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Within the context of 2D square lattices, searching for the existence of band gaps assumes a great interest owing to many possible fields of application: from energy absorption devices to noise and vibration controllers, as well as advanced strategies for the seismic isolation.

The underlying microstructure may influence the mechanical response of 2D square lattices according to a complex interplay between different factors. A first one is related to the so-called “size-effect”. A second one relates, instead, to the mass density distribution.

It has been observed that lumped masses may induce additional band gaps to appear and may magnify their width. Finally, an additional factor deals with the inner damping characteristics of the constituent materials, which usually are polymer-based.

This study focuses on the first factor from a specific perspective: to investigate the influence of the size effect on the existence and properties of frequency band gaps.