Tailoring concurrent shear and translational vibration control mechanisms in elastomeric metamaterials for cylindrical structures

The implementation of engineered metamaterials in practical engineering structures for vibration control purposes is challenged by a lack of understanding on the specific interaction mechanisms present among finite-sized metamaterials and the greater host structures. This research begins to address such knowledge gap by establishing an analytical framework to study the dynamic response and coupling mechanisms between elastomeric metamaterial inclusions embedded within a cylindrical host structure, representative of a variety of engineering systems. The analysis is formulated based on energy methods, and approximately solved by the Ritz method. Following experimental validation, the analysis is leveraged to reveal deep understanding on the precise mechanisms of coupling between such elastomeric metamaterial inclusions and the host structure. Several non-intuitive roles of parameter changes are conclusively revealed. For instance, while the decrease in open angle ratio of the inclusion cross-section geometry and the increase in the central core radius both appear to increase the significance of the core mass, the analysis reveals that the primary inclusion characteristic tuned by such parameter changes is the dynamic stiffness of the inclusions. Together, the dynamic mass and dynamic stiffness work to induce two tuned-mass-damper-like behaviors that lead to broadband vibration attenuation capabilities. The results of this research encourage attention to the study of specific problems whereby metamaterials directly interact with host structures to accurately understand the working mechanisms of vibration control for sake of optimal practical implementation.