Abstract
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.
Highlights
The idea of using piezoelectric elements with connected external electric circuits to damp the vibrations of mechanical structures has proved highly efficient and attractive, especially for engineering applications with strict size and weight limits
For the selecting of the parameters of the shunt circuit that provide multimodal damping of vibrations for the corresponding piezoelectric element location an approach is proposed. 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
One can distinguish the following basic approaches to multimodal damping: – the employment of one piezoelectric element and a complex external circuit in which the possibility of damping several modes of vibrations is realized in one way or another [4,5,6,7,8,9,10,11,12,13,14,15]; – the usage of several piezoelectric elements forming an integrated network and connected by one or another method to a single external circuit [16,17,18,19,20,21,22]; – the usage of several piezoelectric elements, each having its own electrical circuit that is not coupled with others to form a joint circuit [23,24,25,26,27]
Summary
The idea of using piezoelectric elements with connected external electric circuits to damp the vibrations of mechanical structures has proved highly efficient and attractive, especially for engineering applications with strict size (miniaturization) and weight (elements of space and aircraft facilities) limits. 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.
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