SUMMARY

Multimodal vibration attenuation can be achieved through the coupling of an analogous passive electrical network that share the approximate modal properties of the mechanical structure. By tuning the electrical network parameters to produce the same modal properties as the governing equations of the mechanical system, the coupled system can achieve a significant vibration attenuation because the modes of the network and the structure match in both frequency and spatial domain. Previous research has demonstrated the feasibility of this concept in rods, bars, beams, plates, and curved beam structures, using piezoelectric patches to couple the structure to an electric network with identical plate-like and beam-like mode shapes. This study revisits previously developed analogous electrical network models with new enhancements for improved frequency coherence with thicker cross-section structures. Furthermore, the analogous network concept is extended from plates and beams to circular symmetric shells such as rings and other applications to cylindrical shells. When revisiting the analogues for beams and plates, improvements will be made to the networks to account for shear stiffness and rotary inertia, which will more accurately model thicker cross section structures. Next, an analytical model will be developed that defines the in-plane dynamics of a thin circular ring and its analogous electrical network. This will be done first using the classical extensional equations of a thin circular ring, which will then be simplified using the inextensional equations. The analytical solutions to the in-plane multimodal vibration of rings will be verified through experimental and numerical methods. Further studies will combine both the shear stiffness and rotary inertia network enhancement with the in-plane and out-of-plane analogous network to develop a comprehensive method for attenuating all types of vibration modes exhibited by rings. Finally, the feasibility of extending the analogous concept to thin circular cylindrical shells will also be explored by combining known analogous networks.