Multimodal vibration damping of a three-dimensional circular ring coupled to analogous piezoelectric networks

Abstract

Analogous piezoelectric networks have been shown to be effective for multimodal vibration attenuation in structures, including beams, plates, and rings. Previous studies for rings have only accounted for in-plane transverse vibration attenuation and disregarded the out-of-plane vibration modes. Furthermore, these previous numerical models and experiments have only been studied on thin rings, which ignore the effects of shear deformation and rotary inertia. As a result, these networks are not suitable for attenuating vibrations in thick rings. This study enhances on the previous electrical networks, considering both shear deformation and rotary inertia for both in-plane and out-of-plane vibrations. A new passive network topology is developed for the out-of-plane dynamics of thick rings, and the existing passive analogous network of in-plane vibration of thin rings is enhanced by considering the effects of shear deformation and rotary inertia. Combined, these new networks are capable of multimodal vibration damping of a thick ring in three-dimensions, encompassing primarily six types of vibration modes: the inextensional bending modes, the extensional modes, the thickness-shear modes, the coupled twist-bending modes, the torsional modes, and the transverse thickness-shear modes. By using piezoelectric elements to couple two separate analogous passive electrical networks derived from both the in-plane and out-of-plane governing equations of a ring and optimizing the internal resistance in each unit cell, it becomes possible to replicate the dynamics and effectively attenuate different types of vibration modes. This study serves as a theoretical foundation for implementations of passive vibration attenuation in ring structures.