Bandgap widening by optimized disorder in one-dimensional locally resonant piezoelectric metamaterials

Abstract

Locally resonant piezoelectric metamaterials offer outstanding vibration attenuation properties with the versatility in updating local resonances using either analog or digital electric circuits. The typically narrow bandgap observed in this sort of metamaterial can be enlarged through perturbations (or disorder) on the target frequencies of the resonant attachments, which also induce localization of vibration energy near the excitation source. This paper presents an optimization procedure for locally resonant piezoelectric metamaterial beams that enhances their vibration attenuation performance and avoids energy localization. Differently from the optimizations usually observed in the literature, the proposed one relies on an objective function that also considers the vibration along the whole one-dimensional structure. The large number of design variables given by the number of unit cells in the finite metastructure is tackled by following genetic-algorithm heuristics. The results evidence enhanced vibration attenuation performance due to the non-uniform distribution of target frequencies along a beam with periodic spatial distribution of piezoelements. While the bandgap width of the disordered metastructure is wider than that of a periodic reference case, the vibration localization is avoided. In this sense, the proposed methodology is a promising tool for achieving programmable and wideband electroelastic metastructures.