Multimodal vibration damping of a plate by piezoelectric coupling to its analogous electrical network

Abstract

Multimodal damping can be achieved by coupling a mechanical structure to an electrical network exhibiting similar modal properties. Focusing on a plate, a new topology for such an electrical analogue is found from a finite difference approximation of the Kirchhoff-Love theory and the use of the direct electromechanical analogy. Discrete models based on element dynamic stiffness matrices are proposed to simulate square plate unit cells coupled to their electrical analogues through two-dimensional piezoelectric transducers. A setup made of a clamped plate covered with an array of piezoelectric patches is built in order to validate the control strategy and the numerical models. The analogous electrical network is implemented with passive components as inductors, transformers and the inherent capacitance of the piezoelectric patches. The effect of the piezoelectric coupling on the dynamics of the clamped plate is significant as it creates the equivalent of a multimodal tuned mass damping. An adequate tuning of the network then yields a broadband vibration reduction. In the end, the use of an analogous electrical network appears as an efficient solution for the multimodal control of a plate.

Damping of piezoelectric space instruments: application to an active optics deformable mirror

“…It is also possible to organize the piezoelectric patches with a more elaborated multi-degree of freedom circuit, in such a way that the "electrical" resonance frequencies and mode shapes match several targeted structural modes, see e.g. [29] and [30]; in this case, several inductors are required.…”

Design of inductors with high inductance values for resonant piezoelectric damping

“…6(a) is usually non-negligible for piezoelectric shunt applications involving high permeability cores [24]. We thus need to ensureR (ω) ≤ R, (25) and the shunt can then be tuned by adding an external resistor R + s . The parallel resistance R p may be difficult to evaluate as it depends on the core material, on the frequency and on the flux density.…”

“…The condition in Eq. (25) necessarily induces that R s ≤ R. Then, Eqs. (22), (23) and (24) leads to the definition of a criterion…”

“…The use of closed magnetic circuits with high permeability materials thus enables the design of inductors with large inductance values and high quality factors [23]. This allows the application of piezoelectric damping strategies with purely passive components [24,25]. The main objective of this paper is to show that resonant piezoelectric damping can be implemented with passive inductors.…”

Passive Damping of Rotationally Periodic Structures with Tuned Piezoelectric Inductive Shunt

“…The RL-shunt involves a set of resistors and inductors, and the electrical network is tuned to the targeted mode. Damping several modes simultaneously is possible [9,10]. The performances are superior to the R-shunt, but the electrical network needs accurate tuning of the electrical frequency on the targeted mode(s); it does not damp the other modes and, for the targeted ones, it is very sensitive to the variation in natural frequencies.…”