Studies on dissipative metamaterials have uncovered means to suppress vibration and wave energy via resonant and bandgap phenomena through such engineered media, while global post-buckling of the infinitely periodic architectures is shown to tailor the attenuation properties and potentially magnify the effective damping effects. Yet, despite the promise suggested, the practical aspects of deploying metamaterials necessitates a focus on finite, periodic architectures, and the potential to therefore only trigger local buckling features when subjected to constraints. In addition, it is likely that metamaterials may be employed as devices within existing engineering systems, so as to motivate investigation on the usefulness of metamaterials when embedded within excited distributed or multidimensional structures. To illuminate these issues, this research undertakes complementary computational and experimental efforts. An elastomeric metamaterial, ideal for embedding into a practical engineering structure for vibration control, is introduced and studied for its relative change in broadband damping ability as constraint characteristics are modified. It is found that triggering a greater number of local buckling phenomena provides a valuable balance between stiffness reduction, corresponding to effective damping magnification, and demand for dynamic mass that may otherwise be diminished in globally post-buckled metamaterials. The concept of weakly constrained metamaterials is also shown to be uniformly more effective at broadband vibration suppression of the structure than solid elastomeric dampers of the same dimensions.

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