Modal-based synthesis of passive electrical networks for multimodal piezoelectric damping

Abstract

This work presents a new approach to design an electrical network which, when coupled to a structure through an array of piezoelectric transducers, provides multimodal vibration mitigation. The characteristics of the network are specified in terms of modal properties. On the one hand, the electrical resonance frequencies are chosen to be close to those of the targeted set of structural modes. On the other hand, the electrical mode shapes are selected to maximize the electromechanical coupling between the mechanical and electrical modes while guaranteeing the passivity of the network. The effectiveness of this modal-based synthesis is demonstrated using a free-free beam and a fully clamped plate.

Figures (14)

• Figure 1: Schematic representation of the electromechanical system \ref{['sfig:sdof_schematics']} and FRF of the structure \ref{['sfig:sdof_FRF']} when the electrodes of the transducer are short-circuited (---) and when they are connected to a parallel RL shunt circuit (---: $K_c=0.01$, ---: $K_c=0.05$, ---: $K_c=0.1$).
• Figure 2: Schematic of a structure (in gray) with multiple piezoelectric transducers (in orange) connected to an electrical network.
• Figure 3: Flowchart of the proposed modal-based synthesis.
• Figure 4: Velocity FRF of the beam with short-circuited patches (---), with the network synthesized with the modal-based approach (---).
• Figure 5: Velocity FRF of the beam with grouped patches connected to a network synthesized with the modal-based approach: $[\overline{d}_{p,1}, \overline{d}_{p,2} ,\overline{d}_{p,3} ,\overline{d}_{p,4}]= [1,1,1,1]$ (---), $[\overline{d}_{p,1}, \overline{d}_{p,2} ,\overline{d}_{p,3} ,\overline{d}_{p,4}]= [2,1,1,1]$ (---), $[\overline{d}_{p,1}, \overline{d}_{p,2} ,\overline{d}_{p,3} ,\overline{d}_{p,4}]= [2,1,0,1]$ (---), $[\overline{d}_{p,1}, \overline{d}_{p,2} ,\overline{d}_{p,3} ,\overline{d}_{p,4}]= [2,2,1,1]$ (-$\cdot$-) and $[\overline{d}_{p,1}, \overline{d}_{p,2} ,\overline{d}_{p,3} ,\overline{d}_{p,4}]= [2,2,2,1]$ (-$\cdot$-).