Abstract Structural vibrations can be reduced by coupling to a piezoelectric electrical network that exhibits analogous modal properties of the structure. This paper considers the multimodal vibration damping of a thin circular ring using this method. The electrical network is derived by applying a finite difference model to the governing equations of motion for a segment of a thin curved beam. An electromechanical analogy is then applied to the physical constants. The resulting passive electrical network unit cell is a topology of capacitors, inductors, and transformers analogous to the dynamics of a segment of curved beam. The electrical network for a curved beam is simplified by considering an inextensional assumption and combining edge components in adjacent unit cells. The resulting simplified discrete network for a curved beam segment is assembled into a complete network for a circular ring. The electrical network for a circular ring displays modal properties similar to its mechanical analogue in both the spatial and frequency domains. As a result of the analogous modal properties across the frequency spectrum, it is shown that the network can be used to achieve multimodal vibration attenuation across a large frequency spectrum. Piezoelectric patches are used to couple the two domains. Numerical simulation of the coupled system demonstrates the effectiveness of the broadband damping effects from the analogous network. Notably, this research establishes a novelty in the field, as it not only introduces experimental validation of curved beam analogues, but also extends the investigation to encompass the coupling between a circular ring and its piezoelectric electrical network counterpart. Further experimental network optimization demonstrate the possibility of tuning the network to adapt to an imperfect mechanical ring.