroelastic structure with an attached piezoelectric element that is shunted with a single external resonant electric circuit. The solution to the problem is complex natural vibration frequencies. The analysis of their behaviour in the space of external circuit parameters (resistance – inductance) allows one to reveal the possibility of natural vibrations control at several frequencies (multimodal vibration damping). The applicability of the proposed approach is demonstrated using a shell structure in the form of a semi-cylinder with a piezoelectric element attached to its surface and shunted with a single-branched resonant electric circuit. Some options are considered that provide multimodal damping at several separated frequencies, which are not from the complete frequency range, and at all the frequencies, which are included in a specified frequency range.
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